Coercing Machine Learning to Output Physically Accurate Results

TL;DR

This paper introduces a method to incorporate physical constraints directly into neural network training, ensuring outputs are physically accurate, demonstrated on cloth mesh prediction with improved results over traditional approaches.

Contribution

The authors propose a novel approach to embed physical constraints into neural networks during training, improving physical accuracy of outputs without postprocessing.

Findings

Physically constrained training reduces errors in cloth mesh predictions.

The method improves energy metrics related to stretching and compression.

Results show significant enhancement over unconstrained models.

Abstract

Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output pairs of the training data are physically accurate (e.g. the results of an experiment or numerical simulation), interpolated quantities can deviate quite far from being physically accurate. Although one could project the output of a network into a physically feasible region, such a postprocess is not captured by the energy function minimized when training the network; thus, the final projected result could incorrectly deviate quite far from the training data. We propose folding any such projection or postprocess directly into the network so that the final result is correctly compared to the training data by the energy function. Although we propose a general approach, we illustrate its efficacy on a specific convolutional neural network that takes in human pose parameters (joint rotations) and outputs a prediction of vertex positions representing a triangulated cloth mesh. While the original network outputs vertex positions with erroneously high stretching and compression energies, the new network trained with our physics prior remedies these issues producing highly improved results.