Langevin Monte Carlo integration with discountinious contribution function for light transport simulation

A. A. Nikolaev, S. V. Ershov, V. A. Frolov


Abstract: Our paper is devoted to the study of the Monte Carlo method based on the Langevin equation as applied to Monte Carlo rendering. We describe a simplified scene with a complex and discountinious density of contribution function, in which we evaluate the influence of the preconditioning matrix in the Langevin equation. Such a scene allows us to obtain explainable and interpretable results, which is difficult in real scenes encountered in Monte Carlo rendering. Test results demonstrate that a properly selected way to build preconditioning matrix can significantly reduce the number of steps of the Monte Carlo method, necessary to achieve the specified accuracy.

Keywords: Langevin dynamics, Monte Carlo, MALA, Metropolis-Hastings method, Markov chain.

DOI: 10.20948/prepr-2024-46