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DY: Fachverband Dynamik und Statistische Physik

DY 6: Machine Learning in Dynamics and Statistical Physics I

DY 6.10: Vortrag

Montag, 9. März 2026, 12:00–12:15, HÜL/S186

Learning Time Trajectories of a Stochastic Dynamical System with a Slowly Varying Parameter — •Changho Kim¹, Zihan Xu¹, Andrew Nonaka², and Yuanran Zhu² — ¹University of California, Merced, California, USA — ²Lawrence Berkeley National Laboratory, Berkeley, California, USA

The statistics-informed neural network (SINN) is a reliable machine learning approach for learning and reproducing stochastic trajectories based on the statistical properties of sample trajectory data, particularly for stationary, Gaussian-like, multidimensional stochastic processes. However, to enable practical applications--such as surrogate modeling for the development of hybrid simulation methods--SINN must be extended to learn quasi-stationary dynamics driven by a slowly varying parameter. We enhance the SINN framework by incorporating this parameter as an additional input and by introducing loss functions to capture its influence, as well as proposing a new neural network structure that takes both white noise sequences and time trajectories of the slowly varying parameter as inputs. Additionally, we propose an alternative method for estimating a conditional probability density function to address computational constraints. We validate our approach through two benchmark problems: the dissociative adsorption problem and Langevin dynamics in an oscillating double-well potential.

Keywords: Stochastic processes; Recurrent neural network; Surrogate modeling; Langevin dyanmics; Kinetic Monte Carlo