LaSDI: Parametric Latent Space Dynamics Identification

Abstract

Enabling fast and accurate physical simulations with data has become an important area of computational physics to aid in inverse problems, design-optimization, uncertainty quantification, and other various decision-making applications. This paper presents a data-driven framework for parametric latent space dynamics identification procedure that enables fast and accurate simulations. The parametric model is achieved by building a set of local latent space model and designing an interaction among them. An individual local latent space dynamics model achieves accurate solution in a trust region. By letting the set of trust region to cover the whole parameter space, our model shows an increase in accuracy with an increase in training data. We introduce two different types of interaction mechanisms, i.e., point-wise and region-based approach. Both linear and nonlinear data compression techniques are used. We illustrate the framework of Latent Space Dynamics Identification (LaSDI) enable a fast and accurate solution process on various partial differential equations, i.e., Burgers' equations, radial advection problem, and nonlinear heat conduction problem, achieving $O(100)$x speed-up and $O(1)\%$ relative error with respect to the corresponding full order models.

33 pages, 19 figures

References in corpus (6)

• Dynamic Mode Decomposition for Large and Streaming Datasets
• A machine learning approach for efficient uncertainty quantification using multiscale methods
• Bayesian operator inference for data-driven reduced-order modeling
• Accelerating design optimization using reduced order models
• Efficient nonlinear manifold reduced order model
• Discovering State Variables Hidden in Experimental Data

Cited by in corpus (16)

• Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials
• Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions
• gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification
• GPLaSDI: Gaussian Process-based Interpretable Latent Space Dynamics Identification through Deep Autoencoder
• Gappy AE: A Nonlinear Approach for Gappy Data Reconstruction using Auto-Encoder
• Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches
• Physics-informed active learning with simultaneous weak-form latent space dynamics identification
• Non-intrusive reduced order models for partitioned fluid-structure interactions
• Evaluating the Stability of Deep Learning Latent Feature Spaces
• Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method
• Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models
• Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
• Hyper-reduction-free reduced-order Newton solvers for projection-based model-order reduction of nonlinear dynamical systems
• Projection-based model-order reduction via graph autoencoders suited for unstructured meshes
• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
• Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs