mlsanityData to 14 Oct 2026

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty

arXiv 2505.13501 ↗First posted 16 May 2025cs.LG physics.comp-phcited by 2

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle simulations, the non-uniqueness of the thermodynamic potentials and operators from given macroscopic dynamics, and the need for efficient uncertainty quantification. This paper introduces Statistical-Physics Informed Epistemic Diffusion Models (SPIEDiff), a machine learning framework designed to overcome these limitations in the context of purely dissipative systems by leveraging statistical physics, conditional diffusion models, and epinets. We evaluate the proposed framework on stochastic Arrhenius particle processes and demonstrate that SPIEDiff can accurately uncover both thermodynamics and kinetics, while enabling reliable long-time macroscopic predictions using only short-time particle simulation data. SPIEDiff can deliver accurate predictions with quantified uncertainty in minutes, drastically reducing the computational demand compared to direct particle simulations, which would take days or years in the examples considered. Overall, SPIEDiff offers a robust and trustworthy pathway for the data-driven discovery of thermodynamic models.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 26 of its 50 references that are in the map. First posted on arXiv 16 May 2025.

Builds on

26 of 50 references.

Closest ancestors · 3

Same direction, newest first

  1. 2024Tutorial on Diffusion Models for Imaging and Vision26 Mar
  2. 2020Denoising Diffusion Implicit Models6 Oct
  3. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 23

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,324
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  4. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 634
  5. 2019Deep Ensembles: A Loss Landscape Perspectivecited by 443
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  7. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  8. 2018Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 120
  9. 2021Epistemic Neural Networkscited by 120
  10. 2020Structure-preserving neural networkscited by 55
  11. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  12. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
11 more
  1. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 39
  2. 2021From Predictions to Decisions: The Importance of Joint Predictive Distributionscited by 29
  3. 2021The Neural Testbed: Evaluating Joint Predictionscited by 22
  4. 2021PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physicscited by 21
  5. 2022PI-VAE: Physics-Informed Variational Auto-Encoder for stochastic differential equationscited by 21
  6. 2024Efficiently Parameterized Neural Metriplectic Systemscited by 19
  7. 2020The Curious Case of Convex Neural Networkscited by 16
  8. 2021Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networkscited by 16
  9. 2023Physics-Informed Polynomial Chaos Expansionscited by 16
  10. 2024Composite Bayesian Optimization In Function Spaces Using NEON -- Neural Epistemic Operator Networkscited by 10
  11. 2025E-PINNs: Epistemic Physics-Informed Neural Networkscited by 4

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentialscited by 1
  2. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0

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