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

DOI10.1016/j.cma.2023.115944OpenAlexW4321465178MaRDI QIDQ2693426

Erdogan Madenci, Arda Mavi, Ali C. Bekar, Ehsan Haghighat

Publication date: 20 March 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.12177

zbMATH Keywords

deep learningperidynamic differential operatorconvolutional-recurrent learning

Mathematics Subject Classification ID

Computer science (68-XX) Quantum theory (81-XX)

Related Items (1)

The fully coupled thermo-mechanical dual-horizon peridynamic correspondence damage model for homogeneous and heterogeneous materials

Uses Software

• Chebfun
• redbKIT
• DiffSharp
• ImageNet
• Adam
• Tensor2Tensor
• SciANN
• AlexNet
• DeepONet
• NSFnets

Cites Work

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• Convergence of peridynamics to classical elasticity theory
• Multilayer feedforward networks are universal approximators
• SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
• PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
• A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
• nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications
• Peridynamics enabled learning partial differential equations
• NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations
• PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain
• Parallel physics-informed neural networks via domain decomposition
• When and why PINNs fail to train: a neural tangent kernel perspective
• An optimization-based approach to parameter learning for fractional type nonlocal models
• Physics-informed neural networks for inverse problems in supersonic flows
• Physics-informed neural networks for high-speed flows
• Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
• Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Physics-informed multi-LSTM networks for metamodeling of nonlinear structures
• On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
• A nonlocal physics-informed deep learning framework using the peridynamic differential operator
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Peridynamic differential operator and its applications
• A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
• Multi-fidelity surrogate modeling using long short-term memory networks
• Machine learning of nonlocal micro-structural defect evolutions in crystalline materials
• Absolute Stability of Wavetrains Can Explain Spatiotemporal Dynamics in Reaction-Diffusion Systems of Lambda-Omega Type
• Spectral Methods for Time-Dependent Problems
• Plane Wave Solutions to Reaction-Diffusion Equations
• Finite Volume Methods for Hyperbolic Problems
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• Solving high-dimensional partial differential equations using deep learning
• When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
• Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
• On the Partial Difference Equations of Mathematical Physics

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