HopCast: Calibration of Autoregressive Dynamics Models

TL;DR

This paper introduces HopCast, a novel Predictor-Corrector method using Modern Hopfield Networks to improve uncertainty calibration and accuracy in multi-step dynamical system predictions.

Contribution

It proposes a new approach called HopCast that learns error correction during autoregression, enhancing calibration and accuracy over existing methods.

Findings

Sharper, well-calibrated prediction intervals achieved

Higher predictive accuracy compared to baselines

First benchmarking of uncertainty propagation methods based on calibration errors

Abstract

Deep learning models are often trained to approximate dynamical systems that can be modeled using differential equations. Many of these models are optimized to predict one step ahead; such approaches produce calibrated one-step predictions if the predictive model can quantify uncertainty, such as Deep Ensembles. At inference time, multi-step predictions are generated via autoregression, which needs a sound uncertainty propagation method to produce calibrated multi-step predictions. This work introduces an alternative Predictor-Corrector approach named \hop{} that uses Modern Hopfield Networks (MHN) to learn the errors of a deterministic Predictor that approximates the dynamical system. The Corrector predicts a set of errors for the Predictor's output based on a context state at any timestep during autoregression. The set of errors creates sharper and well-calibrated prediction intervals with higher predictive accuracy compared to baselines without uncertainty propagation. The calibration and prediction performances are evaluated across a set of dynamical systems. This work is also the first to benchmark existing uncertainty propagation methods based on calibration errors.