Title: PAINT: Parallel-in-time Neural Twins for Dynamical System Reconstruction
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: neural surrogate, digital twin, PDE modeling, dynamical systems, fluid mechanics, turbulence

Abstract: Neural surrogates have shown great potential in simulating dynamical systems, while offering real-time capabilities. We envision Neural Twins as a progression of neural surrogates, aiming to create digital replicas of real systems. A neural twin consumes measurements at test time to update its state, thereby enabling context-specific decision-making. A critical property of neural twins is their ability to remain on-trajectory, i.e., to stay close to the true system state over time. We introduce **Pa**rallel-in-t**i**me **N**eural **T**wins (PAINT), an architecture-agnostic family of methods for modeling dynamical systems from measurements. PAINT trains a generative neural network to model the distribution of states parallel over
time. At test time, states are predicted from measurements in a sliding window fashion. Our theoretical analysis shows that PAINT is on-trajectory, whereas autoregressive models generally are not. Empirically, we evaluate our method on a challenging two-dimensional turbulent fluid dynamics problem. The results demonstrate that PAINT stays on-trajectory and predicts system states from sparse measurements with high fidelity. These findings underscore PAINT’s potential for developing neural twins that stay on-trajectory, enabling more accurate state estimation and decision-making.

TL;DR: We introduce Parallel-in-time Neural Twins (PAINT), an architecture-agnostic family of methods for predicting states from measurements of dynamical systems.