arXiv Machine Learning June 24, 2026 By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai

Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training

Read the original on arXiv Machine Learning →

arXiv:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.

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arXiv AI

Jul 24

PILD: Physics-Informed Learning via Diffusion

arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.

By Tianyi Zeng, Tianyi Wang, Jiaru Zhang, Zimo Zeng, Feiyang Zhang, Yiming Xu, Sikai Chen, Junfeng Jiao, Christian Claudel, Xinbo Chen

diffusion safety

arXiv AI

Jul 1

Physics-Constrained Fine-Tuning of Flow-Matching Models for Generation and Inverse Problems

arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.

By Jan Tauberschmidt, Sophie Fellenz, Sebastian J. Vollmer, Andrew B. Duncan

fine-tuning benchmarks

arXiv Machine Learning

Sep 10

Multi-Fidelity Physics-Informed Neural Networks with Bayesian Uncertainty Quantification and Adaptive Residual Learning for Efficient Solution of Parametric Partial Differential Equations

arXiv:2602.01176v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...

By Olaf Yunus Laitinen Imanov

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arXiv Machine Learning

Jun 3

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.

By Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu

diffusion safety

arXiv AI

Aug 25

One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEs

arXiv:2608.22026v1 Announce Type: new Abstract: Accurate simulation of the long-time evolution of systems governed by partial differential equations (PDEs) is central to scientific computing. Among e...

By Maqun Zhang, Feng Gao, Wankun Chen, Hui Yu, Yanhai Gan, Junyu Dong

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arXiv Machine Learning

Sep 15

Backward SDEs-based Diffusion for Physics-Constrained Generation

arXiv:2609.15702v1 Announce Type: new Abstract: Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is of...

By Zihao Wang

diffusion

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