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. 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. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqN
This research addresses a fundamental limitation in neural operator technology, driven by the increasing need for high-fidelity, rapid PDE solutions in various scientific and engineering fields.
Improved neural operators can significantly accelerate scientific discovery, engineering design, and real-time simulation across industries where complex physical phenomena are modeled.
The reliability and accuracy of neural operator surrogates for fine-scale structures will improve, making them viable for more critical applications previously limited by spectral bias.
- · AI/ML researchers in scientific computing
- · Engineering simulation software providers
- · Industries relying on complex PDE solutions (e.g., aerospace, climate modeling,
- · Traditional numerical solvers in specific use cases
- · Organizations slow to adopt advanced AI-driven simulation
Neural operators become more widely adopted as reliable surrogates for physical simulations.
Accelerated design cycles and reduced R&D costs across various high-tech sectors due to faster and more accurate simulations.
New classes of AI-driven materials discovery and optimization become feasible, leading to novel industrial applications.
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