In recent years, the complexity of multi-scale, multi-uncertainty and multi-physics problems has posed unprecedented challenges across various scientific and engineering disciplines. These intricate issues arise from the interplay of phenomena occurring at different spatial and temporal scales, coupled with uncertainties in material behavior, boundary conditions and model assumptions. Effectively addressing these challenges demands advanced computational frameworks capable of capturing essential system behaviors while accounting for variability and interactions among diverse physical fields.
This guest editorial introduces the latest advancements in computational methods tailored to analyse and investigate such multifaceted problems. By leveraging state-of-the-art numerical techniques and machine learning tools, researchers are developing accurate, efficient and predictive models that provide deeper insight into system performance and behaviour. The studies presented here demonstrate the transformative potential of these approaches, with applications spanning materials science, structural engineering, geomechanics, energy systems and beyond. Interdisciplinary collaboration remains key to advancing the field and meeting the evolving demands of real-world multi-physics systems.
This special issue compiles 20 contributions that exemplify recent progress in this domain. Most of the papers were presented at the ECCOMAS thematic conference on Computational Modeling of Multi-Scale, Multi-Uncertainty and Multi-Physics Problems, held from 11 to 13 September 2023 in Porto, Portugal. Together, they offer a comprehensive snapshot of emerging computational strategies, theoretical developments and applied innovations. We hope this curated selection stimulates further research and serves as a valuable reference for those exploring uncertainty quantification, model reduction, homogenisation and coupled physics phenomena.
The contributions span a wide range of topics and methodologies. Several works explore advanced approaches to uncertainty quantification and predictive modeling. One study proposes a machine learning strategy for improved importance sampling, while another addresses multiaxial fatigue life prediction by leveraging neural networks pretrained on uniaxial data.
In the field of constitutive modeling, new formulations are proposed to describe long-term creep deformation in heat-resistant steels, along with computational frameworks for identifying macroscopic parameters of polycrystalline materials. Approaches based on dislocation mechanics also provide insights into the effective behavior of structured metamaterials.
Reduced-order modeling and digital twin technologies are explored through data-efficient frameworks and physics-informed neural architectures for inverse analysis. Contributions in mathematical modeling extend to novel semi-analytical methods for nonlinear and fractional-order problems, as well as analytical strategies for simulating biological transport phenomena under complex geometries.
Multi-physics problems feature prominently. Fully coupled models are developed to study processes in hydrate-bearing sediments, and thermo-hydro-mechanical coupling is applied to improve the efficiency of geothermal extraction systems. Advanced simulation techniques, such as peridynamics, are introduced for modeling fracture in porous media.
Several papers address challenges in numerical stability and accuracy. A positivity-preserving finite volume scheme is introduced for convection-diffusion problems on distorted meshes. Other contributions investigate structural response under impact loading and develop high-fidelity models for magnetic and soft-matter systems using Monte Carlo techniques and spring-exchange mechanics.
Real-world engineering applications are represented by works focusing on large-scale construction logistics, design of reinforced concrete retaining walls using metaheuristic algorithms and optimisation strategies in defense-related systems. Lastly, the intersection of computational mechanics and biological modeling is explored through machine learning approaches that capture emergent behavior in complex microstructures.
We are confident that readers will find this special issue both informative and inspiring. The diverse techniques and applications featured here reflect the breadth of challenges and opportunities in modeling and simulation of multi-scale, multi-uncertainty and multi-physics systems. We hope these contributions foster further innovation, dialogue and collaboration within the computational mechanics community.
