Neural Control Variates with Automatic Integration

Abstract

approximate the anti-derivative of the integrand. This allows us to use automatic dierentiation to create a function whose integration can be constructed by the antiderivative network. We validate our method by applying it to solve partial dierential equations using the Walk-on-sphere algorithm [Sawhney and Crane 2020].Our results indicate that this approach is unbiased using various network architectures and can achieve lower variance compared to other control variate methods.