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physics-informed machine learning covers several different approaches to infusing the existing knowledge of the world around us with the powerful techniques in machine learning. one area of intense research attention is using deep learning to augment large-scale simulations of complex systems such as the climate. here, data from satellites is used with simulation data to predict the evolution of these complex systems. while there is a wealth of data and the computational models have achieved remarkable maturity, the tools used in machine learning are often less constrained than the laws that govern physical processes. non-physical results can be produced by deep learning predictions unless proper constraints are implemented.

using deep learning toolbox™ in matlab^® r2020b, new loss functions can be easily implemented and tested on the fly. to demonstrate, in this talk a simple case of pendulum dynamics will be discussed and the prediction of motion is shown by using two neural networks, one trained with traditional loss function, and one with a physics-based loss function. the results show that the extra constraints allow the network to predict the motion of the system far more accurately than the conventional approach. while this represents a simple proof-of-concept, this model features many common aspects of more complex physical systems and allows for a fast and informative testing platform.