NVIDIA Corporation
NEURAL NETWORK CONTROL VARIATES

Abstract:

Monte Carlo and quasi-Monte Carlo integration are simple numerical recipes for solving complicated integration problems, such as valuating financial derivatives or synthesizing photorealistic images by light transport simulation. A drawback of a straightforward application of (quasi-)Monte Carlo integration is the relatively slow convergence rate that manifests as high error of Monte Carlo estimators. Neural control variates may be used to reduce error in parametric (quasi-)Monte Carlo integration--providing more accurate solutions in less time. A neural network system has sufficient approximation power for estimating integrals and is efficient to evaluate. The efficiency results from the use of a first neural network that infers the integral of the control variate and using normalizing flows to model a shape of the control variate.