research-article

Neural control variates

Authors:

Thomas Müller,

Fabrice Rousselle,

Alexander Keller,

Jan NovákAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 39, Issue 6

Article No.: 243, Pages 1 - 19

https://doi.org/10.1145/3414685.3417804

Published: 27 November 2020 Publication History

Abstract

We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand that is cheap to integrate. We show that a set of neural networks can face that challenge: a normalizing flow that approximates the shape of the integrand and another neural network that infers the solution of the integral equation. We also propose to leverage a neural importance sampler to estimate the difference between the original integrand and the learned control variate. To optimize the resulting parametric estimator, we derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. When applied to light transport simulation, neural control variates are capable of matching the state-of-the-art performance of other unbiased approaches, while providing means to develop more performant, practical solutions. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.

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Zeltner TRousselle FWeidlich AClarberg PNovák JBitterli BEvans ADavidovič TKallweit SLefohn A(2024)Real-time Neural Appearance ModelsACM Transactions on Graphics10.1145/365957743:3(1-17)Online publication date: 20-Apr-2024
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Index Terms

Neural control variates
1. Computing methodologies
  1. Computer graphics
    1. Rendering
      1. Ray tracing
    2. Shape modeling
  2. Machine learning
    1. Learning paradigms
      1. Supervised learning
        Supervised learning by regression
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Sequential Monte Carlo methods

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 39, Issue 6

December 2020

1605 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3414685

Editor:
Karol Myszkowski
MPI Informatik

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Published: 27 November 2020

Published in TOG Volume 39, Issue 6

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