An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator

• URL: http://arxiv.org/abs/2210.12177v1
• Date: Fri, 21 Oct 2022 18:09:23 GMT
• Title: An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator
• Authors: A. Mavi, A.C. Bekar, E. Haghighat, E. Madenci
• Abstract summary: Unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs) PDDO is employed as a convolutional filter for evaluating derivatives the field variable. NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a convolutional filter for evaluating derivatives the field variable. The NN captures the time-dynamics in smaller latent space through encoder-decoder layers with a Convolutional Long-short Term Memory (ConvLSTM) layer between them. The ConvLSTM architecture is modified by employing a novel activation function to improve the predictive capability of the learning architecture for physics with periodic behavior. The physics is invoked in the form of governing equations at the output of the NN and in the latent (reduced) space. By considering a few benchmark PDEs, we demonstrate the training performance and extrapolation capability of this novel NN architecture by comparing against Physics Informed Neural Networks (PINN) type solvers. It is more capable of extrapolating the solution for future timesteps than the other existing architectures.

Related papers

• DimOL: Dimensional Awareness as A New 'Dimension' in Operator Learning [63.5925701087252]
  We introduce DimOL (Dimension-aware Operator Learning), drawing insights from dimensional analysis. To implement DimOL, we propose the ProdLayer, which can be seamlessly integrated into FNO-based and Transformer-based PDE solvers. Empirically, DimOL models achieve up to 48% performance gain within the PDE datasets.
  arXiv  Detail & Related papers  (2024-10-08T10:48:50Z)
• Parametric Taylor series based latent dynamics identification neural networks [0.3139093405260182]
  A new latent identification of nonlinear dynamics, P-TLDINets, is introduced. It relies on a novel neural network structure based on Taylor series expansion and ResNets.
  arXiv  Detail & Related papers  (2024-10-05T15:10:32Z)
• RBF-MGN:Solving spatiotemporal PDEs with Physics-informed Graph Neural Network [4.425915683879297]
  We propose a novel framework based on graph neural networks (GNNs) and radial basis function finite difference (RBF-FD) RBF-FD is used to construct a high-precision difference format of the differential equations to guide model training. We illustrate the generalizability, accuracy, and efficiency of the proposed algorithms on different PDE parameters.
  arXiv  Detail & Related papers  (2022-12-06T10:08:02Z)
• 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)
• Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs [70.51212431290611]
  Partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. We propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d Navier-Stokes equation.
  arXiv  Detail & Related papers  (2022-04-13T08:53:41Z)
• Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations [62.81701992551728]
  We present a physics-informed framework for solving time-dependent partial differential equations. Our model utilizes discrete cosine transforms to encode spatial and recurrent neural networks. We show experimental results on the Taylor-Green vortex solution to the Navier-Stokes equations.
  arXiv  Detail & Related papers  (2022-02-24T20:46:52Z)
• Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamics [73.77459272878025]
  We propose to enhance the supervised signal in learning dynamics by pre-training a neural differential operator (NDO) NDO is pre-trained on a class of symbolic functions, and it learns the mapping between the trajectory samples of these functions to their derivatives. We provide theoretical guarantee on that the output of NDO can well approximate the ground truth derivatives by proper tuning the complexity of the library.
  arXiv  Detail & Related papers  (2021-06-08T08:04:47Z)
• Delay Differential Neural Networks [0.2538209532048866]
  We propose a novel model, delay differential neural networks (DDNN), inspired by delay differential equations (DDEs) For training DDNNs, we provide a memory-efficient adjoint method for computing gradients and back-propagate through the network. Experiments conducted on synthetic and real-world image classification datasets such as Cifar10 and Cifar100 show the effectiveness of the proposed models.
  arXiv  Detail & Related papers  (2020-12-12T12:20:54Z)
• Liquid Time-constant Networks [117.57116214802504]
  We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations.
  arXiv  Detail & Related papers  (2020-06-08T09:53:35Z)
• A nonlocal physics-informed deep learning framework using the peridynamic differential operator [0.0]
  We develop a nonlocal PINN approach using the Peridynamic Differential Operator (PDDO)---a numerical method which incorporates long-range interactions and removes spatial derivatives in the governing equations. Because the PDDO functions can be readily incorporated in the neural network architecture, the nonlocality does not degrade the performance of modern deep-learning algorithms. We document the superior behavior of nonlocal PINN with respect to local PINN in both solution accuracy and parameter inference.
  arXiv  Detail & Related papers  (2020-05-31T06:26:21Z)
• Solving inverse-PDE problems with physics-aware neural networks [0.0]
  We propose a novel framework to find unknown fields in the context of inverse problems for partial differential equations. We blend the high expressibility of deep neural networks as universal function estimators with the accuracy and reliability of existing numerical algorithms.
  arXiv  Detail & Related papers  (2020-01-10T18:46:50Z)

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.