TY  - COMP
TI  - Weak-Form Latent Space Dynamics Identification
AB  - This software showcases the enhanced capabilities of the Latent Space Dynamics Identification (LaSDI)
algorithm through the application of the weak form, resulting in WLaSDI. WLaSDI first compresses the
data, then projects it onto test functions, and subsequently learns the local latent space models. Notably,
WLaSDI demonstrates significantly improved robustness to noise. Using weak-form equation learning
techniques, WLaSDI achieves local latent space modeling. Compared to the standard sparse
identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form
ensures robust and precise latent space recovery, enabling fast, robust, and accurate simulations.
We demonstrate the efficacy of WLaSDI against LaSDI using several common benchmark examples,
including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in 1D inviscid
Burgers' simulations with up to 100% Gaussian white noise, WLaSDI maintains relative errors
consistently below 6%, whereas LaSDI errors can exceed 10,000%. Similarly, in radial advection
simulations, WLaSDI keeps relative errors below 16%, compared to potential errors of up to 10,000% with
LaSDI. Additionally, WLaSDI achieves significant speedups, such as a 140X speedup in 1D Burgers'
simulations compared to the corresponding full order model.
AU  - Choi, Youngsoo
AU  - He, Xiaolong
AU  - Tran, Chi
AU  - Bortz, David
DO  - https://doi.org/10.11578/dc.20240904.1
UR  - https://www.osti.gov/doecode/biblio/142351
CY  - United States
PY  - 2024
DA  - 2024-07-05
LA  - English
C1  - Research Org.: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
C2  - Sponsor Org.: USDOE National Nuclear Security Administration (NNSA)
C4  - Contract Number: AC52-07NA27344
ER  -