Abstract
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.
- Developers:
-
Choi, Youngsoo [1] ; He, Xiaolong [1] ; Tran, Chi [1] ; Bortz, David [2]
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- University of Colorado, Boulder
- Release Date:
- 2024-07-05
- Project Type:
- Open Source, Publicly Available Repository
- Software Type:
- Scientific
- Version:
- 0.1
- Licenses:
-
MIT License
- Sponsoring Org.:
-
USDOE National Nuclear Security Administration (NNSA)Primary Award/Contract Number:AC52-07NA27344
- Code ID:
- 142351
- Site Accession Number:
- LLNL-CODE-867254
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Country of Origin:
- United States
Citation Formats
Choi, Youngsoo, He, Xiaolong, Tran, Chi K., and Bortz, David.
Weak-Form Latent Space Dynamics Identification.
Computer Software.
https://github.com/MathBioCU/PyWLaSDI.
USDOE National Nuclear Security Administration (NNSA).
05 Jul. 2024.
Web.
doi:10.11578/dc.20240904.1.
Choi, Youngsoo, He, Xiaolong, Tran, Chi K., & Bortz, David.
(2024, July 05).
Weak-Form Latent Space Dynamics Identification.
[Computer software].
https://github.com/MathBioCU/PyWLaSDI.
https://doi.org/10.11578/dc.20240904.1.
Choi, Youngsoo, He, Xiaolong, Tran, Chi K., and Bortz, David.
"Weak-Form Latent Space Dynamics Identification." Computer software.
July 05, 2024.
https://github.com/MathBioCU/PyWLaSDI.
https://doi.org/10.11578/dc.20240904.1.
@misc{
doecode_142351,
title = {Weak-Form Latent Space Dynamics Identification},
author = {Choi, Youngsoo and He, Xiaolong and Tran, Chi K. and Bortz, David},
abstractNote = {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.},
doi = {10.11578/dc.20240904.1},
url = {https://doi.org/10.11578/dc.20240904.1},
howpublished = {[Computer Software] \url{https://doi.org/10.11578/dc.20240904.1}},
year = {2024},
month = {jul}
}