Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones

• URL: http://arxiv.org/abs/2309.17240v1
• Date: Fri, 29 Sep 2023 13:50:32 GMT
• Title: Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones
• Authors: Junchao Chen, Jin Song, Zijian Zhou, Zhenya Yan
• Abstract summary: We study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate.
• Score: 3.522950356329991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.

Related papers

• Learning solutions of parametric Navier-Stokes with physics-informed neural networks [0.3989223013441816]
  We leverageformed-Informed Neural Networks (PINs) to learn solution functions of parametric Navier-Stokes equations (NSE) We consider the parameter(s) of interest as inputs of PINs along with coordinates, and train PINs on numerical solutions of parametric-PDES for instances of the parameters. We show that our proposed approach results in optimizing PINN models that learn the solution functions while making sure that flow predictions are in line with conservational laws of mass and momentum.
  arXiv  Detail & Related papers  (2024-02-05T16:19:53Z)
• Grad-Shafranov equilibria via data-free physics informed neural networks [0.0]
  We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity.
  arXiv  Detail & Related papers  (2023-11-22T16:08:38Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• A predictive physics-aware hybrid reduced order model for reacting flows [65.73506571113623]
  A new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. The number of degrees of freedom is reduced from thousands of temporal points to a few POD modes with their corresponding temporal coefficients. Two different deep learning architectures have been tested to predict the temporal coefficients.
  arXiv  Detail & Related papers  (2023-01-24T08:39:20Z)
• Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations [64.78260098263489]
  In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs) We show that PINNs eventually fail to produce correct solutions to these benchmarks as their complexity increases. We identify several reasons why this may be the case, including insufficient network capacity, poor conditioning of the ODEs, and high local curvature, as measured by the Laplacian of the PINN loss.
  arXiv  Detail & Related papers  (2022-10-14T15:01:32Z)
• Wave simulation in non-smooth media by PINN with quadratic neural network and PML condition [2.7651063843287718]
  The recently proposed physics-informed neural network (PINN) has achieved successful applications in solving a wide range of partial differential equations (PDEs) In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source perturbation. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement.
  arXiv  Detail & Related papers  (2022-08-16T13:29:01Z)
• Neural Basis Functions for Accelerating Solutions to High Mach Euler Equations [63.8376359764052]
  We propose an approach to solving partial differential equations (PDEs) using a set of neural networks. We regress a set of neural networks onto a reduced order Proper Orthogonal Decomposition (POD) basis. These networks are then used in combination with a branch network that ingests the parameters of the prescribed PDE to compute a reduced order approximation to the PDE.
  arXiv  Detail & Related papers  (2022-08-02T18:27:13Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Physics-Informed Neural Network Method for Solving One-Dimensional Advection Equation Using PyTorch [0.0]
  PINNs approach allows training neural networks while respecting the PDEs as a strong constraint in the optimization. In standard small-scale circulation simulations, it is shown that the conventional approach incorporates a pseudo diffusive effect that is almost as large as the effect of the turbulent diffusion model. Of all the schemes tested, only the PINNs approximation accurately predicted the outcome.
  arXiv  Detail & Related papers  (2021-03-15T05:39:17Z)
• On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks [0.0]
  We show that neural networks (PINNs) struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. We construct novel architectures that employ multi-scale random observational features and justify how such coordinate embedding layers can lead to robust and accurate PINN models.
  arXiv  Detail & Related papers  (2020-12-18T04:19:30Z)
• Multipole Graph Neural Operator for Parametric Partial Differential Equations [57.90284928158383]
  One of the main challenges in using deep learning-based methods for simulating physical systems is formulating physics-based data. We propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.
  arXiv  Detail & Related papers  (2020-06-16T21:56:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.