Coercing Machine Learning to Output Physically Accurate Results

Zhenglin Geng, Daniel Johnson, Ronald Fedkiw

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.