Residual-augmented flow matching operators for probabilistic partial differential equations
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
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.
arXiv:2606. 09857v1 Announce Type: new Abstract: Reduced-order models (ROMs) provide an efficient surrogate for complex multiscale systems, but their predictive accuracy is often compromised by truncation errors and the inadequate representation of interactions between resolved and unresolved scales.
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.
arXiv:2606. 20417v1 Announce Type: new Abstract: Inverse problems for differential equations arise throughout science and engineering, where one seeks to infer unknown model parameters from noisy or incomplete observations.
ReAl: Refine neural operators via aligning dynamical flow introduces a model‑agnostic plug‑in that enhances pretrained PDE surrogates by adding a refinement stage with a conditional flow‑matching model to recover missing high‑frequency structures, and an alignment stage that generates multiple trajectories and uses trajectory‑level rewards to stabilize long‑horizon predictions. The method improves high‑frequency fidelity, forecasting accuracy, and long‑horizon stability across diverse surrogate architectures and PDE tasks.
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.