핵심 개념
Proposing a data-driven method, tLaSDI, that embeds thermodynamics in latent space dynamics identification.
초록
The article introduces tLaSDI, a method that embeds thermodynamics in latent space dynamics identification. It utilizes an autoencoder to learn latent variables and a neural network-based model to construct dynamics. The method is compared with other models in numerical examples, demonstrating robust generalization and correlation with entropy production rates.
- Introduction
- Scientific research evolution from first principles to data-driven approaches.
- Success of Reduced Order Models (ROMs) in various physical models.
- Preliminaries and Problem Formulation
- Description of dynamical systems and need for ROMs.
- Thermodynamics-informed Learning for Latent Space Dynamics
- Proposal of tLaSDI method embedding thermodynamics in latent dynamics.
- Abstract Error Estimate
- Theoretical error estimate for ROM approximation.
- Numerical Examples
- Performance comparison of tLaSDI with other models in extrapolation and parametric PDEs.
통계
"The latent dimension is set to n = 10."
"The total number of parameters for hyper-autoencoder and GFINNs in tLaSDI are approximately 905K and 35K respectively."
"tLaSDI is trained by Adam optimizer for 42K iterations."
인용구
"We propose a data-driven latent space dynamics identification method (tLaSDI) that embeds the first and second principles of thermodynamics."
"Numerical examples are presented to demonstrate the performance of tLaSDI, which exhibits robust generalization ability, even in extrapolation."