Hugging Face Trending Papers June 2, 2026

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

Read the original on Hugging Face Trending Papers →

Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain.

Summary generated by The Flow from the publisher's feed. The full article lives at Hugging Face Trending Papers.

arXiv Machine Learning

Jun 3

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

arXiv:2606. 03936v1 Announce Type: new Abstract: Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters.

By Niccol\`o Perrone, Fanny Lehmann, Stefania Fresca, Filippo Gatti

diffusion safety

arXiv Machine Learning

Jul 17

Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

arXiv:2607. 14193v1 Announce Type: cross Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex.

By Boyuan Deng, Kshitiz Upadhyay, Michael Shields

benchmarks

arXiv Machine Learning

Jun 17

Operator Boosting Produces Pareto-Efficient PDE Surrogates

arXiv:2606. 17460v1 Announce Type: new Abstract: Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-query scientific workflows.

By Lennon J. Shikhman

benchmarks

arXiv Machine Learning

Jun 16

ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.

By Rajyasri Roy, Dibyajyoti Nayak, Somdatta Goswami

arXiv Machine Learning

Jun 26

Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems

arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).

By Yuanzhe Wang, Alexandre M. Tartakovsky

diffusion

arXiv AI

Jun 10

Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training

arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.

By Pierre Cesar (DATAMOVE), Sofya Dymchenko (DATAMOVE), Abhishek Purandare (DATAMOVE), Bruno Raffin (DATAMOVE)

diffusion

Related stories

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

Operator Boosting Produces Pareto-Efficient PDE Surrogates

ANCHOR: Error-Controlled Adaptive Numerical Correction for Neural Operator Time Marching

Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems

Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training