arXiv subjects

Jonathan Viquerat

Publications and source records attributed to Jonathan Viquerat.

At least 19 recordsLinked to original sources

arXiv2026

Heuristic Learning for Active Flow Control Using Coding Agents

Active flow control involves nonlinear dynamics, partial observations, and computationally expensive simulations, making controller design particularly challenging. Deep reinforcement learning (DRL) has emerged as a powerful framework for such problems, but its success typically relies on large numbers of simulator interactions and produces neural-network policies whose decision process often remains difficult to interpret. In this work, we investigate a different paradigm: instead of optimizing neural-network parameters, we use modern coding agents to search directly for explicit executable feedback laws. We introduce a constrained heuristic-learning protocol in which an agent iteratively proposes, evaluates, and revises controller implementations while interacting exclusively through the public benchmark interface. The proposed framework is evaluated on 13 active flow-control benchmarks spanning one, two, and three-dimensional problems and compared against the strongest available DRL baselines under identical simulation budgets. The discovered heuristic controllers match or outperform the best DRL policy in 10 of the 13 environments while remaining compact, interpretable, and directly inspectable. Beyond aggregate performance, the resulting controllers reveal physically meaningful feedback mechanisms, transfer successfully across more challenging configurations, and remain competitive under varying Reynolds and Rayleigh numbers, actuator counts, and observation sparsity. These results suggest that heuristic learning through coding agents constitutes a credible and complementary alternative to conventional reinforcement learning, combining competitive performance with physically interpretable controller representations. Prompts and source code are available at https://github.com/DonsetPG/fluid-heuristic-learning.

cs.LG↗

arXiv2025

Graph Deep Learning for Intracranial Aneurysm Blood Flow Simulation and Risk Assessment

Intracranial aneurysms remain a major cause of neurological morbidity and mortality worldwide, where rupture risk is tightly coupled to local hemodynamics particularly wall shear stress and oscillatory shear index. Conventional computational fluid dynamics simulations provide accurate insights but are prohibitively slow and require specialized expertise. Clinical imaging alternatives such as 4D Flow MRI offer direct in-vivo measurements, yet their spatial resolution remains insufficient to capture the fine-scale shear patterns that drive endothelial remodeling and rupture risk while being extremely impractical and expensive. We present a graph neural network surrogate model that bridges this gap by reproducing full-field hemodynamics directly from vascular geometries in less than one minute per cardiac cycle. Trained on a comprehensive dataset of high-fidelity simulations of patient-specific aneurysms, our architecture combines graph transformers with autoregressive predictions to accurately simulate blood flow, wall shear stress, and oscillatory shear index. The model generalizes across unseen patient geometries and inflow conditions without mesh-specific calibration. Beyond accelerating simulation, our framework establishes the foundation for clinically interpretable hemodynamic prediction. By enabling near real-time inference integrated with existing imaging pipelines, it allows direct comparison with hospital phase-diagram assessments and extends them with physically grounded, high-resolution flow fields. This work transforms high-fidelity simulations from an expert-only research tool into a deployable, data-driven decision support system. Our full pipeline delivers high-resolution hemodynamic predictions within minutes of patient imaging, without requiring computational specialists, marking a step-change toward real-time, bedside aneurysm analysis.

cs.LG↗

arXiv2025

TRELLIS-Enhanced Surface Features for Comprehensive Intracranial Aneurysm Analysis

Intracranial aneurysms pose a significant clinical risk yet are difficult to detect, delineate and model due to limited annotated 3D data. We propose a cross-domain feature-transfer approach that leverages the latent geometric embeddings learned by TRELLIS, a generative model trained on large-scale non-medical 3D datasets, to augment neural networks for aneurysm analysis. By replacing conventional point normals or mesh descriptors with TRELLIS surface features, we systematically enhance three downstream tasks: (i) classifying aneurysms versus healthy vessels in the Intra3D dataset, (ii) segmenting aneurysm and vessel regions on 3D meshes, and (iii) predicting time-evolving blood-flow fields using a graph neural network on the AnXplore dataset. Our experiments show that the inclusion of these features yields strong gains in accuracy, F1-score and segmentation quality over state-of-the-art baselines, and reduces simulation error by 15\%. These results illustrate the broader potential of transferring 3D representations from general-purpose generative models to specialized medical tasks.

cs.CV↗

arXiv2025

Automated discovery of finite volume schemes using Graph Neural Networks

Graph Neural Networks (GNNs) have deeply modified the landscape of numerical simulations by demonstrating strong capabilities in approximating solutions of physical systems. However, their ability to extrapolate beyond their training domain (\textit{e.g.} larger or structurally different graphs) remains uncertain. In this work, we establish that GNNs can serve purposes beyond their traditional role, and be exploited to generate numerical schemes, in conjunction with symbolic regression. First, we show numerically and theoretically that a GNN trained on a dataset consisting solely of two-node graphs can extrapolate a first-order Finite Volume (FV) scheme for the heat equation on out-of-distribution, unstructured meshes. Specifically, if a GNN achieves a loss $\varepsilon$ on such a dataset, it implements the FV scheme with an error of $\mathcal{O}(\varepsilon)$. Using symbolic regression, we show that the network effectively rediscovers the exact analytical formulation of the standard first-order FV scheme. We then extend this approach to an unsupervised context: the GNN recovers the first-order FV scheme using only a residual loss similar to Physics-Informed Neural Networks (PINNs) with no access to ground-truth data. Finally, we push the methodology further by considering higher-order schemes: we train (i) a 2-hop and (ii) a 2-layers GNN using the same PINN loss, that autonomously discover (i) a second-order correction term to the initial scheme using a 2-hop stencil, and (ii) the classic second-order midpoint scheme. These findings follows a recent paradigm in scientific computing: GNNs are not only strong approximators, but can be active contributors to the development of novel numerical methods.

cs.LG↗

arXiv2025

Training Transformers for Mesh-Based Simulations

Simulating physics using Graph Neural Networks (GNNs) is predominantly driven by message-passing architectures, which face challenges in scaling and efficiency, particularly in handling large, complex meshes. These architectures have inspired numerous enhancements, including multigrid approaches and $K$-hop aggregation (using neighbours of distance $K$), yet they often introduce significant complexity and suffer from limited in-depth investigations. In response to these challenges, we propose a novel Graph Transformer architecture that leverages the adjacency matrix as an attention mask. The proposed approach incorporates innovative augmentations, including Dilated Sliding Windows and Global Attention, to extend receptive fields without sacrificing computational efficiency. Through extensive experimentation, we evaluate model size, adjacency matrix augmentations, positional encoding and $K$-hop configurations using challenging 3D computational fluid dynamics (CFD) datasets. We also train over 60 models to find a scaling law between training FLOPs and parameters. The introduced models demonstrate remarkable scalability, performing on meshes with up to 300k nodes and 3 million edges. Notably, the smallest model achieves parity with MeshGraphNet while being $7\times$ faster and $6\times$ smaller. The largest model surpasses the previous state-of-the-art by $38.8$\% on average and outperforms MeshGraphNet by $52$\% on the all-rollout RMSE, while having a similar training speed. Code and datasets are available at https://github.com/DonsetPG/graph-physics.

cs.LG↗

arXiv2025

Dragonfly: a modular deep reinforcement learning library

Dragonfly is a deep reinforcement learning library focused on modularity, in order to ease experimentation and developments. It relies on a json serialization that allows to swap building blocks and perform parameter sweep, while minimizing code maintenance. Some of its features are specifically designed for CPU-intensive environments, such as numerical simulations. Its performance on standard agents using common benchmarks compares favorably with the literature.

cs.LG↗

arXiv2025

Mixed-variable policy-based optimization

The optimization of mixed-variable problems remains a significant challenge. We propose an extension of the policy-based optimization method that handles mixed-variables problems in a natural way, through a simple policy combination. This is achieved by independently sampling from a multivariate normal distribution for the continuous domain, and from multiple categorical distributions for the discrete choices. Results demonstrate that the agent successfully yields high-quality solutions on a classical problem of electromagnetics, showcasing its robustness.

math.OC↗

arXiv2025

MeshMask: Physics-Based Simulations with Masked Graph Neural Networks

We introduce a novel masked pre-training technique for graph neural networks (GNNs) applied to computational fluid dynamics (CFD) problems. By randomly masking up to 40\% of input mesh nodes during pre-training, we force the model to learn robust representations of complex fluid dynamics. We pair this masking strategy with an asymmetric encoder-decoder architecture and gated multi-layer perceptrons to further enhance performance. The proposed method achieves state-of-the-art results on seven CFD datasets, including a new challenging dataset of 3D intracranial aneurysm simulations with over 250,000 nodes per mesh. Moreover, it significantly improves model performance and training efficiency across such diverse range of fluid simulation tasks. We demonstrate improvements of up to 60\% in long-term prediction accuracy compared to previous best models, while maintaining similar computational costs. Notably, our approach enables effective pre-training on multiple datasets simultaneously, significantly reducing the time and data required to achieve high performance on new tasks. Through extensive ablation studies, we provide insights into the optimal masking ratio, architectural choices, and training strategies.

cs.LG↗

arXiv2024

Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics

Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural Networks (CNNs) have found success in CFD by mapping meshes into images, recent attention has turned to leveraging Graph Neural Networks (GNNs) for direct mesh processing. This paper introduces a novel model merging Self-Attention with Message Passing in GNNs, achieving a 15\% reduction in RMSE on the well known flow past a cylinder benchmark. Furthermore, a dynamic mesh pruning technique based on Self-Attention is proposed, that leads to a robust GNN-based multigrid approach, also reducing RMSE by 15\%. Additionally, a new self-supervised training method based on BERT is presented, resulting in a 25\% RMSE reduction. The paper includes an ablation study and outperforms state-of-the-art models on several challenging datasets, promising advancements similar to those recently achieved in natural language and image processing. Finally, the paper introduces a dataset with meshes larger than existing ones by at least an order of magnitude. Code and Datasets will be released at https://github.com/DonsetPG/multigrid-gnn.

cs.LG↗

arXiv2024

Beacon, a lightweight deep reinforcement learning benchmark library for flow control

Recently, the increasing use of deep reinforcement learning for flow control problems has led to a new area of research, focused on the coupling and the adaptation of the existing algorithms to the control of numerical fluid dynamics environments. Although still in its infancy, the field has seen multiple successes in a short time span, and its fast development pace can certainly be partly imparted to the open-source effort that drives the expansion of the community. Yet, this emerging domain still misses a common ground to (i) ensure the reproducibility of the results, and (ii) offer a proper ad-hoc benchmarking basis. To this end, we propose Beacon, an open-source benchmark library composed of seven lightweight 1D and 2D flow control problems with various characteristics, action and observation space characteristics, and CPU requirements. In this contribution, the seven considered problems are described, and reference control solutions are provided. The sources for the following work are available at https://github.com/jviquerat/beacon.

physics.comp-ph↗

arXiv2023

Autoregressive Transformers for Data-Driven Spatio-Temporal Learning of Turbulent Flows

A convolutional encoder-decoder-based transformer model is proposed for autoregressively training on spatio-temporal data of turbulent flows. The prediction of future fluid flow fields is based on the previously predicted fluid flow field to ensure long-term predictions without diverging. A combination of convolutional neural networks and transformer architecture is utilized to handle both the spatial and temporal dimensions of the data. To assess the performance of the model, a priori assessments are conducted, and significant agreements are found with the ground truth data. The a posteriori predictions, which are generated after a considerable number of simulation steps, exhibit predicted variances. The autoregressive training and prediction of a posteriori states are deemed crucial steps towards the development of more complex data-driven turbulence models and simulations. The highly nonlinear and chaotic dynamics of turbulent flows can be handled by the proposed model, and accurate predictions over long time horizons can be generated. Overall, the potential of using deep learning techniques to improve the accuracy and efficiency of turbulence modeling and simulation is demonstrated by this approach. The proposed model can be further optimized and extended to incorporate additional physics and boundary conditions, paving the way for more realistic simulations of complex fluid dynamics.

physics.flu-dyn↗

arXiv2021

Policy-based optimization: single-step policy gradient method seen as an evolution strategy

This research reports on the recent development of a black-box optimization method based on single-step deep reinforcement learning (DRL), and on its conceptual proximity to evolution strategy (ES) techniques. In the fashion of policy gradient (PG) methods, the policy-based optimization (PBO) algorithm relies on the update of a policy network to describe the density function of its next generation of individuals. The method is described in details, and its similarities to both ES and PG methods are pointed out. The relevance of the approach is then evaluated on the minimization of standard analytic functions, with comparison to classic ES techniques (ES, CMA-ES). It is then applied to the optimization of parametric control laws designed for the Lorenz attractor. Given the scarce existing literature on the method, this contribution definitely establishes the PBO method as a valid, versatile black-box optimization technique, and opens the way to multiple future improvements allowed by the flexibility of the neural networks approach.

math.OC↗

arXiv2021

A twin-decoder structure for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles

Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the prediction of aerodynamic coefficients. Overall, exceptional levels of accuracy have been obtained, but the robustness and reliability of the proposed approaches remain to be explored, particularly outside of the confidence region defined by the training dataset. In this contribution, we present a twin auto-encoder network for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles. The proposed architecture is trained over a dataset composed of numerically-computed laminar flows around 12,000 random shapes, and naturally enforces a quasi-linear relation between a geometric reconstruction branch and the flow prediction decoder. Based on this feature, two uncertainty estimation processes are proposed, allowing either a binary decision (accept or reject prediction), or proposing a confidence interval along with the flow quantities prediction (u,v,p). Results over dataset samples as well as unseen shapes show a strong positive correlation of this reconstruction score to the mean-squared error of the flow prediction. Such approaches offer the possibility to warn the user of trained models when the provided input shows too large deviation from the training data, making the produced surrogate model conservative for fast and reliable flow prediction.

physics.flu-dyn↗

arXiv2021

Graph neural networks for laminar flow prediction around random 2D shapes

In the recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) have attracted a considerable attention in the computational fluid dynamics (CFD) community. In this contribution, we proposed a GCNN structure as a surrogate model for laminar flow prediction around 2D obstacles. Unlike traditional convolution on image pixels, the graph convolution can be directly applied on body-fitted triangular meshes, hence yielding an easy coupling with CFD solvers. The proposed GCNN model is trained over a data set composed of CFD-computed laminar flows around 2,000 random 2D shapes. Accuracy levels are assessed on reconstructed velocity and pressure fields around out-of-training obstacles, and are compared with that of standard U-net architectures, especially in the boundary layer area.

physics.flu-dyn↗

arXiv2021

Robust deep learning for emulating turbulent viscosities

From the simplest models to complex deep neural networks, modeling turbulence with machine learning techniques still offers multiple challenges. In this context, the present contribution proposes a robust strategy using patch-based training to learn turbulent viscosity from flow velocities, and demonstrates its efficient use on the Spallart-Allmaras turbulence model. Training datasets are generated for flow past two-dimensional (2D) obstacles at high Reynolds numbers and used to train an auto-encoder type convolutional neural network with local patch inputs. Compared to a standard training technique, patch-based learning not only yields increased accuracy but also reduces the computational cost required for training.

physics.flu-dyn↗

arXiv2021

Deep reinforcement learning for the control of conjugate heat transfer with application to workpiece cooling

This research gauges the ability of deep reinforcement learning (DRL) techniques to assist the control of conjugate heat transfer systems governed by the coupled Navier--Stokes and heat equations. It uses a novel, "degenerate" version of the proximal policy optimization (PPO) algorithm, intended for situations where the optimal policy to be learnt by a neural network does not depend on state, as is notably the case in optimization and open-loop control problems. The numerical reward fed to the neural network is computed with an in-house stabilized finite elements environment combining variational multi-scale (VMS) modeling of the governing equations, immerse volume method, and multi-component anisotropic mesh adaptation. Several test cases of natural and forced convection in two and three dimensions are used as testbed for developing the methodology. The approach successfully alleviates the natural convection induced enhancement of heat transfer in a two-dimensional, differentially heated square cavity controlled by piece-wise constant fluctuations of the sidewall temperature. It also proves capable of improving the homogeneity of temperature across the surface of two and three-dimensional hot workpieces under impingement cooling. Various cases are tackled, in which the position of multiple cold air injectors is optimized relative to a fixed workpiece position. The flexibility of the numerical framework makes it tractable to solve also the inverse problem, i.e., to optimize the workpiece position relative to a fixed injector distribution. The obtained results showcase the potential of the method for black-box optimization of practically meaningful computational fluid dynamics (CFD) conjugate heat transfer systems.

physics.flu-dyn↗

arXiv2021

A review on Deep Reinforcement Learning for Fluid Mechanics

Deep reinforcement learning (DRL) has recently been adopted in a wide range of physics and engineering domains for its ability to solve decision-making problems that were previously out of reach due to a combination of non-linearity and high dimensionality. In the last few years, it has spread in the field of computational mechanics, and particularly in fluid dynamics, with recent applications in flow control and shape optimization. In this work, we conduct a detailed review of existing DRL applications to fluid mechanics problems. In addition, we present recent results that further illustrate the potential of DRL in Fluid Mechanics. The coupling methods used in each case are covered, detailing their advantages and limitations. Our review also focuses on the comparison with classical methods for optimal control and optimization. Finally, several test cases are described that illustrate recent progress made in this field. The goal of this publication is to provide an understanding of DRL capabilities along with state-of-the-art applications in fluid dynamics to researchers wishing to address new problems with these methods.

physics.comp-ph↗

arXiv2020

Direct shape optimization through deep reinforcement learning

Deep Reinforcement Learning (DRL) has recently spread into a range of domains within physics and engineering, with multiple remarkable achievements. Still, much remains to be explored before the capabilities of these methods are well understood. In this paper, we present the first application of DRL to direct shape optimization. We show that, given adequate reward, an artificial neural network trained through DRL is able to generate optimal shapes on its own, without any prior knowledge and in a constrained time. While we choose here to apply this methodology to aerodynamics, the optimization process itself is agnostic to details of the use case, and thus our work paves the way to new generic shape optimization strategies both in fluid mechanics, and more generally in any domain where a relevant reward function can be defined.

cs.CE↗