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

ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction