Title: Partial Differential Equation-Regularized Neural Networks: An Application to Image Classification. Abstract: Differential equations can be used to design neural networks. For instance, neural ordinary differential equations (neural ODEs) can be considered as a continuous generalization of residual networks. In this work, we present a novel partial differential equation (PDE)-based approach for image classification, where we construct a continuous-depth and continuous-width neural network as a form of solutions of PDEs, and the PDEs defining the evolution of the solutions also are learned from data. Owing to the recent advancement of identifying PDEs, the presented novel concept, called PR-Net, can be implemented. Our method shows comparable (or better) accuracy and robustness for various datasets and tasks in comparison with neural ODEs and Isometric MobileNet V3. Thanks to the efficient nature of PR-Net, it is suitable to be deployed in resource-scarce environments, e.g., deployed instead of MobileNet.