AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations
This work addresses the challenge of automatically finding conservation laws in physics and engineering, which is incremental as it builds on prior methods with a focus on independence and broader applicability.
The authors tackled the problem of discovering conservation laws from differential equations by developing a machine learning algorithm that identifies both numerical and symbolic conservation laws while ensuring functional independence, validated on examples like the 3-body problem and KdV equation.
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 Schrödinger equation.