Coercing Machine Learning to Output Physically Accurate Results

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.

References in corpus (12)

• ADADELTA: An Adaptive Learning Rate Method
• DGM: A deep learning algorithm for solving partial differential equations
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• Machine Learning of Linear Differential Equations using Gaussian Processes
• Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
• Deep learning algorithm for data-driven simulation of noisy dynamical system
• Computing Curvature for Volume of Fluid Methods using Machine Learning
• Identification of physical processes via combined data-driven and data-assimilation methods
• Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks
• A Pixel-Based Framework for Data-Driven Clothing
• Improved Search Strategies with Application to Estimating Facial Blendshape Parameters

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• Differentiating through Log-Log Convex Programs
• Recovering Geometric Information with Learned Texture Perturbations
• Alternating ConvLSTM: Learning Force Propagation with Alternate State Updates
• Constrained Adversarial Learning for Automated Software Testing: a literature review
• Nonseparable Symplectic Neural Networks