Using Gradient to Boost the Generalization Performance of Deep Learning Models for Fluid Dynamics

TL;DR

This paper introduces a method to improve the generalization of deep learning models for fluid dynamics by incorporating physical gradients, validated through empirical experiments and ablation studies.

Contribution

It proposes a novel approach of using physical gradients in deep learning models to enhance their ability to generalize in fluid dynamics applications.

Findings

Improved generalization performance with gradient incorporation

Empirical validation shows better extrapolation beyond training data

Ablation study confirms the effectiveness of the proposed method

Abstract

Nowadays, Computational Fluid Dynamics (CFD) is a fundamental tool for industrial design. However, the computational cost of doing such simulations is expensive and can be detrimental for real-world use cases where many simulations are necessary, such as the task of shape optimization. Recently, Deep Learning (DL) has achieved a significant leap in a wide spectrum of applications and became a good candidate for physical systems, opening perspectives to CFD. To circumvent the computational bottleneck of CFD, DL models have been used to learn on Euclidean data, and more recently, on non-Euclidean data such as unstuctured grids and manifolds, allowing much faster and more efficient (memory, hardware) surrogate models. Nevertheless, DL presents the intrinsic limitation of extrapolating (generalizing) out of training data distribution (design space). In this study, we present a novel work to increase the generalization capabilities of Deep Learning. To do so, we incorporate the physical gradients (derivatives of the outputs w.r.t. the inputs) to the DL models. Our strategy has shown good results towards a better generalization of DL networks and our methodological/ theoretical study is corroborated with empirical validation, including an ablation study.