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.
FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime
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.
Related stories
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.
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).
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.
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.
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).
arXiv Machine Learning
Jun 8
Architecture Shapes Transfer Specificity in Implicit Neural Representations
arXiv:2606. 06827v1 Announce Type: new Abstract: Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear.
arXiv Machine Learning
Jun 11
Spectrally Regularized Latent Flow Matching for Turbulence Generation
arXiv:2606. 11691v1 Announce Type: new Abstract: Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes.
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.
arXiv Machine Learning
Aug 6
TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning
arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv Machine Learning
Jun 5
PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction
arXiv:2604. 01349v4 Announce Type: replace Abstract: Reservoir simulation workflows face a fundamental data asymmetry: input parameter fields (geostatistical permeability realizations, porosity distributions) are free to generate in arbitrary quantities, yet existing neural operator surrogates require large corpora of expensive labeled simulation trajectories and cannot exploit this unlabeled structure.
arXiv Machine Learning
Jun 10
Rank Collapse, Fixed Points, and the Renormalization Group Structure of MLP Residual Networks
arXiv:2606. 10324v1 Announce Type: new Abstract: The analogy between deep neural network forward passes and renormalization group (RG) flows has been repeatedly noted in the literature, but existing treatments remain qualitative: depth is described as a coarse-graining scale, attention is likened to a partition function, and representations are said to flow toward fixed points.