Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants

被引:3
作者
Gao, L. Mars [1 ]
Kutz, J. Nathan [2 ]
机构
[1] Univ Washington, Paul G Allen Sch Comp Sci Engn, Seattle, WA 98195 USA
[2] Univ Washington, Dept Appl Math & Elect & Comp Engn, Seattle, WA USA
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2024年 / 480卷 / 2286期
基金
美国国家科学基金会;
关键词
model discovery; dynamical systems; machine learning; Bayesian deep learning; Bayesian sparse inference; autoencoder; SPARSE IDENTIFICATION; VARIABLE SELECTION; SYSTEMS; NETWORKS; SPIKE; SINDY;
D O I
10.1098/rspa.2023.0506
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
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 Spike-and-slab Gaussian Lasso prior. Bayesian SINDy autoencoder enables the joint discovery of governing equations and coordinate systems with uncertainty estimate. To resolve the challenging computational tractability of the Bayesian hierarchical setting, we adapt an adaptive empirical Bayesian method with Stochastic 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, withaccurate 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.
引用
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页数:26
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