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AI Poincar\'{e} 2.0: Machine Learning Conservation Laws from Differential Equations. (arXiv:2203.12610v2 [cs.LG] UPDATED)
Nov. 1, 2022, 1:12 a.m. | Ziming Liu (MIT), Varun Madhavan (IIT), Max Tegmark (MIT)
cs.LG updates on arXiv.org arxiv.org
We present a machine learning algorithm that discovers conservation laws from
differential equations, both numerically (parametrized as neural networks) and
symbolically, ensuring their functional independence (a non-linear
generalization of linear independence). Our independence module can be viewed
as a nonlinear generalization of singular value decomposition. Our method can
readily handle inductive biases for conservation laws. We validate it with
examples including the 3-body problem, the KdV equation and nonlinear
Schr\"odinger equation.
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