用热力学约束提升降阶模型效率，实现快速高精度模拟。
Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems
- 结合自编码器与热力学神经网络，学习参数化系统的低维动态。
- 速度提升3528倍，误差仅1%-3%，训练与推理成本降低超50%。
- 适合需要物理一致性建模的工程仿真与复杂系统研究者。
我们提出一种高效的热力学约束隐空间动态识别框架（tLaSDI），用于参数化非线性动力系统降阶建模。该框架将自编码器与新型参数化GENERIC形式主义神经网络（pGFINNs）结合，能够在保持自由能守恒、熵生成等关键热力学原理的前提下，高效学习参数空间中的隐空间动态。为进一步提升模型性能，引入基于残差的物理感知主动学习策略，通过贪婪误差指标自适应采样高信息量训练数据，在等价计算成本下优于均匀采样。在Burgers方程和1D/1V Vlasov-Poisson方程上的数值实验表明，该方法可实现最高3,528倍的速度提升，相对误差仅为1%-3%，训练成本降低50%-90%，推理成本降低57%-61%。此外，学习得到的隐空间动态揭示了系统的潜在热力学行为，为物理空间动力学提供了深入洞察。
原文摘要 · Abstract (English)
We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality reduction with newly developed parametric GENERIC formalism-informed neural networks (pGFINNs), which enable efficient learning of parametric latent dynamics while preserving key thermodynamic principles such as free energy conservation and entropy generation across the parameter space. To further enhance model performance, a physics-informed active learning strategy is incorporated, leveraging a greedy, residual-based error indicator to adaptively sample informative training data, outperforming uniform sampling at equivalent computational cost. Numerical experiments on the Burgers' equation and the 1D/1V Vlasov-Poisson equation demonstrate that the proposed method achieves up to 3,528x speed-up with 1-3% relative errors, and significant reduction in training (50-90%) and inference (57-61%) cost. Moreover, the learned latent space dynamics reveal the underlying thermodynamic behavior of the system, offering valuable insights into the physical-space dynamics.
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