# Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2105.01838 · HTML: https://mlsanity.com/paper/2105.01838/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 5 May 2021.

## Builds on (most cited first, 14 of 14)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Label-Free Supervision of Neural Networks with Physics and Domain Knowledge](https://mlsanity.com/paper/1609.05566/) (2016)
- [Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks](https://mlsanity.com/paper/2005.03596/) (2020)
- [Data-driven discovery of PDEs in complex datasets](https://mlsanity.com/paper/1808.10788/) (2018)

## Built on by (most cited first, 1 of 1)

- [Improving deep learning with prior knowledge and cognitive models: A survey on enhancing explainability, adversarial robustness and zero-shot learning](https://mlsanity.com/paper/2403.07078/) (2024)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems. They have been particularly effective in the area of inverse problems, where boundary conditions may be ill-defined, and data-absent scenarios, where typical supervised learning approaches will fail. Here, we further explore the use of this modeling methodology to surrogate modeling of a fluid dynamical system, and demonstrate additional undiscussed and interesting advantages of such a modeling methodology over conventional data-driven approaches: 1) improving the model's predictive performance even with incomplete description of the underlying physics; 2) improving the robustness of the model to noise in the dataset; 3) reduced effort to convergence during optimization for a new, previously unseen scenario by transfer optimization of a pre-existing model. Hence, we noticed the inclusion of a physics-based regularization term can substantially improve the equivalent data-driven surrogate model in many substantive ways, including an order of magnitude improvement in test error when the dataset is very noisy, and a 2-3x improvement when only partial physics is included. In addition, we propose a novel transfer optimization scheme for use in such surrogate modeling scenarios and demonstrate an approximately 3x improvement in speed to convergence and an order of magnitude improvement in predictive performance over conventional Xavier initialization for training of new scenarios.