  Deep neural networks (DNN) have shown great capacity of modeling a dynamical
system; nevertheless, they usually do not obey physics constraints such as
conservation laws. This paper proposes a new learning framework named ConCerNet
to improve the trustworthiness of the DNN based dynamics modeling to endow the
invariant properties. ConCerNet consists of two steps: (i) a contrastive
learning method to automatically capture the system invariants (i.e.
conservation properties) along the trajectory observations; (ii) a neural
projection layer to guarantee that the learned dynamics models preserve the
learned invariants. We theoretically prove the functional relationship between
the learned latent representation and the unknown system invariant function.
Experiments show that our method consistently outperforms the baseline neural
networks in both coordinate error and conservation metrics by a large margin.
With neural network based parameterization and no dependence on prior
knowledge, our method can be extended to complex and large-scale dynamics by
leveraging an autoencoder.
