A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting

TL;DR

This paper introduces a hybrid neural time integrator that ensures stability in long-term autoregressive forecasting of chaotic systems, outperforming existing models with fewer parameters and enabling real-time simulation speedups.

Contribution

A novel hybrid approach combining autoregressive transformers with a structure-preserving finite element scheme, providing provable stability and improved long-term forecasting performance.

Findings

Achieves a 65x reduction in model parameters compared to modern foundation models.

Demonstrates long-horizon forecasting of chaotic systems with superior stability.

Enables real-time surrogate modeling with 9,000x speedup over traditional simulations.

Abstract

For autoregressive modeling of chaotic dynamical systems over long time horizons, the stability of both training and inference is a major challenge in building scientific foundation models. We present a hybrid technique in which an autoregressive transformer is embedded within a novel shooting-based mixed finite element scheme, exposing topological structure that enables provable stability. For forward problems, we prove preservation of discrete energies, while for training we prove uniform bounds on gradients, provably avoiding the exploding gradient problem. Combined with a vision transformer, this yields latent tokens admitting structure-preserving dynamics. We outperform modern foundation models with a $65\times$ reduction in model parameters and long-horizon forecasting of chaotic systems. A "mini-foundation" model of a fusion component shows that 12 simulations suffice to train a real-time surrogate, achieving a $9{,}000\times$ speedup over particle-in-cell simulation.