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

2025-10-14

AI Summary

To address the off-trajectory drift prevalent in long-term prediction by neural digital twins of dynamical systems, this paper proposes PAINT—a model-agnostic, parallel temporal modeling framework. PAINT abandons conventional autoregressive dependencies and instead employs a generative neural network to model the state distribution, infers system states from sparse measurements via sliding windows, and achieves theoretically guaranteed on-trajectory consistency over extended horizons through parallel temporal unrolling. Crucially, PAINT is the first neural twin approach to rigorously enforce alignment between model outputs and the true system’s dynamical trajectories, thereby overcoming the fundamental error accumulation bottleneck. In benchmark experiments on two-dimensional turbulent fluid dynamics, PAINT demonstrates significantly higher state reconstruction fidelity and superior long-term estimation stability compared to state-of-the-art autoregressive baselines.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Intelligent Robots: State Estimation
• Multiagent Systems: Adversarial Agents

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

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 Parallel-in-time Neural Twins (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.

Problem

• Creating neural twins for dynamical system reconstruction from measurements
• Ensuring neural models remain on-trajectory with true system states
• Predicting system states from sparse measurements with high fidelity

Innovation

• Parallel-in-time neural network training method
• Generative modeling of state distribution over time
• Sliding window state prediction from sparse measurements