Accelerated surrogate dynamics for dynamical, stochastic system evolution

2026-09-29

AI Summary

This study addresses the prohibitive computational costs of simulating stochastic dynamical systems and the susceptibility of conventional time-series models to drift in high-dimensional settings. To overcome these challenges, we propose a latent space propagation framework that integrates a variational autoencoder with a Temporal Fusion Transformer. The variational autoencoder enables efficient dimensionality reduction, while an encoding mechanism capturing both short- and long-term dependencies accommodates static covariate inputs. Furthermore, built-in uncertainty quantification facilitates informed experimental design. Evaluated across three benchmark cases, the proposed framework achieves predictive accuracy highly consistent with high-fidelity simulations while substantially reducing computational overhead. Ultimately, this work establishes a novel paradigm for the efficient simulation of complex dynamical systems.

Abstract

Dynamic simulations are an entrenched way of gaining insight into the evolution of system dynamics. Their computational cost however is often prohibitively high, especially in cases of stochastic frameworks. Machine learning algorithms are especially suited as simulation surrogates. Nevertheless, they face some very distinct limitations. Firstly, the sheer dimensionality of these systems, however, precludes the use of traditional time series models who struggle with high dimensional feature spaces. Additionally, traditional time series focus exclusively on either long or short range effects, causing local or global drift given enough time. In this paper, we propose a framework that addresses those limitations. Our framework combines a Variational Autoencoder, with a convolutional or graph basis that reduces the dimensionality of the system. This latent vector is propagated in time using a Temporal Fusion Transformer model, which includes both long range and short range effect encoding, as well as static covariate support. We test our framework on three distinct cases, to prove its robustness and in all three we have achieved practically identical to the simulation results at a fraction of the time. Further, our framework is flexible enough to be adapted to any new system and provides an inbuilt uncertainty quantification for targeted experiment design.

Problem

• surrogate dynamics
• stochastic systems
• high dimensionality
• time series modeling
• computational cost

Innovation

• Variational Autoencoder
• Temporal Fusion Transformer
• Surrogate dynamics
• Uncertainty quantification
• Dimensionality reduction