gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification

TL;DR

gLaSDI is a novel parametric reduced-order modeling framework that combines autoencoders, local dynamics models, and adaptive greedy sampling to efficiently and accurately model high-dimensional nonlinear systems with significant speed-up.

Contribution

It introduces an integrated adaptive greedy sampling and local dynamics interpolation approach within a physics-informed latent space framework for improved reduced-order modeling.

Findings

Achieves 17 to 2,658x speed-up over high-fidelity models.

Maintains 1 to 5% relative error in various nonlinear problems.

Outperforms uniform sampling in accuracy and efficiency.

Abstract

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. An interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a k-nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658x speed-up with 1 to 5% relative errors.