Physics Informed Neural Networks for Modeling of 3D Flow-Thermal Problems with Sparse Domain Data

TL;DR

This paper demonstrates that Physics Informed Neural Networks can effectively model complex 3D flow-thermal problems using sparse data, providing accurate solutions and real-time surrogates for engineering applications.

Contribution

The study introduces a hybrid data-PINNs approach for 3D flow-thermal problems, showing improved performance with sparse data and complex geometries compared to traditional methods.

Findings

PINNs can solve 3D Navier-Stokes equations with sparse data.

Hybrid data-PINNs outperform standard neural networks in surrogate modeling.

PINNs are effective for complex geometries and high Reynolds numbers.

Abstract

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at moderate to high Reynolds numbers for complex geometries. The presented method utilizes very sparsely distributed solution data in the domain. A detailed investigation on the effect of the amount of supplied data and the PDE-based regularizers is presented. Additionally, a hybrid data-PINNs approach is used to generate a surrogate model of a realistic flow-thermal electronics design problem. This surrogate model provides near real-time sampling and was found to outperform standard data-driven neural networks when tested on unseen query points. The findings of the paper show how PINNs can be effective when used in conjunction with sparse data for solving 3D nonlinear PDEs or for surrogate modeling of design spaces governed by them.