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# Learning Dynamics Across Similar Spatiotemporally-Evolving Physical Systems

*Proceedings of the 1st Annual Conference on Robot Learning*, PMLR 78:472-481, 2017.

#### Abstract

We present a differentially-constrained machine learning model that can generalize over similar spatiotemporally evolving dynamical systems. It is shown that not only can an E-GP model be used to estimate the latent state of large-scale physical systems of this type, but that a single E-GP model can generalize over multiple physically-similar systems over a range of parameters using only a few training sets. This is demonstrated on computational flow dynamics (CFD) data sets on fluid flowing past a cylinder at different Reynolds numbers. Though these systems are governed by highly nonlinear partial differential equations (the Navier-Stokes equations), we show that their major dynamical modes can be captured by a linear dynamical layer over the temporal evolution of the weights of stationary kernels. Furthermore, the model generated by this method provides easy access to physical insights into the system, unlike comparable methods like Recurrent Neural Networks (RNN). The low computational cost of this method suggests that it has the potential to enable machine learning approximations of complex physical phenomena for autonomy and robotic design tasks.