Invited Sessions

Many challenges across science and engineering are inherently interdisciplinary, involving coupled complex systems with strong interdependence across multiple time and length scales. Effectively addressing these problems requires integrated modelling frameworks that can capture such multiscale dependencies. The increasing availability of data and its integration into modelling frameworks have significantly accelerated the adoption of artificial intelligence (AI), machine learning (ML), and physics-informed methods, enabling more accurate and scalable representations of complex systems. These developments are driving new opportunities for predictive modelling, discovery, and decision-making across diverse application domains. This special session aims to provide a forum for recent advances in mathematical, statistical, and computational modelling of coupled complex systems, with a particular emphasis on multiphysics, multiscale, and AI-enabled approaches. Contributions spanning a broad range of applications, including biomedical, physical, engineering, and social systems, are encouraged. Among others, applications addressing present and emerging societal challenges, particularly those related to global sustainability, resilience, and health, are especially welcome. The session aims to: (a) promote interdisciplinary collaboration; (b) advance mechanistic, data-driven, and hybrid modelling approaches; (c) highlight state-of-the-art computational and AI-based methods; and (d) support model validation through real-world applications. Topics include differential and integral equation-based models; multiphysics and multiscale methods; AI/ML and physics-informed modelling; data analytics and uncertainty quantification; and high-performance computing. Overall, this session aims to contribute to a forward-looking vision for the next generation of modelling scientists, where interdisciplinary collaboration, advanced computation, and AI-driven methodologies collectively address critical challenges in the modelling and simulation of coupled complex systems.

Modern computational mechanics generally rely on coupled problems. How to accurately and efficiently simulate systems where mechanics interacts with thermal, fluid, or material phenomena — and possibly across multiple scales simultaneously? This mini-symposium brings together researchers from computational mechanics, applied mathematics, and engineering around this shared challenge, with a consistent focus on couplings where mechanics plays a central role. Topics include fluid–structure interaction, thermo-mechanical coupling, contact and impact, multiscale modelling and computational homogenization, reduced-order approaches, heterogeneous and multiphase materials, as well as numerical coupling strategies (partitioned, monolithic, hybrid). Special attention is given to localized phenomena, validation and uncertainty quantification. Scalability toward high-performance computing environments is also of interest. The symposium aims to bridge methodological innovation and engineering relevance. Contributions may address both fundamental and applied aspects, from theoretical developments to industrial-scale simulations, including numerical methods.

Computational electromagnetics (CEM) plays a pivotal role in the simulation of most recent technologies, ranging from renewable energies to bioelectromagnetics. Rapid prototyping and virtual modeling, now used in most industrial processes, require the development of robust, accurate, and efficient software capable of handling the inherent complexity of large, discretized CEM models, which typically exhibit multiphysics and multiscale behavior. This session will explore recent advances and approaches in CEM, including (but not limited to) finite element methods, boundary element methods, integral equation methods, hybrid approaches, domain decomposition techniques, multiphysics and multiscale methods, analytical and circuit-based approaches, quantum simulation, AI-based simulation techniques, model order reduction, stochastic modeling, large-scale modeling and parallel computing, optimization and sensitivity analysis.

The brain is a tightly coupled system in which electrical activity, fluid flow, biochemical transport, and tissue mechanics interact across a wide range of spatial and temporal scales. Capturing these multiphysics and multiscale interactions is essential for understanding physiological brain function as well as the onset and progression of neurological and neurodegenerative disorders. Computational multiphysics models provide a unified framework for investigating brain physiology, where spatial heterogeneity, complex geometries, strong physical couplings, and scale separation pose significant mathematical and computational challenges. Addressing these requires accurate discretizations, scalable algorithms and efficient solvers. In addition, information extracted from experimental and clinical data must be systematically incorporated through data-driven and data-assimilation strategies. This invited session brings together researchers in computational mechanics, applied mathematics, biomedical engineering, and neuroscience to present advances in brain multiphysics modeling. Topics include linear and nonlinear tissue mechanics; cerebrospinal and interstitial fluid dynamics; molecular transport and waste clearance, including glymphatic pathways; electrophysiology and neural activation; vascular dynamics; oxygen and nutrient perfusion; prion-like protein propagation. Contributions addressing robust numerical methods, efficient solvers, reduced-order and geometrical model reduction, and applications to epilepsy, stroke, traumatic brain injury, hydrocephalus, and neurodegeneration are particularly welcome.

This mini-symposium aims to bring together researchers in computational mechanics focused on the modeling of building materials under coupled conditions, including advanced constitutive frameworks and multi-physics approaches. Elasto-plasto-damage models with viscous effects provide a comprehensive framework to capture elastic deformation, irreversible plasticity, stiffness degradation, and rate-dependent behavior. Such coupling is essential for materials like concrete, rock, and metals under high stress and varying loading rates, where micro-cracking and void evolution govern the response. These models enable more reliable prediction of failure and structural performance under extreme conditions. At the same time, modern construction materials exhibit complex behavior governed by the interaction of mechanical, thermal, hygric, and chemical processes, requiring advanced numerical and data-driven approaches. This session will highlight advances in coupled modeling of quasi-brittle and ductile materials, as well as composites and sustainable materials, with emphasis on multi-scale modeling, nonlinear phenomena, and integration of experimental data into computational frameworks. The role of artificial intelligence and machine learning will also be explored, including surrogate modeling, hybrid physics-informed approaches, and parameter identification. Topics of interest include, but are not limited to: thermo-mechanical coupling; moisture transport and durability; chemo-mechanical degradation; and fracture and damage, addressed through advanced finite element formulations and/or AI-assisted simulation techniques. Contributions focusing on verification, validation, uncertainty quantification, and real-world engineering applications are especially encouraged.

This invited session aims to provide a forum to discuss the recent developments in the field of computational mechanics of porous multiphase media, including geomaterials like soil and rocks, concrete, biological and engineered porous materials, to meet the challenges posed by complex coupled multiphysics problems arising in the fields of geomechanics, geophysics, geosciences, planetary science, environmental engineering, biomechanics, material sciences and other disciplined of applied science and technology dealing with different kinds of porous materials under quasi-static, dynamic or cycling loading conditions. Contributions related to the following areas will be welcomed: 1) computational methods and algorithms for multiphase thermo-chemo-hydro-mechanical continuum problems; 2) meshless and particle methods for coupled large deformation and flow in granular media; 3) numerical modeling of failure and post-failure conditions including strain localization, damage and fracture; 4) micromechanical modeling of multiphase granular materials in the framework of distinct element method (DEM) and molecular dynamics; 5) multiscale modelling; 6) development, calibration and validation of advanced constitutive models for granular media, including non-local and micromorphic models endowed with internal length scales; 7) AI/Machine learning/Data driven approaches for multiphase porous materials; 8) application to the solution of real problems in all the fields of geomechanics, geophysics, geosciences, planetary science, environmental engineering, biomechanics, material sciences and other disciplined of applied science and technology.

Coupled hydro-mechanical-chemical (HMC) processes govern the behavior of natural and engineered subsurface systems across a wide range of spatial and temporal scales. These interactions are central to understanding and forecasting the evolution of porous and fractured media, particularly in the context of emerging geoenergy and environmental applications. This session aims to bring together contributions that advance the fundamental understanding, modeling, characterization, monitoring, and practical implementation of coupled processes in both deep and shallow subsurface environments. The session will emphasize the interplay between fluid flow, mechanical deformation, and chemical reactions, including fully coupled HMC processes as well as partially coupled interactions, e.g., HC or MC effects. Contributions addressing processes from pore-scale to field-scale, and spanning analytical, numerical, experimental, data-driven approaches, and case studies are welcome. Applications of interest span several domains. These include geoenergy systems in the deep subsurface, such as carbon capture and storage (CCS), geothermal energy production, and underground hydrogen or natural gas storage, which play a critical role in climate change mitigation and the energy transition. Environmental and waste management applications are also of interest, including nuclear waste disposal and groundwater contamination and remediation. In addition, the session addresses the so-called unconventional carbon management approaches, such as carbon mineralization, and soil-based carbon removal and enhanced weathering. Further relevant topics include the understanding of fundamental (hydro)geological processes, such as sediment compaction, channeling and wormhole formation, and karstification. By fostering dialogue across disciplines, this session will contribute to bridging fundamental research and practical applications, thereby advancing the understanding of coupled subsurface processes and addressing key challenges in energy and environmental systems.

There is a growing demand for the understanding (via modelling, simulation and validation) of intelligent materials or engineering components capable of performing in Multiphysics (i.e. chemo-electro-magneto), or even extreme environments (i.e. high temperature, corrosive). This session seeks to gather researchers working at the frontier of computational modelling in these scenarios, where either multiple physics are intrinsically coupled (cannot be easily decoupled/staggered) or where the user cannot easily interact with the problem via accessible (or even safe) laboratory experiments. This mini-symposium’s topics of interested include (but are not limited to) materials for energy storage, soft active materials, material degradation under degenerative environmental conditions, or materials performing under extreme environments. The session is not restricted to a specific continuum formalism or computational modelling technique per sé, but open to the wider audience: mesh based, phase field, and meshless based techniques, scale bridging and homogenisation, stabilisation methods for extreme scenarios and latest Machine Learning approaches for Multiphysics, to name but a few.

The increasing amount of digital personalized data, particularly CT visualization, holds great promises when combined with computational hard-tissue biomechanics for diagnosis and treatment at the patient level. Computational mechanics (CM) combined with Phase Field Model (PFM) for example, for failure initiation based on the available digital data allows for providing patient-specific information which may be directly translated to clinical applications. This information, when fused with artificial intelligence has the potential to be used very successfully in clinical practice. This mini-symposium is devoted to recent developments in CM of hard tissues when applied in clinical practice, with a focus on human bones. Presentations that combine CM methods based on CT with artificial intelligence algorithms are encouraged. Also, personalized treatment strategies that are guided by clinical needs and implemented into clinical practice are of particular interest.

Geological media are a strategic resource to mitigate climate change through the energy transition by means of low-carbon geo-energy applications. Subsurface engineering applications such as nuclear-waste disposal, deep geothermal energy harnessing, geologic carbon storage, and energy storage involve multi-physical processes in porous and fractured rock. These processes include fluid flow, solute and heat transport, rock deformation and geochemical reactions, which occur simultaneously and impact each other. In general, these low-carbon energy-related applications involve injection into and, sometimes, extractions of fluids from the subsurface, which cause pore pressure and temperature changes that deform the rock and in some occasions may lead to fracture and fault reactivation, inducing seismicity. Additionally, the injected fluids alter the geochemical equilibrium, leading to dissolution and/or precipitation of minerals that, in turn, may modify rock properties. These intricate interactions should be accounted for in numerical models to reproduce experimental and field applications and, ultimately, to achieve reliable predictive capability. Therefore, the safe and efficient deployment of such geo-energy applications is bounded to the adequate understanding of these coupled thermo-hydro-mechanical-chemical (THMC) processes, and predictive capabilities heavily rely on numerical models describing the evolution of the multi-physical systems. This Invited Session is dedicated to studies investigating some of these THMC interactions in low-carbon geo-energy applications by means of computational methods. The Invited Session aims at presenting state-of-the-art numerical developments to solve coupled THMC processes as well as applications that advance understanding of coupled processes in porous and fractured media. Welcomed topics include radioactive waste disposal, enhanced geothermal systems, superhot geothermal systems, conventional and alternative concepts for geologic carbon storage, hydrogen storage, energy storage, reservoir stimulation, including hydro-shearing and hydraulic fracturing, reservoir management, fluid injection-induced seismicity.

The rapid advances in technology, data acquisition, storage and computing power have transformed medicine from a traditional discipline that empowered the clinician to a quantitative data science approach that relies on signal, images, and their processing, manipulation, interpretation, and use for various applications. Imaging has become a quintessential tool that enables non-invasive or minimally-invasive exploration of the anatomy and function either to detect and diagnose disease, plan treatments, or guide and deliver therapies. However, to enable all of the above, access to computational modeling and visualization tools is as critical as image acquisition. In concert with these advances, the use of 4D diagnostic imaging has enabled researchers to obtain high-resolution, detailed visualizations of organs and tissues of interest. Artificial intelligence (AI) is being used extensively to extract features of interest from multi-modality, multi-dimensional medical images, classify these features, or track them over time to generate dynamic biomedical models that help assess abnormalities or disease. Computational modeling and simulation are central to the understanding and diagnosis of disease and determination of optimal treatment strategies. Digital twins, i.e., dynamic, virtual patient replicas, are being built using data from medical images, electronic health records, and genomic profiles and are used to perform in silico tests of medical devices or surgeries to predict patient-specific outcomes. Such virtual models are being updated with live data from wearables and sensors and can be used to perform real-time disease monitoring and adjustment of treatment. Mechanistic models are also being combined with data-driven AI models to develop hybrid models for improved prevention, monitoring, and control of diseases. These advancements play a key role in patient-specific disease diagnosis, treatment planning, and even therapy monitoring. This minisymposium is intended to foster an interdisciplinary venue at the intersection of imaging and computing and welcomes participation from computer science, engineering, mathematical modeling, imaging science and other related fields. Featured presentations will range from algorithms for image computing to computational biomedical models and simulations to mixed reality visualization for various biomedical applications.

Fluid flows, whether in a multiphysical context or not, are always coupled problems. In incompressible flows, for example, the velocity-pressure coupling is the main source of numerical and computational challenges. Furthermore, most fluid scenarios in engineering and science involve other types of physics, such as structural mechanics or heat transfer. In this context, a major research topic in numerics and scientific computing is how to efficiently decouple the solution of these different quantities without sacrificing numerical stability or accuracy. Decoupling methods include, e.g., linearisation techniques splitting certain quantities within each iterative loop [1]. Other popular examples are semi-implicit schemes that treat coupling terms explicitly, which includes fractional-step/projection methods [2], fast explicit stepping, and IMEX schemes [3]. This mini-symposium aims to bring together researchers from Computational Fluid Dynamics, Fluid-Structure Interaction and Multi-physics, who work on developing decoupling strategies to improve efficiency and/or simplify implementation for such complex problems. Contributions are sought, for instance, involving multiphase flows, non-Newtonian fluids, phase change, partitioned FSI, and thermally coupled problems, ranging from computational aspects to numerical analysis.

This invited session deals with the structure-preserving discretization and the control of coupled problems. Structure-preserving schemes come with the promise of enhanced numerical stability and robustness. They can be viewed as extensions of conserving schemes, which were previously developed in the context of conservative Hamiltonian systems with symmetry, to coupled dissipative systems. The coupling of several fields makes the design of structure-preserving schemes particularly demanding. Moreover, the interactions of different fields may cause numerical instabilities when applying standard discretization techniques. Structure-preserving methods have the potential to correctly reproduce coupling effects in the discrete setting and are thus less prone to numerical instabilities. The discretization in space and time of coupled problems is strongly affected by the way in which the underlying field equations are written, including the choice of variables. The structure of the underlying balance laws is built into specific descriptions such as GENERIC, metriplectic dynamics or the port-Hamiltonian formulation which thus might be of advantage for the design of structure-preserving schemes. Exploiting the structure of thermodynamically consistent models can be beneficial for the optimization of coupled processes and the efficient numerical solutions of control problems. The present invited session aims at bringing together researchers from different fields dealing with the design of structure-preserving discretization methods for coupled problems, their optimization and control. Applications may focus on both dissipative solids as well as fluids. Specific applications may deal with, among others, large-strain thermo-elasticity, electro-magneto-mechanics, or thermo-chemo-mechanics. Also control-theoretic contributions, which leverage the physical structure are welcome.

n this section we are considering flow in deformable porous media, also called poromechanics. There are plenty relevant applications of poromechanics, e.g. CO2 storage, enhanced geothermal energy extraction or soil pollution, to name a few. The mathematical models behind are based on different variants of Biot’s model (quasi-static, nonlinear, dynamic, multiphase flow…), consisting on coupled partial, possible degenerate, differential equations which are very difficult to be solved. Here, we will focus on efficient solvers for poromechanics. This will include splitting schemes, discretization methods, parallel algorithms and algebraic solvers. Important aspects like convergence, optimization and stabilization of the schemes will be discussed.

Modern clinical biomechanics has reached a transformative juncture where medical imaging, experimental quantification, and numerical simulation are no longer isolated disciplines but are inextricably integrated. Across the diverse spectrum of human physiological systems, biomechanical behavior is rarely governed by a single field variable or confined to a single spatial or temporal scale. Rather, the underlying phenomena involve intricate multidisciplinary couplings, including nonlinear solid deformation, fluid dynamics, mass transport, and fluid-structure interaction, often occurring alongside long-term biological growth and tissue remodeling. For these complex systems, achieving high mechanical fidelity requires advanced computational frameworks where imaging defines patient-specific anatomy, experimental measurements inform constitutive behavior, and robust numerical methods resolve the resulting coupled field equations. This invited session aims to highlight recent advances in mathematical modeling, numerical discretization, inverse analysis, data assimilation, and validation of coupled biomechanical systems. Particular emphasis is placed on methodological developments that bridge data-driven paradigms and physics-based modeling. This focus aligns directly with the core themes of the ECCOMAS Thematic Conference on Coupled Problems, including data-driven modeling approaches, multidisciplinary formulations, and efficient solution techniques. We invite contributions covering a broad range of topics, including image-based model construction; segmentation and registration; inverse estimation of constitutive parameters and boundary conditions; uncertainty quantification; reduced-order modeling; and hybrid machine-learning and mechanistic formulations. Applications of interest include, but are not limited to, ventricular and vascular hemodynamics, congenital heart disease, heart valve mechanics, musculoskeletal and soft-tissue systems, and orthopedic joint biomechanics. By bringing together experts working at the interface of imaging, experimentation, and simulation, this session seeks to foster a comprehensive dialogue on the future of predictive, patient-specific modeling in clinical biomechanics.

The proposed Invited Session addresses the emerging role of Artificial Intelligence and Machine Learning as enabling technologies for the modelling and solution of coupled engineering problems. This session aims to provide a focused forum for the presentation and discussion of recent developments in data-driven and hybrid modelling techniques that enhance classical computational mechanics frameworks. The central objective is to explore how machine learning approaches can be systematically integrated with physics-based models to improve predictive accuracy, computational efficiency, and robustness in complex engineering systems. Particular emphasis will be placed on methodologies that respect underlying physical constraints while leveraging large datasets and advanced learning architectures. The session will cover a broad spectrum of topics aligned with the conference scope, including: physics-informed machine learning for multiphysics simulations; data-driven model reduction and surrogate modelling; digital twins and real-time monitoring of coupled systems; uncertainty quantification and probabilistic learning in engineering analysis; reinforcement learning for control and optimization of coupled processes; and hybrid approaches combining numerical methods with artificial intelligence. Contributions addressing applications in structural mechanics, fluid–structure interaction, energy systems, materials engineering, and bioengineering are especially encouraged, reflecting the multidisciplinary nature of coupled problems. By fostering interaction between experts in computational mechanics, applied mathematics, and artificial intelligence, this session seeks to identify new research directions and promote the development of scalable, interpretable, and reliable AI-enhanced computational tools. Ultimately, the session aims to contribute to the next generation of intelligent simulation frameworks capable of addressing the increasing complexity of real-world engineering systems.

Immersed Boundary Methods (IBM) have attracted a substantial increase in attention over the past ten to fifteen years. Their central principle is to extend a computational domain to a larger one, typically with a simple shape that is easy to mesh. A finite element computation is performed on this extended domain, distinguishing interior and exterior regions from the original domain. Under the denotation ‘fictitious domain’ or ‘embedded domain methods’, the central principle has been followed since the 1960s. The recent new interest results from innovative and efficient algorithmic developments, mathematical analysis showing optimal convergence despite cut elements, the possibility to efficiently link these methods to various geometric models, and many new engineering applications. Many variants of Immersed Boundary Methods have been developed, like CutFEM, the Finite Cell Method, Unfitted Finite Elements, the Shifted Boundary Method, and Trimmed Isogeometric Analysis, to name a few. Challenges arising in Immersed Boundary Methods are closely related and even surpassed by those of problems with immersed interfaces, if these are not aligned to boundaries of elements. These issues naturally arise in coupled problems, where the coupling conditions – which are often associated with reduced continuity conditions – must be formulated in an immersed sense. In this Invited Session, we will focus on recent developments in Immersed Boundary and Interface Methods in a broad sense. Particular topics of interest include new algorithmic and theoretical developments, implementation aspects such as solvers, efficient treatment of different geometric models, open-source software, and applications focusing mainly on challenges for coupled problems.

Artificial Intelligence and Machine Learning provide new approaches for huge classes of engineering problems including coupled ones. However, such data-based methods often fail when it comes to issues like physical interpretability, explainability, reliability, certification and a posteriori error control, just to name a few. In this session we aim to discuss approaches to combine numerical efficiency, mathematical certification and data assimilation. Possible methods may include nonlinear model reduction, structure preservation, manifold learning, deep learning, data-based models, nonintrusive methods, adaptivity, space-time coupling, and many more. However, the focus of the session is on the development and justification of mathematical rigor in terms of (e.g.) error estimates, convergence proofs (qualitative and quantitative), well-posedness, approximability, reducibility, structure preservation and efficiency. There are several recent advances in that direction which will be addressed in this session with particular emphasis on coupled problems.

Cracks and discontinuities are pivotal in determining the behavior of quasi-brittle materials, including geo-materials, concrete, ceramics, ice, etc. Achieving a comprehensive understanding and accurate modelling of these phenomena remains a significant challenge for engineers and scientists alike. When subjected to mechanical loads beyond a certain limit, these materials can develop distributed micro-cracks, some of which may eventually merge to form localized macrocracks. Additionally, degradation can arise from environmental influences. The impact of such environmental factors is particularly crucial because of the interaction effects between reactive transport phenomena in the environment, such as moisture movement, radiation exposure or chemical activity, and mechanical response and cracking. Similarly, the flow of pressurized fluids through the porosity and cracks of the material can instigate crack propagation, leading to significant coupled effects. To effectively understand and evaluate the various deterioration mechanisms that concurrently affect quasi-brittle materials, complex multi-physics computational models are necessary. These models should encompass mechanical behavior as well as flow, diffusion, reaction, and transport processes, including the inception and propagation of fractures. The development of such models poses several numerical challenges, due to the possible different time and space scale of the processes of interest, and the intrinsic ill-conditioning of the resulting discretized equations. The use of multi-scale models, such as micro or meso-mechanical approaches that explicitly account for the possibly heterogeneous nature of the material, can help simplify the constitutive description, but at the cost of significant computational efforts that often require high-performance computing (HPC) resources. The present mini-symposium is intended to gather contributions and advances on modelling coupled phenomena in quasi-brittle fractured materials, including both theoretical and numerical issues. Classical models based on a continuum or a discrete approach, as well as more recent techniques such as XFEM, EDFM, phase field, etc., their solvers and implementation in an HPC environment, are welcome.

Additive Manufacturing (AM) has become a key enabling technology for producing complex, high-performance components with controlled precision and tailored functionality. Metal AM processes such as Wire Arc Additive Manufacturing (WAAM), Directed Energy Deposition (DED), and Laser Powder Bed Fusion (LPBF) present unique multi-physics and multi-scale challenges that require advanced modelling and simulation tools for process optimization and part qualification. The objective of this Thematic Session is to share recent advances in numerical simulation, experimental analysis, and data-driven modelling of AM processes at the component and part scales. The session aims to bring together experts from academia and industry to discuss predictive and efficient computational methods capable of capturing the coupled thermal, mechanical, and metallurgical phenomena inherent to AM. Topics of interest may include: • Process simulation and optimization at meso- and macro-scales. • Novel space discretization and time-integration schemes for accurate and efficient part-scale analysis. • Reduced-order and data-driven modelling for simulation acceleration. • Multi-physics and multi-scale approaches for microstructure and defect prediction. • Material modelling including thermo-mechanical–microstructural coupling. • Prediction and mitigation of residual stresses, distortion, and warpage. • Combined simulation and in-situ monitoring for calibration, validation, and qualification. • Machine learning and feedback-control strategies for process optimization and quality assurance. • Optimization of process windows and scanning strategies. The Thematic Session welcomes contributions covering various AM technologies (LPBF, DED, WAAM, etc.) and materials. The session will serve as a forum for discussing the latest research trends and for fostering collaborations aimed at advancing predictive, high-fidelity simulation tools that accelerate the industrial adoption and certification of additive manufacturing technologies.

preCICE is an open-source coupling library and ecosystem for general partitioned multi-physics and multi-scale simulations, including surface and volume coupling. It enables the efficient, robust, and parallel coupling of separate single-physics solvers. This includes, but is not restricted to, fluid-structure interaction. preCICE treats these solvers as black boxes, and thus, only minimally invasive changes are necessary to prepare a solver for coupling. Ready-to-use adapters for well-known open-source solvers, including OpenFOAM, SU2, CalculiX, FEniCS, deal.II, DuMux, and more, are available. The software offers methods for equation coupling, fully parallel communication, data mapping, and time interpolation. This minisymposium brings together users and developers of the software. It enables the exchange of users among themselves, who otherwise would not know much of each other. Furthermore, the developer team can get direct feedback from users, who they sometimes only know from forum conversations. Lastly, the software and its capabilities can be presented to others in a full and broad sense, as not only the developers discuss their software, but also users report on experiences. Recent work focuses on extending preCICE towards two-scale macro-micro coupling, volume coupling including large-scale data mapping, dynamic meshes, and other applications than fluid-structure interaction. For more information, please visit https://precice.org.

The coordinated contraction of the heart results from a complex interaction between electrophysiology and mechanics, readily assessed on the organ-scale in terms of electrical signal conduction and motion, but driven by electro-chemo-mechanical interactions at the scale of individual proteins. Existing computational models rely on extensive volume averaging for bridging these highly disparate scales, which limit their ability to study the coupling between molecular perturbations and tissue behavior. Recent advances have highlighted the need for accurately capturing the details on the nanoscale, see, e.g., [1, 2], but the crucial coupling of electrophysiology and mechanics at this scale remains underexplored. This session addresses multiscale models of cardiac electromechanical coupling, with particular emphasis on the coupling of mechanisms at sub-cellular scale and how they translate to tissue and organ function. Topics of particular interest include: • Nanoscale electrodiffusion and its coupling to local calcium dynamics and contractile machinery. • Spatially explicit Monte Carlo and finite element (FE) models of sarcomere mechanics. • The Extracellular-Membrane-Intracellular (EMI) framework for cell-level resolution in electrophysiology and mechanics. • Multi-scale modeling of excitation-contraction (EC) coupling in health and disease. • Efficient solvers and splitting methods for complex electro-mechanical systems.

Surface tension acts at the interface of two immiscible fluids, leading to the minimization of the contact area. This quantity is therefore of primary importance in a wide range of phenomena determining, for example, the shape, breakdown or coalescence of droplets or bubbles. Consequently, it is a crucial parameter for understanding, modelling and simulating the behaviour of a droplet on a solid surface, or a liquid against a wall, that play an important role in many natural or industrial processes. Computationally, surface tension and capillarity present several challenges. Simulations must be stable, efficient, and accurate, avoiding parasitic currents and excessively constrained time steps. Additionnaly, an accurate coupling between fluid/solid mechanics problems and interface geometry is essential. Fulfilling these criteria requires making several choices when elaborating the numerical strategy. First, different numerical strategies are available to describe moving (fluid-fluid or fluid-solid) interfaces, such as the Level-Set, Phase-Field, or Volume-Of-Fluid methods. However, the surface tension term depends on curvature, i.e. on second-order derivatives of the surface parametrization. Second, surface tension term is specified on a manifold of dimension 1 or 2 embedded into an ambiant space. This can be treated by transforming the surface term into a volume term via a smoothed Dirac delta function or by reconstructing the interface locally. Finally, at the interface, differences in materials properties, create discontinuities in the pressure gradient, while the pressure is discontinuous due to the curvature. Various strategies can address these discontinuities, including smoothing material properties, refining quadrature rules, adapting the mesh, or enriching approximation spaces (e.g., E-FEM, X-FEM). This session will review recent advancements in computational mechanics for simulating flows involving surface tension. The mentioned points are not exhaustive, and contributions on related topics are welcome. Additionally, introducing a third phase, such as a solid substrate, adds complexity through capillarity and wetting phenomena at the triple junction.

This invited session will focus on multiscale methods in Computational Fluid Dynamics (CFD), emphasizing recent advancements in numerical techniques designed to capture complex dynamics across multiple scales. Particular attention is given to hybrid approaches combining traditional methods with data-driven and machine learning techniques, including turbulence closure modeling, reduced-order models, and surrogate approaches, to enhance flow and heat transfer simulations. One of the central challenges is the coupling of turbulence modeling with aerodynamic, urban, and environmental flow applications. A key area of focus will be the accurate representation of boundary layer phenomena, which are critical for understanding drag, flow separation, and overall system performance, especially in coupled thermo-fluid problems. In addition, the session will address the multiscale coupling of particulate flow dynamics in air, where upscaling approaches for modeling interactions between the carrier fluid and dispersed phases play a crucial role. Topics such as urban pollutant dispersion and particle-induced erosion will be explored, highlighting the importance of flow-particle interactions. By covering a broad range of challenges in turbulent, thermal, and multiphase flow phenomena, and incorporating multiscale and data-driven techniques, this session aims to promote discussion on advanced numerical methods and foster cross-disciplinary collaboration in fluid dynamics. Contributions ranging from theoretical developments to applied studies are welcome, spanning a wide variety of engineering and environmental flow problems. Organized in celebration of the 80th anniversary of Prof. Sergio Idelsohn, this session recognizes his contributions to computational mechanics and coupled numerical methods, while fostering discussion on advanced numerical approaches in fluid dynamics.

This mini-symposium focuses on recent advances in partitioned approaches for the analysis of coupled dynamical systems, with particular emphasis on interface dynamics and stability in strongly coupled problems. Partitioned methods have become a key enabler for the simulation of multiphysics systems, allowing the reuse of specialized solvers and promoting modular, flexible computational frameworks. However, ensuring robustness, accuracy, and efficiency across interfaces remains a central challenge, especially in transient and nonlinear regimes. Recent developments in coupling algorithms, interface treatments, and hybrid numerical strategies have significantly improved the stability and convergence properties of partitioned schemes. At the same time, emerging approaches such as data-driven modeling, reduced-order techniques, and uncertainty quantification, are opening new possibilities for scalable and predictive simulations. This mini-symposium aims to bring together contributions addressing both foundational and applied aspects of partitioned methods, with a particular focus on - advanced interface coupling strategies and domain decomposition methods - stability, accuracy, and energy conservation in transient coupled problems - non-matching discretizations and evolving interface techniques - and contact, impact, and nonlinear interface phenomena. The session also welcomes contributions integrating modern methodologies, including reduced-order modeling, machine learning, and multidisciplinary design optimization, within partitioned frameworks. Applications of interest include fluid-structure interaction, thermo-mechanical and electro-mechanical systems, and multiphysics problems in solid mechanics, such as smart materials and adaptive structures. Industrial applications and production-level implementations are particularly encouraged. By emphasizing interface dynamics as a unifying theme, this mini-symposium aims to foster discussion on robust and scalable partitioned strategies for next-generation multiphysics simulations.

Reduced Order Methods (ROMs) aim at constructing surrogate models that approximate complex parametric systems with reduced computational cost, enabling efficient simulations in real-time and many-query scenarios. Intrusive approaches, such as Galerkin methods, rely on the explicit knowledge of the governing equations to derive reduced models. While they typically ensure high accuracy and strong physical consistency, their efficiency may deteriorate when dealing with nonlinear dynamics or strongly coupled systems. On the other hand, non-intrusive approaches, often based on data-driven and machine learning techniques, exploit data from experiments or high-fidelity simulations to extract underlying patterns. These methods are flexible and broadly applicable, but they may require large datasets, extensive training, and often lack rigorous error estimation, physical interpretability, and structure preservation. Combining physics-based and data-driven methodologies offers a promising pathway to overcome these limitations. Hybrid strategies can enhance both predictive accuracy and computational efficiency, while improving model interpretability and robustness for complex systems. This mini-symposium aims to stimulate discussion on intrusive and non-intrusive ROMs, providing a comparative perspective on their strengths, limitations, and applicability across academic, industrial, and engineering contexts. Particular attention will be devoted to emerging methodologies that integrate ROMs with machine learning and advanced data-driven paradigms, including physics-informed approaches, hybrid modeling strategies, and surrogate models in a broader sense.

The increasing complexity of coupled multiphysics systems in science and engineering spanning applications in energy systems, advanced materials, fluid–structure interaction, and biomedical modeling, poses significant challenges for classical computational methods. These challenges are particularly acute in the presence of strong nonlinearities, multiscale interactions, and high-dimensional parameter spaces, where traditional solvers face limitations in scalability and computational cost. This invited session aims to explore emerging quantum and hybrid quantum–classical computational paradigms as transformative approaches for the modeling and simulation of such coupled systems. Recent advances in quantum algorithms, including quantum linear system solvers, Hamiltonian simulation, and quantum signal processing, provide new avenues for accelerating core numerical kernels underlying multiphysics simulations. When combined with classical preprocessing, discretization, and domain decomposition strategies, hybrid quantum–classical workflows offer a pragmatic pathway toward near-term applicability on noisy intermediate-scale quantum (NISQ) devices. In this context, particular emphasis will be placed on block-encoding techniques, operator splitting formulations, and iterative coupling schemes that enable the decomposition of complex multiphysics operators into structures amenable to quantum acceleration. The session will highlight methodological developments, theoretical foundations, and proof-of-concept applications demonstrating how quantum-enhanced techniques can be integrated with established numerical frameworks. Topics of interest include quantum algorithms for coupled PDE systems, hybrid solvers for nonlinear and time-dependent problems, multiscale coupling strategies, and applications relevant to Department of Energy priorities such as subsurface flow, plasma physics, and advanced manufacturing. By bringing together researchers from computational science, applied mathematics, and quantum information, this session seeks to define a coherent research agenda at the intersection of multiphysics coupling and quantum computing, and to identify opportunities for advancing the formulation and solution of real-world coupled systems beyond the limits of classical computation.

Complex multiphysics systems arising in engineering, environmental sciences, and biomedical applications often require the solution of strongly coupled nonlinear partial differential equations. High-fidelity numerical simulations (e.g., CFD, FSI, thermo-fluid, and reactive transport problems) remain computationally demanding, particularly in parametric studies, optimization, uncertainty quantification, and real-time decision support. This invited session aims to explore recent advances in Scientific Machine Learning (SciML) and Reduced-Order Modeling (ROM) for accelerating and enhancing the simulation of coupled multiphysics systems. Particular emphasis will be placed on hybrid methodologies that integrate physics-based discretization techniques (e.g., POD-Galerkin, projection-based ROMs, stabilized formulations) with data-driven components such as neural networks, operator learning methods, and surrogate modeling strategies. Topics of interest include, but are not limited to: • Reduced-order modeling for coupled PDE systems • Data-driven closures for turbulence and multiscale effects • Operator learning (e.g., Neural Operators) for parametric multiphysics problems • Hybrid physics-informed and data-driven frameworks • Bayesian and data assimilation techniques for inverse multiphysics problems • Uncertainty quantification in reduced models • Real-time digital twins for urban, environmental, and biomedical applications The objective of this session is to bring together researchers working at the interface of computational mechanics, numerical analysis, and machine learning to discuss emerging methodologies, theoretical challenges, and practical implementations. The session seeks to foster interdisciplinary dialogue and identify promising research directions for scalable, reliable, and interpretable reduced models of coupled systems.

Computational Modeling of Coupled Thermomechanical Large Deformation Processes has been a strongly active research field in the last few decades. Significant advances in this field have been made as the result of interdisciplinary multi-physics and multiscale research in related fields of computational mechanics, nonlinear constitutive material models, mathematical analysis, and numerical methods. Additionally, during this period, industry has shown a growing interest in incorporating numerical techniques as a valuable tool for material design and process optimization. This IS aims to collect and show up the last developments attained by young and well-known researchers actively working in the field. Topics addressed in this IS may include but are not limited to computational modeling and numerical simulation of finite deformation coupled thermomechanical problems, material modeling, contact mechanics, stabilization methods, metals, polymers, advanced numerical methods, and industrial applications, such as Additive Manufacturing (AM), Friction Stir Welding (FSW), Welding, Friction Melt Bonding, Casting, Rolling, Hydroforming, Thixoforming, Roll forming, Automatic Fiber Placement (AFP), tube drawing, sheet blanking, laser forming and general sheet metal forming processes…

Transport phenomena in soft, porous materials govern numerous natural and engineered systems, from biological tissues to geomaterials and advanced functional composites. The nature of this transport is inherently coupled: fluid flow, mass and heat transport, deformation, and chemical activity interact across scales, raising significant theoretical and computational challenges. This Invited Session aims to explore recent advances in modeling, simulation, and experimental characterization of transport processes in deformable porous media. Emphasis is placed on multiphysics coupling between fluid–structure interaction, diffusion, consolidation, swelling, and reactive transport. Contributions addressing nonlinear constitutive behavior, large deformations, and evolving microstructure, and emerging perspectives from poromechanics, mixture theory, and multiphase continuum frameworks are particularly desired. The Invited Session aims at embracing challenges in the mechanics of functional materials, including gels and polymeric mixtures, in soil mechanics, including consolidation, seepage, unsaturated flow, and in biological media, including swelling, liquefaction, interaction between charged ions. Transport-driven instabilities, localization, fracture, and phase separation in both geomaterials and hydrated soft networks are potential sources of relevant discussion. Advanced numerical strategies, including multiscale, meshless, and data-driven approaches, are welcome, alongside experimental validation techniques. Important topics such as identifying governing dimensionless parameters and scaling laws across biological and technical contexts are particularly interesting. By stimulating interactions among active scientists in the fields of mechanics, materials science, bioengineering, and geomechanics, this session aims to share and improve the knowledge of coupled transport in soft porous materials, possibly advancing predictive capabilities for biological tissues, environmental systems, and multifunctional materials.

Modeling and simulation of coupled and multiphysics systems are central challenges in computational science, and prerequisite for identification or optimization. Such systems arise in a wide range of applications – from biomedical engineering to geophysics – and often require the integration of heterogeneous physical processes across multiple scales and domains. This minisymposium brings together researchers developing robust, efficient, and scalable numerical methods for coupled problems, with a particular emphasis on addressing nonlinear interactions, heterogeneous materials, and stochastic effects. The focus is on innovative algorithms that account for the mathematical structure of coupled problems leveraging the potential of modern computing architectures. Key topics include: • Hybrid and data-driven methods for coupled PDE systems, including scientific machine learning to accelerate simulations and integrate experimental data; • Scalable solvers for nonlinear dynamical systems, such as those in cardiac electrophysiology or fluid-structure interaction; • Variational and constraint-based formulations for problems involving contact, friction, or other nonsmooth coupling conditions; • Adaptive discretization strategies guided by physical laws or a posteriori error estimators to enhance accuracy in critical regions; • Domain decomposition methods for strongly coupled systems bridging heterogeneous subdomains or distinct physical models; • Communication reduction techniques to overcome scalability bottlenecks in parallel environments, especially in multiphysics coupling; and • Randomized and stochastic approaches to improve determinism and scalability in coupled simulations. The invited session aims to foster interdisciplinary exchange among theorists, algorithm developers, and practitioners. It highlights not only the mathematical foundations of these methods but also their practical implementation in real-world applications. By emphasizing cross-disciplinary approaches, the invited session seeks to inspire new directions in addressing complex coupled problems.

The numerical simulation of parametrized coupled multi-physics systems such as fluid-structure interaction to thermo-hydro-mechanical processes are computationally challenging. This complexity is amplified in outer loop applications where the high-fidelity model must be evaluated for several parameters instances. Examples of such applications are Uncertainty Quantification (UQ), optimization, inverse problems and parameters estimation. In these scenarios, traditional full-order models (FOMs) are often computationally prohibitive, necessitating the development of efficient and reliable surrogate models. Model Order Reduction (ROM) bridge the gap between high-fidelity accuracy and real-time or many-query efficiency. This invited session focuses on recent algorithmic and theoretical developments in ROM specifically tailored for coupled systems. We seek contributions that address the unique challenges of coupling, including stability preservation, interface treatment, domain decomposition, and the preservation of physical constraints within the reduced-order manifold. Key topics of interest include but are not limited to: ROMs for UQ and sensitivity analysis, inverse problems and data assimilation, optimization, Scientific Machine Learning and hybrid approaches integrating data-driven techniques with projection-based ROMs for enhanced robustness. The goal of this session is to bring together researchers from various disciplines to exchange ideas on how reduced-order techniques can enable the next generation of predictive modelling for complex, coupled real-world problems. We welcome contributions demonstrating both fundamental methodological advances and impactful applications in engineering and the geosciences.

This special session will be dedicated to the multiscale, multiphysics, and multiphase modelling of liquid jets as they appear in a multitude of technological applications, from cooling large steel ingots on tens of meters scale to microfluidic applications associated with sample delivery systems in synchrotrons and X-ray Free Electron Lasers. Liquid jets can include droplets of mixing or non-mixing fluids, gas bubbles, or solid particles. They can form simple shapes like falling water films to complex structures generated by swirling nozzles under the assistance of focusing gas or external electromagnetic and ultrasound fields. They can be laminar or turbulent and designed to stay focused or atomised. The aim of this session is to bring together experts in this field and to present their state-of-the-art research in the understanding and computational modelling of the associated coupled problems.

Multi-physics systems often involve the solution of coupled partial differential equations (PDEs) defined across domains with different topological dimensions. This scenario is common in various fields, among them geology, biomedicine, cell biology, fracture mechanics, material modeling, or fluid-structure interaction to only name a few. Mixed-dimensional modeling addresses these challenges by simultaneously solving PDEs of varying dimensionality. With its many applications and recent progress in modeling and the analysis of the underlying PDEs, mixed-dimensional modeling has recently become a lively field of research with its own identity. The differences in dimensionality across the coupled PDEs introduce unique challenges throughout the simulation process: During the modeling phase, suitable coupling conditions must be established to bridge the dimensionality gap. In the discretization phase, careful consideration is required to ensure accuracy and stability, particularly in the imposition of coupling conditions. Furthermore, the resulting systems of equations need to be solved both accurately and efficiently. This minisymposium is dedicated to all aspects of mixed-dimensional modeling of multi-physics systems. Topics of interest range from modeling aspects, mathematical analysis, innovative discretization approaches, computer implementation, as well as efficient solvers and preconditioners. It will offer a forum to showcase challenging applications of mixed-dimensional models in science, engineering and biomedicine. The minisymposium is aiming to attract scientists form a broad range of scientific communities who are currently using mixed-dimensional PDE models for their research to foster discussions and share insights and ideas.

Coupled problems are ubiquitous across many applications in computational science and engineering. The coupling between different physical phenomena and spatio-temporal scales can give rise to strongly non-linear, non-convex, non-smooth, or highly ill-conditioned large-scale systems of equations, which require efficient coupling and solution strategies. In this minisymposium, we discuss the state-of-the-art and emerging trends in designing efficient and robust iterative methods for solving such systems of equations on modern computing architectures. We invite contributions related, but not limited to: - Preconditioning strategies - Domain decomposition and multilevel methods - Field-split methods - Acceleration techniques - Novel coupling strategies - Parallel algorithms and high-performance computing - AI enhanced numerical methods

The invited session on Numerical Modeling of Welding, Joining, and Processing focuses on recent advances in computational methods for understanding, predicting, and optimizing manufacturing operations involving material joining and processing. Numerical modeling has become a key tool in engineering, enabling improved process efficiency, enhanced product quality, and reduced reliance on costly experimental trials. By simulating process parameters, heat transfer, and material behavior, these approaches provide valuable insight into weld pool evolution, phase transformations, residual stress development, and resulting mechanical and metallurgical properties. Welding, joining, and processing operations involve complex, strongly coupled physical phenomena, including melting and solidification, fluid flow, thermal and mass transport, microstructural evolution, and stress formation. Addressing these challenges requires robust multiphysics and multiscale modeling frameworks. Contributions are encouraged using a wide range of numerical techniques such as finite element and finite volume methods, smoothed particle hydrodynamics, Monte Carlo simulations, and phase-field approaches, enabling predictive capabilities across different spatial and temporal scales. The session covers a broad spectrum of technologies, including fusion welding, solid-state processes (such as friction stir and friction deposition), as well as brazing, soldering, adhesive bonding, mechanical joining, and other material processing techniques. Both fundamental modeling developments and industrial applications are welcome. Emerging data-driven approaches, including artificial intelligence, machine learning, and digital twin frameworks for process optimization, real-time monitoring, and control, are also of particular interest. Special emphasis is placed on the processing and joining of advanced and dissimilar materials, including lightweight alloys, polymers, and composite systems. The session aims to provide a platform for sharing state-of-the-art developments and fostering collaboration between academia and industry in the field of computational modeling of joining and processing technologies.