Computing Large Deviation Rate Functions of Entropy Production for Diffusion Processes by an Interacting Particle Method
Year: 2025
Type: article
Abstract: . We develop an interacting particle method (IPM) for computing the large deviation rate function of entropy production for diffusion processes, with emphasis on the vanishing-noise limit and high dimensions. The crucial ingredient for obtaining the rate function is the computation of the principal eigenvalue [Formula: see text] of elliptic, non-self-adjoint operators. We show that this principal eigenvalue can be approximated in terms of the spectral radius of a discretized evolution operator, which is obtained from an operator splitting scheme and an Euler–Maruyama scheme with a small time step size. We also show that this spectral radius can be accessed through a large number of iterations of this discretized semigroup, which is suitable for computation using the IPM. The IPM applies naturally to problems in unbounded domains and scales easily to high dimensions. We show numerical examples of dimensions up to 16, and the results show that our numerical approximation of [Formula: see text] converges to the analytical vanishing-noise limit within visual tolerance with a fixed number of particles and a fixed time step size. It is numerically shown that the IPM can adapt to singular behaviors in the vanishing-noise limit. We also apply the IPM to explore situations with no explicit formulas of the vanishing-noise limit. Our paper appears to be the first to obtain numerical results of principal eigenvalue problems for non-self-adjoint operators in such high dimensions.
DOI: 10.1137/24m1720172
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1894105111, Adaptive computational methods for high-dimensional parametric PDEs arising from reduced-order modeling and uncertainty quantification, Novel particle-based numerical methods and analyses for high-dimensional eigenvalue problems and homogenization of convection-diffusion equations in unbounded domains, Deep Particle Algorithms and Advection-Reaction-Diffusion Transport Problems, G7161194048, Efficient interacting particle-field methods for 3D chemotaxis-type parabolic PDE systems: algorithms, analyses, and applications
OpenAlex ID: W4415907159