1. AI Poincar\'{e} 2.0: Machine Learning Conservation Laws from Differential Equations
- Author
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Liu, Ziming, Madhavan, Varun, and Tegmark, Max
- Subjects
Computer Science - Machine Learning ,Astrophysics - Earth and Planetary Astrophysics ,Nonlinear Sciences - Exactly Solvable and Integrable Systems ,Physics - Classical Physics ,Physics - Fluid Dynamics - Abstract
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., Comment: 15 pages, 12 figures
- Published
- 2022
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