mlsanityData to 7 Oct 2026

DiffGrad for Physics-Informed Neural Networks

arXiv 2409.03239 ↗First posted 5 Sep 2024cs.LG cs.AI physics.comp-phcited by 0

Not on the map. Why?

Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) are regarded as state-of-the-art tools for addressing highly nonlinear problems based on partial differential equations. Despite their broad range of applications, PINNs encounter several performance challenges, including issues related to efficiency, minimization of computational cost, and enhancement of accuracy. Burgers' equation, a fundamental equation in fluid dynamics that is extensively used in PINNs, provides flexible results with the Adam optimizer that does not account for past gradients. This paper introduces a novel strategy for solving Burgers' equation by incorporating DiffGrad with PINNs, a method that leverages the difference between current and immediately preceding gradients to enhance performance. A comprehensive computational analysis is conducted using optimizers such as Adam, Adamax, RMSprop, and DiffGrad to evaluate and compare their effectiveness. Our approach includes visualizing the solutions over space at various time intervals to demonstrate the accuracy of the network. The results show that DiffGrad not only improves the accuracy of the solution but also reduces training time compared to the other optimizers.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 13 of its 43 references that are in the map. First posted on arXiv 5 Sep 2024.

Builds on

13 of 43 references.

References · 13

  1. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  3. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
  4. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  5. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  6. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  7. 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
  8. 2020Physics-informed neural network for ultrasound nondestructive quantification of surface breaking crackscited by 67
  9. 2020Physics-informed deep learning for incompressible laminar flowscited by 54
  10. 2023A practical PINN framework for multi-scale problems with multi-magnitude loss termscited by 15
  11. 2023Neural oscillators for generalization of physics-informed machine learningcited by 9
  12. 2023Augmenting a Physics-Informed Neural Network for the 2D Burgers Equation by Addition of Solution Data Pointscited by 5
1 more
  1. 2023Amplifying Sine Unit: An Oscillatory Activation Function for Deep Neural Networks to Recover Nonlinear Oscillations Efficientlycited by 3

Built on by

Not cited yet.