Model reduction for the material point method via an implicit neural representation of the deformation map

DOI10.1016/j.jcp.2023.111908OpenAlexW4317213985MaRDI QIDQ2687512

Peter Yichen Chen, Kevin T. Carlberg, Maurizio M. Chiaramonte, Eitan Grinspun

Publication date: 7 March 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.12390

zbMATH Keywords

model reductiondeep learningmaterial point methodreal-time simulationnonlinear manifoldsimplicit neural representation

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical and other methods in solid mechanics (74Sxx) Controllability, observability, and system structure (93Bxx)

Uses Software

• PyTorch
• DeepSDF

Cites Work

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• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method
• Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison
• A priori hyperreduction method: an adaptive approach
• Reduced-order fluid/structure modeling of a complete aircraft configuration
• Stable Galerkin reduced-order models for linearized compressible flow
• Enablers for robust POD models
• Application of a particle-in-cell method to solid mechanics
• A spectral viscosity method for correcting the long-term behavior of POD models.
• Galerkin v. least-squares Petrov-Galerkin projection in nonlinear model reduction
• Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations
• Time-series learning of latent-space dynamics for reduced-order model closure
• Time-series machine-learning error models for approximate solutions to parameterized dynamical systems
• Machine learning for fast and reliable solution of time-dependent differential equations
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Non-linear Petrov-Galerkin methods for reduced order hyperbolic equations and discontinuous finite element methods
• The affine particle-in-cell method
• OmniAD
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
• A low-cost, goal-oriented ‘compact proper orthogonal decomposition’ basis for model reduction of static systems
• A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations
• Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation
• Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
• Nonlinear model order reduction based on local reduced-order bases
• Adaptiveh-refinement for reduced-order models
• Interpolatory Projection Methods for Parameterized Model Reduction
• Optimal rotary control of the cylinder wake using proper orthogonal decomposition reduced-order model
• An efficient reduced-order modeling approach for non-linear parametrized partial differential equations
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• A method for interpolating on manifolds structural dynamics reduced-order models
• Large Sample Properties of Simulations Using Latin Hypercube Sampling
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• A New Look at Proper Orthogonal Decomposition
• Fluid-membrane interaction based on the material point method
• A subspace approach to balanced truncation for model reduction of nonlinear control systems
• Augmented MPM for phase-change and varied materials
• A material point method for snow simulation
• Parametric model order reduction of thermal models using the bilinear interpolatory rational Krylov algorithm
• Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
• Reduced-Order Modeling and ROM-Based Optimization of Batch Chromatography
• Non‐linear model reduction for uncertainty quantification in large‐scale inverse problems
• MODEL REDUCTION FOR FLUIDS, USING BALANCED PROPER ORTHOGONAL DECOMPOSITION
• Linearly Recurrent Autoencoder Networks for Learning Dynamics
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• Lagrangian numerical simulation of particulate flows
• Coupling of substructures for dynamic analyses.

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