The paper presents an interacting particle method (IPM) for numerically computing the large deviation rate function of entropy production for diffusion processes. The key aspects are:
The method is based on a discretization of the Feynman-Kac semigroup associated with the principal eigenvalue problem, which is then accessed through the spectral radius of the discretized semigroup.
The IPM naturally handles unbounded domains, high dimensions, and singular behaviors in the vanishing-noise limit, which are challenges for traditional mesh-based numerical methods.
Numerical examples in dimensions up to 16 demonstrate the scalability and robustness of the method, with the numerical results converging to the analytical vanishing-noise limit.
Techniques for setting the initial measure of the particles are introduced to obtain faster convergence of the method.
The empirical density of particles at the final time accurately captures the singular behavior of the vanishing-noise limit, as predicted by the theory.
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