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Identifying underlying governing equations and physical relevant informationfrom high-dimensional observable data has always been a challenge in physicalsciences. With the recent advances in sensing technology and availabledatasets, various machine learning techniques have made it possible to distillunderlying mathematical models from sufficiently clean and usable datasets.However, most of these techniques rely on prior knowledge of the system andnoise-free data obtained by simulation of physical system or by directmeasurements of the signals. Hence, the inference obtained by using thesetechniques is often unreliable to be used in the real world where observed datais noisy and requires feature engineering to extract relevant features. In thiswork, we provide a deep-learning framework that extracts relevant informationfrom real-world videos of highly stochastic systems, with no prior knowledgeand distills the underlying governing equation representing the system. Wedemonstrate this approach on videos of confined multi-agent/particle systems ofants, termites, fishes as well as a simulated confined multi-particle systemwith elastic collision interactions. Furthermore, we explore how theseseemingly diverse systems have predictable underlying behavior. In this study,we have used computer vision and motion tracking to extract spatialtrajectories of individual agents/particles in a system, and by using LSTM VAEwe projected these features on a low-dimensional latent space from which theunderlying differential equation representing the data was extracted usingSINDy framework.

Dominant motion identification of multi-particle system using deep learning from video