arXiv Machine Learning October 12, 2026 By Jaehyeon Park, Inhyeok Jeong, Noseong Park

SBNO : Schr\"odinger Bridge Neural Operator for the Forward and Inverse Problems under Missing Information

Read the original on arXiv Machine Learning →

SBNO (Schr"odinger Bridge Neural Operator) is an equation‑free framework that learns conditional operators for both forward and inverse PDE problems using paired data and a diffusion Schr"odinger bridge matching approach. It preserves empirical input‑solution pairing through a mask‑aware endpoint coupling and supports both task directions within a single model. At inference, SBNO generates deterministic reconstructions via a probability‑flow ODE, achieving comparable or superior accuracy on five PDE benchmarks with only 5% observations, while being at least 9.7× faster and using 4.3× less GPU memory than guided‑diffusion baselines.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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

arXiv Machine Learning

Sep 10

Residual-augmented flow matching operators for probabilistic partial differential equations

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

diffusion safety

arXiv Machine Learning

Sep 30

SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference

arXiv:2609.36527v1 Announce Type: new Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. D...

By Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, Yuefan Deng

rag diffusion

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

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

Aug 14

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).

By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi

rag diffusion benchmarks

One email a morning, machine-written

Related stories

Backward SDEs-based Diffusion for Physics-Constrained Generation

Residual-augmented flow matching operators for probabilistic partial differential equations

SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference

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

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

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations