Stochastic Scaling in Loss Functions for Physics-Informed Neural Networks

TL;DR

This paper explores how stochastic variations in loss functions can improve neural network methods for solving complex differential equations, especially in biological contexts.

Contribution

It introduces stochastic scaling techniques in loss functions to enhance the efficiency of neural networks solving differential equations.

Findings

Stochastic loss scaling improves neural network training efficiency.

Enhanced methods enable solving more complex biological differential equations.

Potential for broader application in scientific computing.

Abstract

Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex differential equations and necessitating sophisticated numerical methods to approximate solutions. Trained neural networks act as universal function approximators, able to numerically solve differential equations in a novel way. In this work, methods and applications of neural network algorithms for numerically solving differential equations are explored, with an emphasis on varying loss functions and biological applications. Variations on traditional loss function and training parameters show promise in making neural network-aided solutions more efficient, allowing for the investigation of more complex equations governing biological principles.