1. Introduction
Computer simulation is central to modern science and engineering.
It allows researchers to test hypotheses, observe inaccessible quantities and explore designs before costly experiments. Yet deformable-object problems remain computationally demanding. Large strains, contact, plasticity and moving fluid-solid interfaces require fine discretisations, small time steps and repeated nonlinear solves. When simulation is placed inside parameter studies or design loops, thousands of geometries, materials and operating conditions may need to be evaluated. This limits the questions that can be asked, not merely the speed at which answers are obtained.
This PhD approaches AI4Science through a sustainability lens. It will develop physics-structured neural surrogates that learn complex multi-physics behaviour from fewer simulations and less computation. It aligns directly with the SustAI Sustainable AI theme by increasing the scientific capability delivered per unit of computation while retaining accuracy, physical consistency and reliability. Sustainability will be evaluated across data generation, model development and repeated virtual experiments, rather than inferred from inference speed alone.
Research foundation and gap
Scientific machine learning currently follows three main routes. Physics-informed neural networks embed governing equations in the loss but often require instance-specific optimisation [6]; neural operators learn mappings between function spaces and can generalise across parameters, although global layers may remain costly on large irregular domains [7]; and mesh-based graph networks respect unstructured discretisations but may need many message-passing steps [8]. The central AI4Science challenge is not simply to approximate a solver, but to preserve the structure of the scientific problem. Green AI adds a connected requirement: resources used to gain scientific insight must be measured and justified [9], including the numerical simulations used as training data.
The project builds on a coherent sequence of prior work by the proposed research team. LaDEEP introduced a staged Transformer surrogate for elastic-plastic stretch bending and demonstrated practical acceleration in industrial design [1]. Unisoma then represented solids, contacts and loads explicitly, improving generalisation and keeping memory low as the number of
Fisale extended explicit modelling to two-way fluid-structure interaction through latent arbitrary Lagrangian-Eulerian grids and partitioned coupling [4]. FilDeep addressed the data bottleneck by learning jointly from plentiful low-fidelity simulations and scarce high-fidelity examples [5]. Fisale extended explicit modelling to two-way fluid-structure interaction through latent arbitrary Lagrangian-Eulerian grids and partitioned coupling [4]. FilDeep addressed the data bottleneck by learning jointly from plentiful low-fidelity simulations and scarce high-fidelity examples [5].
Together, these studies establish that physical structure can improve both accuracy and efficiency. However, they optimise architectures primarily for predictive error, runtime or memory on a fixed task. They do not yet ask how a learning system should allocate computational effort across objects, interfaces, spatial scales and fidelity levels, or how much high-fidelity simulation is genuinely needed to support a scientific conclusion. The central hypothesis is that explicit physical decomposition, adaptive multiscale modelling and principled multi-fidelity learning can reduce the total computational footprint of scientific simulation while expanding the range of tractable multi-physics questions.
Aim and research questions
The aim is to create a data- and compute-efficient AI4Science framework for neural simulation and inverse design of coupled deformable systems. The research asks:
How should the scientific value and full computational cost of a neural surrogate be assessed across numerical data generation, model development and repeated virtual experiments?
Can object-, interface- and volume-aware representations concentrate computation where coupled physical dynamics are most complex without sacrificing conservation or rollout stability?
How can multi-fidelity and actively selected data reduce high-fidelity simulation demand while preserving out-of-distribution reliability?
Can sustainable neural surrogates enable reliable inverse design and scientific exploration across coupled systems under explicit accuracy and compute budgets?
Methodology and work programme
WP1 - AI4Science benchmark and whole-workflow sustainability. Existing datasets and solvers from stretch bending, multi-solid stamping and extrusion, flexible-wing aerodynamics and venous-valve flow will form a reproducible benchmark. It will connect predictive quality to the resources required to produce it, including data generation, model training, model selection and repeated scientific queries. Measures will include field and interface error, time-to-solution, energy use, memory, carbon dioxide equivalent under transparent electricity assumptions, and the number of high-fidelity simulations avoided. Accuracy-cost Pareto curves and break-even query counts will show when a learned surrogate becomes a more sustainable scientific instrument than direct FEM/CFD and when it does not.
WP2 - Physics-structured adaptive neural simulation. A modular encoder-processor-decoder will represent deformable bodies, rigid bodies, loads, contact surfaces, fluid regions and coupling interfaces as distinct physical tokens. Cell-facet-vertex mappings will retain geometry under coarse discretisation, while multiscale latent grids will carry long-range information. An adaptive mechanism will allocate resolution and processor depth according to the evolving physics: emerging contact, plastic yielding and moving interfaces will receive more computation, whereas smooth or weakly coupled regions will use simpler pathways. Prediction losses will be combined with conservation and stability constraints so that computational savings do not come at the expense of scientifically meaningful behaviour.
WP3 - Data-efficient scientific learning. FilDeep's cross-fidelity learning will be extended from two fixed fidelity levels to a hierarchy of mesh resolutions, time steps and solver tolerances. Uncertainty-aware active learning will request a high-fidelity simulation only where it is expected to change the learned model or the scientific conclusion. Transfer across related geometries, materials and coupling regimes will be investigated so that knowledge acquired in one physical setting can reduce data demand in another. The resulting learning strategy will be evaluated by the accuracy and calibration achieved for a fixed simulation budget, with particular attention to rare contacts, localised stresses and other scientifically important events that average-error metrics can hide.
WP4 - Sustainable simulation-to-discovery and design. The surrogate will be used for virtual experimentation, sensitivity analysis and inverse design. Case studies will progress from elastic-plastic stretch bending, through variable-cardinality multi-solid manufacturing, to two-way fluid-structure interaction. The framework will expose how geometry, material properties, contacts and coupling conditions govern system behaviour, rather than functioning only as a fast black-box predictor. Gradient-based and Bayesian optimisation will then search for designs under explicit accuracy and computational budgets. Uncertainty thresholds will trigger additional high-fidelity evidence or fallback to a trusted numerical solver, creating a reliable hybrid scientific workflow.
Evaluation, outcomes and impact
Evaluation will compare FEM/CFD, established neural operators and mesh-based graph networks, the team's prior models, and the proposed adaptive architecture using consistent datasets and computational accounting. Tests will cover unseen geometries, material properties, numbers of solids, contact patterns and coupling regimes. Scientific metrics will include field error, surface/contact error, conservation residuals, long-horizon stability, calibrated uncertainty and the fidelity of derived design decisions. Sustainability metrics will include total simulation data required, training and query energy, time-to-solution, peak memory, carbon dioxide equivalent and amortised cost over realistic research workloads. Ablations will isolate the value of physical decomposition, adaptive resolution and multi-fidelity selection.
Expected outputs are: an open benchmark for sustainable AI4Science in continuum mechanics; a physics-structured, compute-adaptive neural simulator for coupled deformable systems; methods for uncertainty-aware multi-fidelity learning; and validated demonstrators for virtual experimentation and design in manufacturing and fluid-structure interaction. The broader contribution is a transferable sustainability principle for AI4Science: encode what is known about the physical system so that learning focuses data and computation on what remains uncertain. This can make sophisticated simulation accessible to a wider research community, enable more extensive scientific exploration, and reduce the computational and experimental burden of simulation-led engineering.
Feasibility, training and risk management
Feasibility is supported by existing code, datasets and expertise spanning elastic-plastic deformation, multi-object contact, mesh-aware learning, two-way fluid-structure interaction and deployment. The student will receive training in scientific machine learning, computational mechanics, uncertainty quantification, sustainability assessment, high-performance computing and responsible research software. Key risks are uncertain workflow accounting, loss of physical accuracy under adaptation and weak extrapolation. These will be mitigated through transparent accounting boundaries, repeated resource measurements, dense-to-adaptive training curricula, conservation-aware validation, uncertainty calibration and numerical-solver fallback. The staged programme also ensures publishable outcomes from the benchmark and single-physics methods before the most demanding coupled studies.
References:
[1] Tao, S. et al. (2025). LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids. KDD 2025. https://doi.org/10.1145/3711896.3737238
[2] Tao, S. et al. (2025). Unisoma: A Unified Transformer-based Solver for Multi-Solid Systems. ICML 2025, PMLR 267.
[3] Feng, Z. et al. (2026). MAVEN: A Mesh-Aware Volumetric Encoding Network for Simulating 3D Flexible Deformation. ICLR 2026.
[4] Tao, S. et al. (2026). Neural Latent Arbitrary Lagrangian-Eulerian Grids for Fluid-Solid Interaction. ICLR 2026.
[5] Tang, J. et al. (2026). FilDeep: Learning Large Deformations of Elastic-Plastic Solids with Multi-Fidelity Data. KDD 2026. https://doi.org/10.1145/3770854.3783959
[6] Raissi, M., Perdikaris, P. and Karniadakis, G.E. (2019). Physics-informed neural networks. Journal of Computational Physics, 378, 686-707.
[7] Li, Z. et al. (2021). Fourier Neural Operator for Parametric Partial Differential Equations. ICLR 2021.
[8] Pfaff, T. et al. (2021). Learning Mesh-Based Simulation with Graph Networks. ICLR 2021.
[9] Schwartz, R. et al. (2020). Green AI. Communications of the ACM, 63(12), 54-63.