arXiv Machine Learning September 23, 2026 By Takashi Furuya, Anastasis Kratsios

Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs

Read the original on arXiv Machine Learning →

arXiv:2410. 14788v4 Announce Type: replace-cross Abstract: Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery.

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arXiv Machine Learning

4d ago

Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations

arXiv:2112. 08125v3 Announce Type: replace-cross Abstract: We construct and analyze approximation rates of deep operator networks (ONets) between infinite-dimensional spaces that emulate with an exponential rate of convergence the coefficient-to-solution map of elliptic second-order partial differential equations.

By Carlo Marcati, Christoph Schwab

diffusion

arXiv Machine Learning

Jun 17

Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

arXiv:2606. 17319v1 Announce Type: cross Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube.

By Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae

arXiv Statistics ML

Aug 25

Q-Learning with Stable Infinite-Dimensional Linear Function Approximation

arXiv:2608.22636v1 Announce Type: cross Abstract: Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contracti...

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reinforcement-learning

arXiv Machine Learning

Jun 2

Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise

arXiv:2605. 18528v2 Announce Type: replace-cross Abstract: A growing lesson from neural network optimization is that optimizer design should respect how the model is parametrized.

By Jiayu Zhang, Tianyi Lin

arXiv Machine Learning

Aug 4

Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation

arXiv:2605. 08170v2 Announce Type: replace Abstract: Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces.

By Nicole Hao

arXiv Machine Learning

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A Statistical Formulation Gap for Nonlinear Multiscale Physics-Informed Learning

arXiv:2607. 15702v1 Announce Type: cross Abstract: We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations.

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