  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.

Machine Learning;Earth and Planetary Astrophysics;Exactly Solvable and Integrable Systems;Classical Physics;Fluid Dynamics