arXiv subjects

Matthieu Nastorg

Publications and source records attributed to Matthieu Nastorg.

4 recordsLinked to original sources

arXiv2025

PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations

Machine learning-based surrogate models have emerged as a powerful tool to accelerate simulation-driven scientific workflows, but their adoption is limited by the lack of large-scale, diverse, and standardized datasets for physics-based simulations. Existing benchmarks often focus on narrow domains or rely on simplified data models, and fail to capture the heterogeneity arising from variable geometries, meshes, and topologies, which is critical for assessing generalization in realistic settings. We introduce PLAID (Physics-Learning AI Data model), a unified and extensible data layer for heterogeneous physics simulations. It preserves the full complexity of simulation data while enabling efficient and scalable machine learning workflows, together with a library for dataset construction and manipulation~(\href{https://github.com/PLAID-lib/plaid}{github.com/PLAID-lib/plaid}). We release six datasets covering structural mechanics and computational fluid dynamics, designed to reflect realistic industrial scenarios and provide standardized benchmarks. The framework includes reproducible evaluation protocols and is integrated with Hugging Face to enable open, community-driven benchmarking with active user participation (\href{https://huggingface.co/PLAIDcompetitions}{huggingface.co/PLAIDcompetitions}).

cs.LG↗

arXiv2024

Multi-Level GNN Preconditioner for Solving Large Scale Problems

Large-scale numerical simulations often come at the expense of daunting computations. High-Performance Computing has enhanced the process, but adapting legacy codes to leverage parallel GPU computations remains challenging. Meanwhile, Machine Learning models can harness GPU computations effectively but often struggle with generalization and accuracy. Graph Neural Networks (GNNs), in particular, are great for learning from unstructured data like meshes but are often limited to small-scale problems. Moreover, the capabilities of the trained model usually restrict the accuracy of the data-driven solution. To benefit from both worlds, this paper introduces a novel preconditioner integrating a GNN model within a multi-level Domain Decomposition framework. The proposed GNN-based preconditioner is used to enhance the efficiency of a Krylov method, resulting in a hybrid solver that can converge with any desired level of accuracy. The efficiency of the Krylov method greatly benefits from the GNN preconditioner, which is adaptable to meshes of any size and shape, is executed on GPUs, and features a multi-level approach to enforce the scalability of the entire process. Several experiments are conducted to validate the numerical behavior of the hybrid solver, and an in-depth analysis of its performance is proposed to assess its competitiveness against a C++ legacy solver.

cs.LG↗

arXiv2023

An Implicit GNN Solver for Poisson-like problems

This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an "infinitely" deep network, thus avoiding the empirical tuning of the number of required Message Passing layers to attain the solution. Its original architecture explicitly takes into account the boundary conditions, a critical prerequisite for physical applications, and is able to adapt to any initially provided solution. $\Psi$-GNN is trained using a "physics-informed" loss, and the training process is stable by design, and insensitive to its initialization. Furthermore, the consistency of the approach is theoretically proven, and its flexibility and generalization efficiency are experimentally demonstrated: the same learned model can accurately handle unstructured meshes of various sizes, as well as different boundary conditions. To the best of our knowledge, $\Psi$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

cs.LG↗

arXiv2022

DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)

This paper proposes a novel Machine Learning-based approach to solve a Poisson problem with mixed boundary conditions. Leveraging Graph Neural Networks, we develop a model able to process unstructured grids with the advantage of enforcing boundary conditions by design. By directly minimizing the residual of the Poisson equation, the model attempts to learn the physics of the problem without the need for exact solutions, in contrast to most previous data-driven processes where the distance with the available solutions is minimized.

cs.LG↗