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Differential equations are used in a wide variety of disciplines, describingthe complex behavior of the physical world. Analytic solutions to theseequations are often difficult to solve for, limiting our current ability tosolve complex differential equations and necessitating sophisticated numericalmethods to approximate solutions. Trained neural networks act as universalfunction approximators, able to numerically solve differential equations in anovel way. In this work, methods and applications of neural network algorithmsfor numerically solving differential equations are explored, with an emphasison varying loss functions and biological applications. Variations ontraditional loss function and training parameters show promise in making neuralnetwork-aided solutions more efficient, allowing for the investigation of morecomplex equations governing biological principles.

Stochastic Scaling in Loss Functions for Physics-Informed Neural Networks