Integral Equations and Machine Learning

TL;DR

This paper explores using reinforcement learning and neural networks to solve integral equations in light transport simulation, aiming to improve photorealistic image synthesis efficiency by guiding light paths.

Contribution

It introduces a novel approach of representing approximate solutions to integral equations with neural networks and derives a loss function for training, enhancing rendering methods.

Findings

Neural network-based methods can effectively approximate solutions to integral equations.

The proposed techniques outperform traditional Monte Carlo methods in light transport simulation.

The approach enables generating unlimited training samples for improved rendering accuracy.

Abstract

As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, reinforcement learning techniques may be used for photorealistic image synthesis: Efficiency may be dramatically improved by guiding light transport paths by an approximate solution of the integral equation that is learned during rendering. In the light of the recent advances in reinforcement learning for playing games, we investigate the representation of an approximate solution of an integral equation by artificial neural networks and derive a loss function for that purpose. The resulting Monte Carlo and quasi-Monte Carlo methods train neural networks with standard information instead of linear information and naturally are able to generate an arbitrary number of training samples. The methods are demonstrated for applications in light transport simulation.