Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs | Paper Citation Record

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This paper cites Flexible SE(2) graph neural networks with applications to PDE surrogates.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Flexible SE(2) graph neural networks with applications to PDE surrogates

Reference 1

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This paper cites Regularized linear autoencoders recover the principal components, eventually.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Regularized linear autoencoders recover the principal components, eventually

Reference 2

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This paper cites Multiscale graph neural network autoencoders for interpretable scientific machine learning.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Multiscale graph neural network autoencoders for interpretable scientific machine learning

Reference 3

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This paper cites Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction

Reference 4

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This paper cites Benner et al.Model Reduction and Approximation.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Benner et al.Model Reduction and Approximation

Reference 5

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This paper cites Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equa- tions.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equa- tions

Reference 6

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This paper cites Error estimates for deep learning methods in fluid dynamics.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Error estimates for deep learning methods in fluid dynamics

Reference 7

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This paper cites A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Reference 8

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This paper cites Bonneville et al.Extrapolating Phase-Field Simulations in Space and Time with Purely Convolu- tional Architectures.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Bonneville et al.Extrapolating Phase-Field Simulations in Space and Time with Purely Convolu- tional Architectures

Reference 9

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This paper cites Structure-Preserving Operator Learning.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Structure-Preserving Operator Learning

Reference 10

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This paper cites Message Passing Neural PDE Solvers.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Message Passing Neural PDE Solvers

Reference 11

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This paper cites Geometric and Physical Quantities improve E(3) Equivariant Message Passing.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Geometric and Physical Quantities improve E(3) Equivariant Message Passing

Reference 12

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This paper cites Error estimates for POD-DL-ROMs: a deep learning framework for reduced order mod- eling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Error estimates for POD-DL-ROMs: a deep learning framework for reduced order mod- eling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition

Reference 13

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This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 14

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Unresolved cited work

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This paper cites Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Reference 16

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This paper cites Proper Orthogonal Decomposition Extensions for Parametric Applications in Compressible Aerodynamics.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Proper Orthogonal Decomposition Extensions for Parametric Applications in Compressible Aerodynamics

Reference 17

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This paper cites Data-driven discovery of coordinates and governing equations.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Data-driven discovery of coordinates and governing equations

Reference 18

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Neural Ordinary Differential Equations

Reference 19

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This paper cites Chen et al.Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decom- position.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Chen et al.Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decom- position

Reference 20

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This paper cites Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions

Reference 21

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This paper cites A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A non-intrusive approach for the reconstruction of POD modal coefficients through active subspaces

Reference 22

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Reference 23

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This paper cites Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Reference 24

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This paper cites Shallow recurrent decoder for reduced order modeling of E× B plasma dynamics.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Shallow recurrent decoder for reduced order modeling of E× B plasma dynamics

Reference 25

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This paper cites On latent dynamics learning in nonlinear reduced order modeling.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs On latent dynamics learning in nonlinear reduced order modeling

Reference 26

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A comprehensive and biophysically detailed computational model of the whole human heart electromechanics

Reference 27

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs PyG 2.0: Scalable Learning on Real World Graphs

Reference 28

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This paper cites A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations

Reference 29

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This paper cites A practical existence theorem for reduced order models based on convolutional autoencoders.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A practical existence theorem for reduced order models based on convolutional autoencoders

Reference 30

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Approximation bounds for convolutional neural networks in operator learning

Reference 31

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This paper cites Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Deep learning-based surrogate models for parametrized PDEs: Handling geometric variability through graph neural networks

Reference 32

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This paper cites A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A Comprehensive Deep Learning-Based Approach to Reduced Order Modeling of Nonlinear Time-Dependent Parametrized PDEs

Reference 33

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This paper cites LaSDI: Parametric Latent Space Dynamics Identification.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs LaSDI: Parametric Latent Space Dynamics Identification

Reference 34

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This paper cites Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

Reference 35

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This paper cites Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks

Reference 36

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This paper cites Approximation rates for neural networks with encodable weights in smoothness spaces.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Approximation rates for neural networks with encodable weights in smoothness spaces

Reference 38

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Reference 39

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Predicting Physics in Mesh-reduced Space with Temporal Attention

Reference 40

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Thermodynamics-informed graph neural networks

Reference 41

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This paper cites Non-intrusive reduced order modeling of nonlinear problems using neural networks.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Non-intrusive reduced order modeling of nonlinear problems using neural networks

Reference 42

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Certified machine learning: A posteriori error estimation for physics-informed neural networks

Reference 44

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Graph neural PDE solvers with conservation and similarity-equivariance

Reference 45

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This paper cites GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transport.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs GALDS: A Graph-Autoencoder-based Latent Dynamics Surrogate model to predict neurite material transport

Reference 46

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This paper cites Learning continuous-time PDEs from sparse data with graph neural networks.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning continuous-time PDEs from sparse data with graph neural networks

Reference 47

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Optimal transport-based displacement interpolation with data augmentation for reduced order modeling of nonlinear dynamical systems

Reference 48

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Neural operator: learning maps between function spaces with applications to PDEs

Reference 49

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Geometric Operator Learning with Optimal Transport

Reference 50

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Geometry-informed neural operator for large-scale 3D PDEs

Reference 51

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 52

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Enabling Automatic Differentiation with Mollified Graph Neural Operators

Reference 53

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs On the limited memory BFGS method for large scale optimization

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This paper cites SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases

Reference 56

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This paper cites Hierarchical deep learning of multiscale differential equation time-steppers.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Hierarchical deep learning of multiscale differential equation time-steppers

Reference 57

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This paper cites Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Logg, K.-A

Reference 59

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This paper cites Latent space modeling of parametric and time-dependent PDEs using neural ODEs.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Latent space modeling of parametric and time-dependent PDEs using neural ODEs

Reference 60

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning Latent Graph Dynamics for Visual Manipulation of De- formable Objects

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs

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Observation 6b6e87b9-d78a-4f0f-854d-fe210923c1ca · outbound

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs GFN: A graph feedforward network for resolution- invariant reduced operator learning in multifidelity applications

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Reduced Basis Methods: Success, Limitations and Future Challenges

Reference 64

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning two-phase microstructure evolution using neural operators and autoen- coder architectures

Reference 65

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning Mesh-Based Simulation with Graph Networks

Reference 66

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Deflation-Based Certified Greedy Algorithm and Adaptivity for Bifur- cating Nonlinear PDEs

Reference 68

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs DrivingbifurcatingparametrizednonlinearPDEsbyoptimalcontrolstrategies:applica- tion to Navier–Stokes equations with model order reduction

Reference 70

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Graph Neural Ordinary Differential Equations

Reference 71

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Reference 72

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Symmetry breaking and preliminary results about a Hopf bifurcation for incompressible viscous flow in an expansion channel

Reference 73

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Quarteroni.Numerical Models for Differential Problems

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Combining physics-based and data-driven models: advancing the frontiers of research with scientific machine learning

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Quarteroni, A

Reference 76

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This paper cites New York, NY: Springer, 2007.doi:10.1007/b98885.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs New York, NY: Springer, 2007.doi:10.1007/b98885

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Unresolved cited work

Reference 78

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Reference 79

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Rozza et al.Real Time Reduced Order Computational Mechanics: Parametric PDEs Worked Out Problems

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Seydel.Practical Bifurcation and Stability Analysis

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs GraphVAE: Towards Generation of Small Graphs Using Varia- tional Autoencoders

Reference 82

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Mesh neural networks for SE(3)-equivariant hemodynamics estimation on the artery wall

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs A survey on universal approximation and its limits in soft computing techniques

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Observation 85d0c16d-80da-4272-aeee-b6f083680e37 · outbound

This paper cites Sparse identification for bifurcating phenomena in computational fluid dynamics.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Sparse identification for bifurcating phenomena in computational fluid dynamics

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Reduced order modeling with shallow recurrent decoder networks

Reference 86

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks

Reference 87

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Latent Neural Operator Pretraining for Solving Time-Dependent PDEs

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Observation 1d28a5b0-4170-4708-9e4b-aa09de65440a · outbound

This paper cites Model identification of reduced order fluid dynamics systems using deep learning.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Model identification of reduced order fluid dynamics systems using deep learning

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This paper cites Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes

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Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Equivariant graph neural operator for modeling 3D dynamics

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This paper cites Yavich et al.Differentiable Implicit Solver on Graph Neural Networks for Forward and Inverse Problems.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Yavich et al.Differentiable Implicit Solver on Graph Neural Networks for Forward and Inverse Problems

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Observation aefdd8ef-9f73-4dc2-8d5d-833b31199c02 · outbound

This paper cites Combining physics-informed graph neural network and finite difference for solv- ing forward and inverse spatiotemporal PDEs.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs Combining physics-informed graph neural network and finite difference for solv- ing forward and inverse spatiotemporal PDEs

Reference 93

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Observation 3ae00fe9-4f20-4b44-9bb1-5b5e58ce487a · outbound

This paper cites LESnets (large-eddy simulation nets): Physics-informed neural operator for large- eddy simulation of turbulence.

Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs LESnets (large-eddy simulation nets): Physics-informed neural operator for large- eddy simulation of turbulence

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