Meshless Latent Dynamics Models for Model Order Reduction of time-dependent Partial Differential Equations

The paper introduces meshless Latent Dynamics Models (LDMs) for model order reduction of time‑dependent PDEs, using conditioning in Neural Fields to represent spatially continuous dynamics. It presents a unified mathematical framework, proves a Universal Approximation Theorem, and analyzes stability through Lipschitz bounds for different conditioning mechanisms, revealing an expressivity–stability trade‑off. Experiments on Burgers’ equation, Navier–Stokes flow, and linear advection demonstrate that meshless LDMs achieve comparable or better predictive accuracy than mesh‑based models while using only 2% of the parameters and maintaining near‑constant error across spatial discretizations.

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