arXiv subjects

Pierre-Emmanuel Angeli

Publications and source records attributed to Pierre-Emmanuel Angeli.

3 recordsLinked to original sources

arXiv2026

Multi-output Gaussian process prediction of physical fields under linear equality constraints

We address the simultaneous prediction of multiple high-dimensional physical fields governed by linear equality constraints, a setting that arises in many real-world applications in physics machine learning. Gaussian process (GP) regression is a widely used surrogate modeling approach due to its effectiveness in small-sample regimes and its ability to provide uncertainty quantification. However, applying GP models in this setting raises two major challenges: the high dimensionality of the discretized output fields and the enforcement of the physical constraint in predictions. For the latter, a common strategy consists in deducing one output from the others via the constraint relation. Through a benchmark, we show that this deductive approach is sensitive to the arbitrary choice of which output to deduce, affecting both predictive accuracy and uncertainty quantification. Consequently, there is a need for an approach that treats all fields symmetrically while strictly respecting the underlying physics. Motivated by these limitations, we propose a robust framework for jointly modeling constrained multi-field data. Our approach first leverages a specific PCA procedure for multi-field data, coined row-wise PCA, which has the interesting property of preserving the constraint in the latent space. Since standard PCA strategies for multi-field data do not preserve such constraints, we investigate theoretically the optimality of the row-wise choice. In a second step, we consider a linearly-constrained multi-output GP approach based on a specific kernel parametrization which is trained on the latent space of row-wise PCA. The proposed framework is validated on a population dynamics problem and on an industrial CFD application, which involves the prediction of Reynolds stress tensor components under the incompressibility constraint.

stat.ML↗

arXiv2024

Revisiting Tensor Basis Neural Networks for Reynolds stress modeling: application to plane channel and square duct flows

Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence RANS modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM). This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference DNS data. Notably, our shallow network with three layers provides accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. Learning the SDF case is more challenging because of its physical nature and a lack of training data at various regimes. We propose to alleviate this problem based on Transfer Learning (TL). To more efficiently generalize to an unseen intermediate $\mathrm{Re}_τ$ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

physics.flu-dyn↗

arXiv2022

Reynolds Stress Anisotropy Tensor Predictions for Turbulent Channel Flow using Neural Networks

The Reynolds-Averaged Navier-Stokes (RANS) approach remains a backbone for turbulence modeling due to its high cost-effectiveness. Its accuracy is largely based on a reliable Reynolds stress anisotropy tensor closure model. There has been an amount of work aiming at improving traditional closure models, while they are still not satisfactory to some complex flow configurations. In recent years, advances in computing power have opened up a new way to address this problem: the machine-learning-assisted turbulence modeling. In this paper, we employ neural networks to fully predict the Reynolds stress anisotropy tensor of turbulent channel flows at different friction Reynolds numbers, for both interpolation and extrapolation scenarios. Several generic neural networks of Multi-Layer Perceptron (MLP) type are trained with different input feature combinations to acquire a complete grasp of the role of each parameter. The best performance is yielded by the model with the dimensionless mean streamwise velocity gradient $α$, the dimensionless wall distance $y^+$ and the friction Reynolds number $\mathrm{Re}_τ$ as inputs. A deeper theoretical insight into the Tensor Basis Neural Network (TBNN) clarifies some remaining ambiguities found in the literature concerning its application of Pope's general eddy viscosity model. We emphasize the sensitivity of the TBNN on the constant tensor $\textbf{T}^{*(0)}$ upon the turbulent channel flow data set, and newly propose a generalized $\textbf{T}^{*(0)}$, which considerably enhances its performance. Through comparison between the MLP and the augmented TBNN model with both $\{α, y^+, \mathrm{Re}_τ\}$ as input set, it is concluded that the former outperforms the latter and provides excellent interpolation and extrapolation predictions of the Reynolds stress anisotropy tensor in the specific case of turbulent channel flow.

physics.flu-dyn↗