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Joseph Morlier

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EAAI Journal 2025 Journal Article

Automatic selection of inducing points in sparse Gaussian process for approximations of finite element analyses

Heine Havneraas Røstum
Sebastien Gros
Ketil Aas-Jakobsen
Joseph Morlier

Gaussian process regression (GPR) is a widely used regression model, but it has poor scalability. Sparse approximation methods improve scalability by using inducing points to approximate the GPR, but determining the optimal number and placement of these points is challenging. Increasing the number of inducing points generally improves the predictive accuracy, but it comes at a computational cost. This article presents a method to estimate the necessary number of inducing points for accurate predictions of finite element method (FEM) analyses using approximate GPR. The approach leverages the proper orthogonal decomposition (POD) technique, using its modes to determine the inducing points. Results demonstrate that the proposed method identifies a sufficient number of inducing points for approximate GPR to achieve predictive accuracy comparable to full GPR, but with half the training time. This approach ensures computational efficiency without significant loss in accuracy, making it a valuable tool for scalable regression in engineering applications. POD has previously been combined with GPR to provide computationally efficient predictions for the full solution field across unseen variable combinations, treating spatial components separately via reduced basis functions. However, this work treats the spatial component as a variable within the GPR approximation, allowing continuous spatial predictions. This ensures that the covariance in the spatial dimension is captured by a single GPR. The method is applied to simulations of a three-span, post-tensioned concrete girder bridge.

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NeurIPS Conference 2025 Conference Paper

ML4CFD Competition: Results and Retrospective Analysis

Mouadh Yagoubi
David Danan
Milad LEYLI ABADI
Jocelyn Mazari
Jean-Patrick Brunet
Abbas Kabalan
Fabien Casenave
Yuxin Ma

The integration of machine learning (ML) into the physical sciences is reshaping computational paradigms, offering the potential to accelerate demanding simulations such as computational fluid dynamics (CFD). Yet, persistent challenges in accuracy, generalization, and physical consistency hinder the practical deployment of ML models in scientific domains. To address these limitations and systematically benchmark progress, we organized the ML4CFD competition, centered on surrogate modeling for aerodynamic simulations over two-dimensional airfoils. The competition attracted over 240 teams, who were provided with a curated dataset generated via OpenFOAM and evaluated through a multi-criteria framework encompassing predictive accuracy, physical fidelity, computational efficiency, and out-of-distribution generalization. This retrospective analysis reviews the competition outcomes, highlighting several approaches that outperformed baselines under our global evaluation score. Notably, the top entry exceeded the performance of the original OpenFOAM solver on aggregate metrics, illustrating the promise of ML based surrogates to outperform traditional solvers under tailored criteria. However, this does not imply that the winning solution could replace the OpenFOAM solver or that it was overall superior, even for this specific task. Drawing from these results, we analyze the key design principles of top submissions, assess the robustness of our evaluation framework, and offer guidance for future scientific ML challenges.

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