Ứng dụng mạng nơ-ron tích hợp vật lý trong giải và mô phỏng các bài toán vật lý một chiều và hai chiều

Abstract

Physics-informed neural networks constitute an approach that integrates observational data with physical laws expressed in the form of differential equations in order to model and simulate physical systems efficiently. Unlike purely data-driven deep learning methods, this approach directly incorporates physical constraints into the loss function, thereby reducing dependence on large training datasets and improving the model’s generalization capability. In this study, we investigate the applicability of physics-informed neural networks and hybrid differential equation models to solve two representative physical problems: the motion of an object subject to drag forces and the oscillation of a spring-mass system with an unknown damping component. Experimental results demonstrate that the proposed models are capable of accurately reproducing motion trajectories even when the training data are limited and contaminated with noise. This study provides further empirical evidence of the applicability of physics-informed neural networks in modeling physical systems and suggests the potential for extending this approach to a wide range of other problem classes.