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• Approximation Results for Gradient Flow Trained Neural Networks

  Gerrit Welper

  2024-06-27

  25201 2568 Pages:107-175 Open-access

• Spectral Neural Networks: Approximation Theory and Optimization Landscape

  Chenghui Li, Rishi Sonthalia, Nicolás García Trillos

  2026-01-06

  123 206

• The Cost-Accuracy Trade-Off in Operator Learning with Neural Networks

  Maarten V. de Hoop, Daniel Zhengyu Huang, Elizabeth Qian, Andrew M. Stuart

  2022-09-22

  40641 4304 Pages:299-341 Open-access

• Approximation of Functionals by Neural Network Without Curse of Dimensionality

  Yahong Yang, Yang Xiang

  2022-12-30

  35476 4289 Pages:342-372 Open-access

• Beyond the Quadratic Approximation: The Multiscale Structure of Neural Network Loss Landscapes

  Chao Ma, Daniel Kunin, Lei Wu, Lexing Ying

  2022-09-22

  39410 4502 Pages:247-267 Open-access

• On the Existence of Optimal Shallow Feedforward Networks with ReLU Activation

  Steffen Dereich, Sebastian Kassing

  2024-03-21

  25883 2930 Pages:1-22 Open-access

• Variational Formulations of ODE-Net as a Mean-Field Optimal Control Problem and Existence Results

  Noboru Isobe, Mizuho Okumura

  2024-11-07

  17828 2123 Pages:413-444 Open-access

• Interpolating Between BSDEs and PINNs: Deep Learning for Elliptic and Parabolic Boundary Value Problems

  Nikolas Nüsken, Lorenz Richter

  2024-03-21

  36192 4647 Pages:31-64 Open-access

• Embedding Inequalities for Barron-Type Spaces

  Lei Wu

  2023-12-28

  26259 3037 Pages:259-270 Open-access

• A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods

  Charalambos G. Makridakis, Aaron Pim, Tristan Pryer

  2025-09-12

  44196 715 Pages:166-191 Open-access

• Convergence of Stochastic Gradient Descent Schemes for Łojasiewicz-Landscapes

  Steffen Dereich, Sebastian Kassing

  2024-09-21

  20193 2327 Pages:245-281 Open-access