AUTOMATIC NEURAL SPATIAL INTEGRATION
Primary Area: general machine learning (i.e., none of the above)
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Keywords: Monte Carlo, PDE Solver
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TL;DR: An unbias and fast method to use neural network to improve monte carlo estimators for spatial integrals.
Abstract: Spatial integration is essential for a number of scientific computing applications, such as solving Partial Differential Equations.
Numerically computing a spatial integration is usually done via Monte Carlo methods, which produce accurate and unbiased results.
However, they can be slow since it require evaluating the integration many times to achieve accurate low-variance results.
Recently, researchers have proposed to use neural networks to approximate integration results.
While networks are very fast to infer in test-time, they can only approximate the integration results and thus produce biased estimations.
In this paper, we propose to combine these two complementary classes of methods to create a fast and unbiased estimator.
The key idea is instead of relying on the neural network's approximate output directly, we use the network as a control variate for the Monte Carlo estimator.
We propose a principal way to construct such estimators and derive a training object that can minimize its variance.
We also provide preliminary results showing our proposed estimator can both reduce the variance of Monte Carlo PDE solvers and produce unbiased results in solving Laplace and Poisson equations.
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Submission Number: 6433
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