mlsanityData to 7 Oct 2026

Deep learning for solution and inversion of structural mechanics and vibrations

arXiv 2105.09477 ↗First posted 18 May 2021cs.LG stat.COcited by 3

Not on the map. Why?

Abstract (arXiv)

Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems. Demonstration problems involve de-noising data, solution to time-dependent ordinary and partial differential equations, and characterizing the system's response for a given data.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 12 of its 43 references that are in the map. First posted on arXiv 18 May 2021.

Builds on

12 of 43 references.

References · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Automatic differentiation in machine learning: a surveycited by 846
  3. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 581
  4. 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
  5. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 144
  6. 2019PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEscited by 116
  7. 2019Optimization for deep learning: theory and algorithmscited by 70
  8. 2020A nonlocal physics-informed deep learning framework using the peridynamic differential operatorcited by 21
  9. 2020A deep learning framework for solution and discovery in solid mechanicscited by 12
  10. 2020SciANN: A Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networkscited by 5
  11. 2021A Physics-Informed Neural Network Framework For Partial Differential Equations on 3D Surfaces: Time-Dependent Problemscited by 5
  12. 2020A machine learning accelerated FE2 homogenization algorithm for elastic solidscited by 2

Built on by

Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 1.

3 papers.

  1. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  2. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 6
  3. 2024Response Estimation and System Identification of Dynamical Systems via Physics-Informed Neural Networkscited by 4