2022/11/19 by Liyao Gao, J. Nathan Kutz, Gao, L. Mars +1 · 2 citations
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Gamma-ray bursts and supernovae #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2211.10575
openalex publication_date 2022/11/19 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28
Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under ℓ1 constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames. However, it is challenging for ℓ1-based sparse inference to perform correct identification for real data due to the noisy measurements and often limited sample sizes. To address the data-driven discovery of physics in the low-data and high-noise regimes, we propose Bayesian SINDy autoencoders, which incorporate a hierarchical Bayesian sparsifying prior: Spike-and-slab Gaussian Lasso. Bayesian SINDy autoencoder enables the joint discovery of governing equations and coordinate systems with a theoretically guaranteed uncertainty estimate. To resolve the challenging computational tractability of the Bayesian hierarchical setting, we adapt an adaptive empirical Bayesian method with Stochatic gradient Langevin dynamics (SGLD) which gives a computationally tractable way of Bayesian posterior sampling within our framework. Bayesian SINDy autoencoder achieves better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification suggested by the experimental studies. The Bayesian SINDy autoencoder can be applied to real video data, with accurate physics discovery which correctly identifies the governing equation and provides a close estimate for standard physics constants like gravity g, for example, in videos of a pendulum.