Machine Learning and Integral Equations

As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering. In analogy to recent advances in reinforcement learning for playing games, we investigate the training of neural networks to represent this approximate solution in the context of Monte Carlo and quasi-Monte Carlo methods in order to compute functionals of integral equations.