ModalPINN: an extension of Physics-Informed Neural Networks with enforced truncated Fourier decomposition for periodic flow reconstruction using a limited number of imperfect sensors
arXiv:2108.08929 · doi:10.1016/j.jcp.2022.111271
Abstract
Continuous reconstructions of periodic phenomena provide powerful tools to understand, predict and model natural situations and engineering problems. In line with the recent method called Physics-Informed Neural Networks (PINN) where a multi layer perceptron directly approximates any physical quantity as a symbolic function of time and space coordinates, we present an extension, namely ModalPINN, that encodes the approximation of a limited number of Fourier mode shapes. In addition to the added interpretability, this representation performs up to two orders of magnitude more precisely for a similar number of degrees of freedom and training time in some cases as illustrated through the test case of laminar shedding of vortices over a cylinder. This added simplicity proves to be robust in regards to flow reconstruction using only a limited number of sensors with asymmetric data that simulates an experimental configuration, even when a Gaussian noise or a random delay is added, imitating imperfect and sparse information.
arXiv commentPreprint submitted to Journal of Computational Physics (July, 20th 2021)- 2nd version adds the link to the Github repository - 3rd version comes after revision 1 (March 2022)
References in corpus (16)
- TensorFlow: A system for large-scale machine learning
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Machine Learning for Fluid Mechanics
- Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
- Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
- Artificial Neural Networks trained through Deep Reinforcement Learning discover control strategies for active flow control
- Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- Deep Learning of Vortex Induced Vibrations
- Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
- Understanding and mitigating gradient pathologies in physics-informed neural networks
- When and why PINNs fail to train: A neural tangent kernel perspective
- Learning Unknown Physics of non-Newtonian Fluids
- Physics-informed neural networks with hard constraints for inverse design
- Accelerating Physics-Informed Neural Network Training with Prior Dictionaries
- Hard Encoding of Physics for Learning Spatiotemporal Dynamics
- Frequency-compensated PINNs for Fluid-dynamic Design Problems