PAINT: Parallel-in-time Neural Twins for Dynamical System Reconstruction

Neural surrogates have shown great potential for simulating dynamical systems in real time. We envision Neural Twins as an evolution of neural surrogates that continuously consume measurements at test time, acting as digital replicas of real systems and enabling context-specific decision-making. We argue that a natural requirement for Neural Twins is that they remain on-trajectory: staying close to the true system state rather than drifting due to compounding errors. Yet most deep learning approaches for reconstructing high-dimensional dynamical systems are autoregressive: they predict states from previously predicted ones, which makes them inherently susceptible to such drift. We find that parallel-in-time modeling is a viable but underexplored alternative. Rather than sequential rollout, these models jointly predict a full window of states from a corresponding window of measurements. Such models are conceptually simple, scale to state spaces with thousands of dimensions, and avoid rollout degradation. We show theoretically and empirically that autoregressive models generally fail to satisfy the on-trajectory property, whereas parallel-in-time models satisfy it by construction. We call this family of methods PAINT (Parallel-in-time Neural Twins). On a challenging two-dimensional turbulent fluid dynamics problem, our PAINT instantiation using Flow Matching closely follows the trajectory and reconstructs states from sparse measurements with high fidelity. These results establish parallel-in-time modeling as a viable alternative to autoregressive approaches for neural twins and motivate further investigation of this direction.