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This paper presents a deep learning approach that learns the Laplace transform of high-dimensional reflected Brownian motion (RBM) stationary distributions using the basic adjoint relationship. The method demonstrates near-perfect prediction in high-dimensional settings where analytical solutions are unavailable.
This paper establishes a general theory of the Adam optimizer for time-varying and nonstationary stochastic systems, providing parameter tracking and output prediction error bounds under a stochastic excitation condition that allows nonstationary and dependent data.
Proposes a spectral learning method for stochastic nonlinear dynamical systems using deep feature spaces and an operator-based latent state-space model, demonstrating stable performance in forecasting and filtering tasks.
This paper develops a generative flow matching method to capture non-Markovian dynamics in non-equilibrium stochastic systems, demonstrating improved predictions for the Kramers first passage time problem compared to Markovian baselines.