mlsanityData to 7 Oct 2026

DRM Revisited: A Complete Error Analysis

arXiv 2407.09032 ↗First posted 12 Jul 2024math.NA cs.LG cs.NAcited by 4

Not on the map. Why?

Abstract (arXiv)

In this work, we address a foundational question in the theoretical analysis of the Deep Ritz Method (DRM) under the over-parameteriztion regime: Given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision?

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 6 of its 116 references that are in the map. First posted on arXiv 12 Jul 2024.

Builds on

6 of 116 references.

References · 6

  1. 2021Error Estimates for the Deep Ritz Method with Boundary Penaltycited by 14
  2. 2024Deeper or Wider: A Perspective from Optimal Generalization Error with Sobolev Losscited by 14
  3. 2022Exponential Tail Local Rademacher Complexity Risk Bounds Without the Bernstein Conditioncited by 9
  4. 2023Analysis of the expected L2 error of an over-parametrized deep neural network estimate learned by gradient descent without regularizationcited by 4
  5. 2023On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descentcited by 2
  6. 2024Error Analysis of Three-Layer Neural Network Trained with PGD for Deep Ritz Methodcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Adaptive-Growth Randomized Neural Networks for Level-Set Computation of Multivalued Nonlinear First-Order PDEs with Hyperbolic Characteristicscited by 0
  2. 2026Feature Learning for the High Dimensional Stationary Sch"odinger Equation with Deep Ritz Methodcited by 0
  3. 2026Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networkscited by 0
  4. 2026A Hybrid Iterative Deep Ritz Method for Elliptic Interface Problemscited by 0