Sequential decoder training for improved latent space dynamics identification
This incremental improvement addresses the problem of accurate and efficient reduced-order modeling for partial differential equations in scientific computing.
The paper tackles the trade-off between latent dynamics enforcement and reconstruction accuracy in Latent Space Dynamics Identification (LaSDI) for reduced-order models by introducing multi-stage LaSDI (mLaSDI), which sequentially learns decoders to correct errors, resulting in lower prediction errors and reduced training time on the 1D-1V Vlasov equation.
Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.