Conservation Law

Conservation laws, fundamental principles governing the constancy of physical quantities in dynamic systems, are a central focus in scientific computing and machine learning. Current research emphasizes developing and analyzing novel algorithms, including neural networks (e.g., physics-informed neural networks, Fourier neural operators, and Lagrangian flow networks), to accurately and efficiently solve partial differential equations representing these laws, particularly in challenging scenarios like those involving discontinuities or high dimensionality. This work is crucial for improving the accuracy and efficiency of simulations across diverse fields, from fluid dynamics and material science to climate modeling and traffic flow prediction, and for discovering new conservation laws in complex systems.