Physical Gradients for Deep Learning
- URL: http://arxiv.org/abs/2109.15048v2
- Date: Fri, 1 Oct 2021 14:09:49 GMT
- Title: Physical Gradients for Deep Learning
- Authors: Philipp Holl, Vladlen Koltun, Nils Thuerey
- Abstract summary: We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes.
We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques.
- Score: 101.36788327318669
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Solving inverse problems, such as parameter estimation and optimal control,
is a vital part of science. Many experiments repeatedly collect data and employ
machine learning algorithms to quickly infer solutions to the associated
inverse problems. We find that state-of-the-art training techniques are not
well-suited to many problems that involve physical processes since the
magnitude and direction of the gradients can vary strongly. We propose a novel
hybrid training approach that combines higher-order optimization methods with
machine learning techniques. We replace the gradient of the physical process by
a new construct, referred to as the physical gradient. This also allows us to
introduce domain knowledge into training by incorporating priors about the
solution space into the gradients. We demonstrate the capabilities of our
method on a variety of canonical physical systems, showing that physical
gradients yield significant improvements on a wide range of optimization and
learning problems.
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