Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method

ArXi:2602.17776v2 Announce Type: replace-cross Physics-governed models are increasingly paired with machine learning for accelerated predictions, yet most "physics--informed" formulations treat the governing equations as a penalty loss whose scale and meaning are set by heuristic balancing. This blurs operator structure, thereby confounding solution approximation error with governing-equation enforcement error and making the solving and learning progress hard to interpret and control. Here we.