Stochastic Scaling in Loss Functions for Physics-Informed Neural Networks
This work addresses the challenge of solving complex differential equations in biology using neural networks, but appears incremental in nature.
The paper explores neural network methods for solving differential equations, focusing on variations in loss functions and training parameters to improve efficiency for biological applications.
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.