On the Possibility of Small Networks for Physics-Informed Learning

Physics-informed neural networks (PINNs) are a popular method for solving differential equations, but the optimal network size is a hyperparameter that has received little scrutiny. While overparameterized networks can offer regularization benefits, they also increase computational cost. This study investigates whether smaller networks can achieve comparable accuracy to the large models commonly used in the literature. Through examples like phase field fracture and Burgers' equation, it is demonstrated that networks with orders of magnitude fewer parameters can satisfactorily reproduce results for low-frequency solution fields. The conclusion suggests that the number of parameters in a PINN should be as small as possible without sacrificing accuracy, balancing computational efficiency and solution fidelity.