# Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts

arXiv: https://arxiv.org/abs/2509.10495 · HTML: https://mlsanity.com/paper/2509.10495/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks](https://mlsanity.com/paper/2008.10653/) (2020)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [A Data Driven Method for Computing Quasipotentials](https://mlsanity.com/paper/2012.09111/) (2020)
- [Self-test loss functions for learning weak-form operators and gradient flows](https://mlsanity.com/paper/2412.03506/) (2024)
- [Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures](https://mlsanity.com/paper/2508.01854/) (2025)

## 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.