Continuous-Time Probabilistic Correctors (CTPC) for Physics-Based Long-Horizon Trajectory Forecasting

Muhammad Bilal Shahid, Zhanhong Jiang, Soumik Sarkar, Cody Fleming

Abstract:

Long-horizon forecasting in dynamical systems suffers from error
accumulation due to the absence of corrective observations in the
forecast regime, making reliable uncertainty estimation crucial for
safety-critical decision-making. While high-fidelity physics-based
models provide rather accurate deterministic forecasts, they typi-
cally lack calibrated uncertainty estimates over long horizons. We
introduce a Predictor–Corrector framework in which a physics-
based continuous-time deterministic forecaster is augmented with
a learned continuous-time probabilistic Corrector that models fore-
cast errors. The proposed Corrector can be wrapped around an exist-
ing deterministic forecaster to improve forecast accuracy while pro-
ducing sharp and calibrated full-covariance uncertainty estimates.
The corrector is based on Latent Neural Controlled Differential
Equations (Latent NCDEs) and models the probabilistic temporal
evolution of forecast errors in continuous time. We further intro-
duce a loss function that promotes calibration and sharpness in
long-horizon uncertainty propagation. We evaluate the proposed
framework on long-horizon spacecraft trajectory forecasting using
real-world data from NASA’s Crustal Dynamics Data Information
System (CDDIS), wrapping the Corrector around NASA’s General
Mission Analysis Tool (GMAT). Across forecast horizons of 2–4
days without observations, the proposed approach consistently
improves accuracy and uncertainty calibration compared to deter-
ministic baselines and Latent ODE-based correctors, demonstrating
the effectiveness of the continuous-time probabilistic Corrector for
trajectory forecasting.