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.
By Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai
The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy
arXiv:2512.12749v3 Announce Type: replace-cross
Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
By Sahil Bhola, Karthik Duraisamy
arXiv:2608. 11435v1 Announce Type: new Abstract: Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration.
By Qiyao Zhou, Xujia Zhu, Pierre Joli, Yu Cong, Sibo Cheng
arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.
By Yi Zhang, Peng Wang, Difan Zou
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