tLaSDI: Thermodynamics-informed latent space dynamics identification
arxiv(2024)
摘要
We propose a data-driven latent space dynamics identification method (tLaSDI)
that embeds the first and second principles of thermodynamics. The latent
variables are learned through an autoencoder as a nonlinear dimension reduction
model. The dynamics of the latent variables are constructed by a neural
network-based model that preserves certain structures to respect the
thermodynamic laws through the GENERIC formalism. An abstract error estimate of
the approximation is established, which provides a new loss formulation
involving the Jacobian computation of autoencoder. Both the autoencoder and the
latent dynamics are trained to minimize the new loss. Numerical examples are
presented to demonstrate the performance of tLaSDI, which exhibits robust
generalization ability, even in extrapolation. In addition, an intriguing
correlation is empirically observed between the entropy production rates in the
latent space and the behaviors of the full-state solution.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要