The Effect of Non-Reactive Degrees of Freedom on Two-Dimensional Diffusion Processes: Deep Learning and Trajectory Prediction

This paper investigates the stochastic diffusion and saddle-point surmounting of Brownian particles on a two-dimensional quadratic saddle potential driven by Gaussian white noise. By combining Euler-Maruyama simulations with a data-driven autoregressive trajectory prediction model, we systematically examine the effects of the initial incident velocity and angle on trajectory evolution. The results show that, within the parameter range considered, the initial incident velocity mainly determines the particle’s ability to surmount the saddle-point region, whereas the initial incident angle primarily controls the lateral spreading of trajectories and their concentration toward the central region. As the initial incident velocity increases, the particle motion gradually changes from localized diffusion to pronounced saddle-point surmounting. As the incident angle increases, the trajectory distribution becomes more concentrated and tends to evolve along the central channel. Further comparison shows that the data-driven model can reproduce the overall evolution trend and part of the statistical properties of the trajectories. These results indicate that Brownian diffusion in a two-dimensional saddle potential is jointly governed by the potential structure, initial conditions, and stochastic thermal fluctuations, and that data-driven methods provide an effective auxiliary tool for studying such stochastic dynamical systems.