mlsanityData to 7 Oct 2026

Temporal Consistency Loss for Physics-Informed Neural Networks

arXiv 2301.13262 ↗First posted 30 Jan 2023physics.flu-dyn cs.LGcited by 3

Not on the map. Why?

Abstract (arXiv)

Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations in a forward and inverse manner using deep neural networks. However, training these networks can be challenging for multiscale problems. While statistical methods can be employed to scale the regression loss on data, it is generally challenging to scale the loss terms for equations. This paper proposes a method for scaling the mean squared loss terms in the objective function used to train PINNs. Instead of using automatic differentiation to calculate the temporal derivative, we use backward Euler discretization. This provides us with a scaling term for the equations. In this work, we consider the two and three-dimensional Navier-Stokes equations and determine the kinematic viscosity using the spatio-temporal data on the velocity and pressure fields. We first consider numerical datasets to test our method. We test the sensitivity of our method to the time step size, the number of timesteps, noise in the data, and spatial resolution. Finally, we use the velocity field obtained using Particle Image Velocimetry (PIV) experiments to generate a reference pressure field. We then test our framework using the velocity and reference pressure field.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 16 of its 33 references that are in the map. First posted on arXiv 30 Jan 2023.

Builds on

16 of 33 references.

References · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 4,993
  3. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  4. 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
  5. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  6. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 329
  7. 2018Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equationscited by 233
  8. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  9. 2020PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domaincited by 173
  10. 2021Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equationscited by 142
  11. 2019Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networkscited by 76
  12. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
4 more
  1. 2020Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structurescited by 52
  2. 2020A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecturecited by 50
  3. 2020Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equationscited by 24
  4. 2020Physics-informed Neural Networks for Solving Nonlinear Diffusivity and Biot's equationscited by 20

Built on by

Cited by year

Citing papers per year: 2023: 2; 2024: 1.

3 papers.

  1. 2023A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositionscited by 48
  2. 2023About optimal loss function for training physics-informed neural networks under respecting causalitycited by 6
  3. 2024Physics-Informed Neural Network based inverse framework for time-fractional differential equations for rheologycited by 0