AI RESEARCH
A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks
arXiv CS.LG
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ArXi:2604.04971v1 Announce Type: new While Physics-Informed Neural Networks offer a promising framework for solving partial differential equations, the standard $L^2$ loss formulation is fundamentally insufficient when applied to the Bhatnagar-Gross-Krook (BGK) model. Specifically, simply minimizing the standard loss does not guarantee accurate predictions of the macroscopic moments, causing the approximate solutions to fail in capturing the true physical solution. To overcome this limitation, we.