Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
This work addresses a problem in modeling complex open systems, but it appears incremental as it builds on existing methods like DeepRitz for diffusion systems.
The paper tackles the problem of learning drift decompositions in generalized diffusion systems with conservative-dissipative dynamics, proposing a data-driven two-phase method called the Moment-DeepRitz Method, which is shown to be robust to noisy data and adaptable to rough potentials and oscillatory rotations, with effectiveness demonstrated through numerical experiments.
Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift decompositions in generalized diffusion systems involving conservative-dissipative dynamics. The method is robust to noisy data, adaptable to rough potentials and oscillatory rotations. We demonstrate its effectiveness through several numerical experiments.