Numerical Methods for Learning Physical Constraints and their Applications

Abstract

This thesis treats the theory and practice of learning physical constraints, and their use in interpolating and extrapolating motions. With the help of the evolving machine learning techniques, programs are capable of learning the physical properties and simulate future motions. To understand complex physical motions or make computationally expensive simulations much faster, there’s a pressing need to develop a model that can simplify this task. The contributions of this thesis begin with a theory that fits general physical motions into mass-spring models, followed by a neural particle simulator that leverages numerical methods that is end-to-end differentiable and trainable. Using this simulator, we can fit coordinates into this model to infer latent representation of collision radius, mass, spring constants in order to interpolate or extrapolate the motion. In the experiment section, we show that our method improves mean square error in chaotic motions by 100x compared to bilateral interpolation and the state-of-the-art and achieves similar performance in general physics motions.Bachelor of Scienc

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