<ul data-eligibleForWebStory="true"><li>Determining accurate numerical solutions of partial differential equations (PDEs) is crucial, leading researchers to develop reduced-order models (ROMs) like Latent Space Dynamics Identification (LaSDI).</li><li>LaSDI is a data-driven, non-intrusive ROM framework that compresses training data using an autoencoder to learn a system of user-chosen ordinary differential equations (ODEs) for latent space dynamics.</li><li>LaSDI allows for rapid predictions by evolving the low-dimensional ODEs in the latent space.</li><li>The autoencoder in LaSDI can struggle to accurately reconstruct training data and satisfy imposed dynamics in complex or high-frequency scenarios.</li><li>To overcome this challenge, researchers propose multi-stage Latent Space Dynamics Identification (mLaSDI), where several autoencoders are trained sequentially to correct errors from previous stages.</li><li>Applying mLaSDI with small autoencoders leads to lower prediction and reconstruction errors, along with reduced training time compared to LaSDI.</li></ul>

mLaSDI: Multi-stage latent space dynamics identification

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