A Taylor Based Sampling Scheme for Machine Learning in Computational Physics

TL;DR

This paper introduces a Taylor-based sampling scheme that enhances the training of neural networks for solving ODEs in computational physics, leading to improved accuracy without additional computational costs.

Contribution

It proposes a novel Taylor approximation-based data sampling method to reduce neural network errors in physics simulations, advancing surrogate modeling techniques.

Findings

Improved accuracy of neural network solutions for ODEs

Efficient data sampling reduces training error

No additional computational cost during inference

Abstract

Machine Learning (ML) is increasingly used to construct surrogate models for physical simulations. We take advantage of the ability to generate data using numerical simulations programs to train ML models better and achieve accuracy gain with no performance cost. We elaborate a new data sampling scheme based on Taylor approximation to reduce the error of a Deep Neural Network (DNN) when learning the solution of an ordinary differential equations (ODE) system.