arXiv Machine Learning August 5, 2026 By Chuqi Chen, Yang Xiang, Weihong Zhang

Prescribed-Basis Coefficient-to-Coefficient Neural Operator for Partial Differential Equations

Read the original on arXiv Machine Learning →

arXiv:2510. 10350v3 Announce Type: replace-cross Abstract: Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and output functions are represented.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

safety

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Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs

arXiv:2605. 31027v2 Announce Type: replace Abstract: We propose a novel neural network architecture, termed Multi-Scale Separable Fourier Neural Networks (MS-SFNN), for the accurate and efficient solution of linear and nonlinear high-frequency partial differential equations (PDEs).

By Qihong Yang, Qiaolin He

benchmarks

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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.

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benchmarks

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A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.

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reinforcement-learning safety

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rag diffusion benchmarks

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arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.

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Leveraging Differentiable PDE Solvers for Semi-Neural Spatial Reconstruction From Sparse Measurements

arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.

By Ofek Aloni, Barak Fishbain

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