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Bibliographic Details
Main Authors: Kinch, Brooks, Hu, Xiaozhe, Huang, Yilong, Hansen, Martine Dyring, Meltzer, Sunniva, Hamlin, Nathaniel Donald, Sirajuddin, David, Cyr, Eric C., Trask, Nathaniel
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.21101
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author Kinch, Brooks
Hu, Xiaozhe
Huang, Yilong
Hansen, Martine Dyring
Meltzer, Sunniva
Hamlin, Nathaniel Donald
Sirajuddin, David
Cyr, Eric C.
Trask, Nathaniel
author_facet Kinch, Brooks
Hu, Xiaozhe
Huang, Yilong
Hansen, Martine Dyring
Meltzer, Sunniva
Hamlin, Nathaniel Donald
Sirajuddin, David
Cyr, Eric C.
Trask, Nathaniel
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_21101
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
Kinch, Brooks
Hu, Xiaozhe
Huang, Yilong
Hansen, Martine Dyring
Meltzer, Sunniva
Hamlin, Nathaniel Donald
Sirajuddin, David
Cyr, Eric C.
Trask, Nathaniel
Machine Learning
Numerical Analysis
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.
title A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
topic Machine Learning
Numerical Analysis
url https://arxiv.org/abs/2604.21101