Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
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Abstract (arXiv)
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.
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References · 8
- 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
- 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
- 2020Weak SINDy For Partial Differential Equationscited by 155
- 2020Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networkscited by 52
- 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
- 2020A Data Driven Method for Computing Quasipotentialscited by 11
- 2024Self-test loss functions for learning weak-form operators and gradient flowscited by 4
- 2025Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structurescited by 1
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