Computing large deviation rate functions of entropy production for diffusion processes in the vanishing-noise limit and high dimensions by an interacting particle method
CoRR(2024)
摘要
We study 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 to obtain the rate function is the computation of the principal
eigenvalue λ 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 obtained from an operator splitting scheme and
an Euler–Maruyama scheme with a small time step size, and we show that this
spectral radius can be accessed through a large number of iterations of this
discretized semigroup, suitable for the IPM. The IPM applies naturally to
problems in unbounded domains, scales easily to high dimensions, and adapts to
singular behaviors in the vanishing-noise limit. We show numerical examples in
dimensions up to 16. The numerical results show that our numerical
approximation of λ converges to the analytical vanishing-noise limit
with a fixed number of particles and a fixed time step size. Our paper appears
to be the first one to obtain numerical results of principal eigenvalue
problems for non-self-adjoint operators in such high dimensions.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要