An Adaptive Random Fourier Features approach Applied to Learning Stochastic Differential Equations

The efficient identification of dynamical systems from data is a fundamental challenge in many scientific and engineering domains. Classical parameter estimation techniques for stochastic differential equations (SDEs) - including maximum likelihood estimation, the method of moments, and Bayesian inference [15], [21], have widespread applications in physics [19], [23], finance [1], [8] and biology [20]. Despite their utility, these methods impose strong model assumptions, demand substantial analytical effort, and often become computationally intractable for complex or high-dimensional systems. Recent advances in machine learning have offer new options for data-driven modelling of dynamical systems [17]. Deep learning frameworks, such as residual networks, neural ordinary differential equations [3], and neural partial differential equations (PDEs) [14, 18], demonstrate significant promise in approximating complex dynamical systems.