tLaSDI: Thermodynamics-informed Latent Space Dynamics Identification

แนวคิดหลัก

Proposing a data-driven method, tLaSDI, that embeds thermodynamics in latent space dynamics identification.

บทคัดย่อ

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.

1. Introduction

• Scientific research evolution from first principles to data-driven approaches.
• Success of Reduced Order Models (ROMs) in various physical models.

2. Preliminaries and Problem Formulation

• Description of dynamical systems and need for ROMs.

3. Thermodynamics-informed Learning for Latent Space Dynamics

• Proposal of tLaSDI method embedding thermodynamics in latent dynamics.

4. Abstract Error Estimate

• Theoretical error estimate for ROM approximation.

5. Numerical Examples

• Performance comparison of tLaSDI with other models in extrapolation and parametric PDEs.

สถิติ

"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."

คำพูด

"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."

ข้อมูลเชิงลึกที่สำคัญจาก

tLaSDI

by Jun Sur Rich... ที่ arxiv.org 03-12-2024

https://arxiv.org/pdf/2403.05848.pdf

สอบถามเพิ่มเติม

어떻게 tLaSDI의 동시 훈련 방식이 분리된 훈련 방법과 비교하여 성능에 영향을 미치나요?

tLaSDI의 동시 훈련 방식은 자동 인코더와 잠재 공간 역학을 동시에 학습시키는 접근 방식을 채택합니다. 이 방식은 자동 인코더가 발견한 잠재 변수와 잠재 역학 모델이 상호작용하도록 하는데 도움이 됩니다. 이는 잠재 변수와 역학이 상호 호환되도록 하여 모델의 성능을 향상시키는 데 중요합니다. 반면 분리된 훈련 방법은 자동 인코더와 잠재 역학을 독립적으로 학습시키는데, 이는 잠재 변수와 역학 사이의 상호작용을 강조하지 않을 수 있습니다. tLaSDI의 동시 훈련 방식은 잠재 변수와 역학을 동시에 최적화하여 모델의 일관성을 유지하고 성능을 향상시킵니다.