Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs

In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) inf

Holy Grail Math 9.2 Rigor 6.8 ·  May 8, 2024

Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs

Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between theory and practice: worst-case parameter bounds from universa

Lab Rats Math 9 Rigor 3.5 ·  August 20, 2025

Global universal approximation of functional input maps on weighted spaces

We introduce so-called functional input neural networks defined on a possibly infinite dimensional weighted space with values also in a possibly infinite dimensional output space. To this end, we use an additive family to map the input weighted space to the hidden layer, on which a non-linear scalar

Lab Rats Math 9.5 Rigor 1.5 ·  June 5, 2023

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