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We propose a neural network based approach for extracting models from dynamicdata using ordinary and partial differential equations. In particular, given atime-series or spatio-temporal dataset, we seek to identify an accurategoverning system which respects the intrinsic differential structure. Theunknown governing model is parameterized by using both (shallow) multilayerperceptrons and nonlinear differential terms, in order to incorporate relevantcorrelations between spatio-temporal samples. We demonstrate the approach onseveral examples where the data is sampled from various dynamical systems andgive a comparison to recurrent networks and other data-discovery methods. Inaddition, we show that for MNIST and Fashion MNIST, our approach lowers theparameter cost as compared to other deep neural networks.

NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data