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

arXiv: https://arxiv.org/abs/2212.00716 · HTML: https://mlsanity.com/paper/2212.00716/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 9 Oct 2022.

## Builds on (most cited first, 20 of 20)

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- [Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020](https://mlsanity.com/paper/2104.10201/) (2021)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
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## Abstract (arXiv)

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.