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Energy landscapes play a crucial role in shaping dynamics of many real-world complex systems. System evolution is often modeled as particles moving on a landscape under the combined effect of energy-driven drift and noise-induced diffusion,…

Computational Engineering, Finance, and Science · Computer Science 2025-03-04 Ruikun Li , Huandong Wang , Qingmin Liao , Yong Li

We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…

Machine Learning · Computer Science 2025-03-11 Riccardo Bonalli , Alessandro Rudi

The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational…

Analysis of PDEs · Mathematics 2021-09-14 Luca Scarpa , Ulisse Stefanelli

Inferring dynamical models from low-resolution temporal data continues to be a significant challenge in biophysics, especially within transcriptomics, where separating molecular programs from noise remains an important open problem. We…

Machine Learning · Computer Science 2023-10-05 Victor Chardès , Suryanarayana Maddu , Michael J. Shelley

In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…

Optimization and Control · Mathematics 2023-08-22 Shuzhen Yang

Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility govern their behavior…

Machine Learning · Computer Science 2025-11-26 Aiqing Zhu , Beatrice W. Soh , Grigorios A. Pavliotis , Qianxiao Li

While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…

Machine Learning · Computer Science 2021-03-30 Ruiqi Gao , Yang Song , Ben Poole , Ying Nian Wu , Diederik P. Kingma

We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…

Statistical Mechanics · Physics 2015-05-27 Valerio Lucarini

The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes…

Statistical Mechanics · Physics 2007-05-23 Serge Shpyrko , V. V. Ryazanov

Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim).…

Chemical Physics · Physics 2023-02-08 Wujie Wang , Zhenghao Wu , Rafael Gómez-Bombarelli

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

Machine Learning · Computer Science 2024-10-07 Yanfang Liu , Yuan Chen , Dongbin Xiu , Guannan Zhang

Stochastic dynamical systems are ubiquitous in physics, biology, and engineering, where both deterministic drifts and random fluctuations govern system behavior. Learning these dynamics from data is particularly challenging in…

Numerical Analysis · Mathematics 2026-03-10 Ziheng Guo , Igor Cialenco , Ming Zhong

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…

Mathematical Physics · Physics 2022-04-20 Shenglin Huang , Zequn He , Bryan Chem , Celia Reina

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…

Machine Learning · Computer Science 2024-05-07 Benjie Wang , Joel Jennings , Wenbo Gong

We present a differentiable formalism for learning free energies that is capable of capturing arbitrarily complex model dependencies on coarse-grained coordinates and finite-temperature response to variation of general system parameters.…

Computational Physics · Physics 2024-05-31 Blake R. Duschatko , Xiang Fu , Cameron Owen , Yu Xie , Albert Musaelian , Tommi Jaakkola , Boris Kozinsky

The stochastic differential equations for a model of dissipative particle dynamics with both total energy and total momentum conservation in the particle-particle interactions are presented. The corresponding Fokker-Planck equation for the…

Statistical Mechanics · Physics 2009-10-30 J. Bonet Avalos , A. D. Mackie

In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high…

Numerical Analysis · Mathematics 2026-03-17 Tao Tang , Jiang Yang , Yuxiang Zhao , Quanhui Zhu

We propose a data-driven approach for propagating uncertainty in stochastic power grid simulations and apply it to the estimation of transmission line failure probabilities. A reduced-order equation governing the evolution of the observed…

Computational Engineering, Finance, and Science · Computer Science 2024-01-08 Hongli Zhao , Tyler E. Maltba , D. Adrian Maldonado , Emil Constantinescu , Mihai Anitescu

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…

Dynamical Systems · Mathematics 2021-11-25 Haijun Yu , Xinyuan Tian , Weinan E , Qianxiao Li

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Machine Learning · Computer Science 2021-11-17 Zhao Chen , Yang Liu , Hao Sun