Kyle Neal | Searcharxiv

arXiv2026

Data Assimilation: Addressing Spurious Correlations and Scalability Issues

Data assimilation in the form of the ensemble Kalman filter (EnKF) is commonly used to combine large-scale physics-based models and real-world observations of a quantity of interest. However, the EnKF is known to be adversely affected by spurious correlations when applied to Numerical Weather Prediction (NWP) models with high-dimensional state spaces. To mitigate the effect of spurious correlations, various localization methods have been proposed in the NWP literature. Unfortunately, the efficacy of and need for these methods in the setting of general PDE-based forward models with large spatial mesh sizes is not well-understood. We conducted a numerical data assimilation experiment on an example PDE model to demonstrate the presence of spurious correlations and need for localization methods outside of the context of NWP. In addition, we compared the computational efficiency of various EnKF implementations in high-dimensional settings for which theoretical complexity bounds are available but empirical costs are unclear.

stat.OT↗

arXiv2025

Closure Term Estimation in Spatiotemporal Models of Dynamical Systems

Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack uncertainty quantification, or require noise-free observations of the temporal derivatives over the system state. We propose a novel, computationally efficient approach for the modeling and estimation of closure terms over the spatiotemporal domain that provides uncertainty quantification and is effective even when the observations of the system state are sparse or contain moderate levels of noise. The efficacy of our approach is demonstrated in both one and two spatial dimensions through numerical experiments using the Fisher-KPP reaction-diffusion equation and the advection-diffusion equation as exemplars.

stat.ME↗