A data-driven method for the steady state of randomly perturbed dynamics
This work addresses the challenge of solving for invariant densities in stochastic dynamics, offering a practical approach for researchers in applied mathematics and physics.
The paper presents a data-driven method for computing the invariant probability density function of randomly perturbed dynamical systems, achieving high accuracy in local areas even when the attractor is not fully covered by the numerical domain.
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem corresponding to a reference solution, which is generated by Monte Carlo simulation. With this method we can solve for the invariant probability density function in any local area with high accuracy, regardless of whether the attractor is covered by the numerical domain.