Machine learning based approach to fluid dynamics

TL;DR

This paper explores using deep neural networks to simulate one-dimensional fluid dynamics, demonstrating significant speed advantages and the ability to extrapolate beyond training data, offering a promising alternative to traditional numerical methods.

Contribution

The study introduces a DNN approach for fluid dynamics simulation that surpasses traditional methods in speed and extends predictive capabilities through effective learning of solution mappings.

Findings

DNN achieves at least 100x faster inference than conventional methods.

Optimal DNN performance occurs when learning fixed time step mappings.

DNN can extrapolate solutions beyond training data in time and geometry.

Abstract

We study the applicability of a Deep Neural Network (DNN) approach to simulate one-dimensional non-relativistic fluid dynamics. Numerical fluid dynamical calculations are used to generate training data-sets corresponding to a broad range of profiles to perform supervised learning with DNN. The performance of the DNN approach is analyzed, with a focus on its interpolation and extrapolation capabilities. Issues such as inference speed, the networks capacities to interpolate and extrapolate solutions with limited training samples from both initial geometries and evolution duration aspects are studied in detail. The optimal DNN performance is achieved when its objective is set to learn the mapping between hydro profiles after a fixed value time step, which can then be applied successively to reach moments in time much beyond the duration contained in the training. The DNN has an advantage over the conventional numerical methods by not being restricted by the Courant criterion, and it shows a speedup over the conventional numerical methods by at least two orders of magnitude.