arXiv Machine Learning August 18, 2026 By Jiyong Kwon, Bongseok Kim, Guang Lin

FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime

Read the original on arXiv Machine Learning →

arXiv:2608. 15408v1 Announce Type: new Abstract: Deep operator networks can become statistically unstable when partial differential equation inputs are observed at thousands of strongly correlated sensors but only a small number of operator samples is available.

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

arXiv Machine Learning

Aug 10

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

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

By Khemraj Shukla, George Em Karniadakis

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

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arXiv Machine Learning

2d ago

Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

arXiv:2608. 13629v1 Announce Type: cross Abstract: Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA).

By Oscar L. Cruz-Gonzalez, Val\'erie Deplano, Badih Ghattas

arXiv AI

Jun 26

Error-Conditioned Neural Solvers

arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.

By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park

arXiv Machine Learning

Jun 30

A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications

arXiv:2606. 28519v1 Announce Type: new Abstract: Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data.

By Christian Munoz, Alexandre Tartakovsky

arXiv Machine Learning

Jun 30

Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

arXiv:2512. 09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs).

By Muhammad Abid, Omer San

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Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

Operator Boosting Produces Pareto-Efficient PDE Surrogates

Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets

Error-Conditioned Neural Solvers

A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications

Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation