mlsanityData to 7 Oct 2026

Bridging the Physics-Data Gap with FNO-Guided Conditional Flow Matching: Designing Inductive Bias through Hierarchical Physical Constraints

arXiv 2510.08295 ↗First posted 9 Oct 2025cs.LGcited by 0

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Conventional time-series generation often ignores domain-specific physical constraints, limiting statistical and physical consistency. We propose a hierarchical framework that embeds the inherent hierarchy of physical laws-conservation, dynamics, boundary, and empirical relations-directly into deep generative models, introducing a new paradigm of physics-informed inductive bias. Our method combines Fourier Neural Operators (FNOs) for learning physical operators with Conditional Flow Matching (CFM) for probabilistic generation, integrated via time-dependent hierarchical constraints and FNO-guided corrections. Experiments on harmonic oscillators, human activity recognition, and lithium-ion battery degradation show 16.3% higher generation quality, 46% fewer physics violations, and 18.5% improved predictive accuracy over baselines.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 17 of its 31 references that are in the map. First posted on arXiv 9 Oct 2025.

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17 of 31 references.

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Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 15

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  8. 2015Variational Inference with Normalizing Flowscited by 2,161
  9. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  11. 2020Lagrangian Neural Networkscited by 388
  12. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
3 more
  1. 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 139
  2. 2019Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networkscited by 127
  3. 2023A physics-informed GAN Framework based on Model-free Data-Driven Computational Mechanicscited by 3

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  1. 2025Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems
  2. 2025Metriplectic Conditional Flow Matching for Dissipative Dynamics
  3. 2026A Kinetic Energy Perspective of Flow Matching
  4. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
  5. 2026Improving Function Space Flow Matching with Kernel Optimal Transport
  6. 2026Conditional flow matching for physics-constrained inverse problems with finite training data
  7. 2025Flow marching for a generative PDE foundation model
  8. 2026Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space