Empirical Mode Modeling: A data-driven approach to recover and forecast nonlinear dynamics from noisy data

TL;DR

Empirical Mode Modeling combines empirical mode decomposition with dynamic modeling to improve analysis and forecasting of nonlinear systems from noisy data, enhancing state-space representations without explicit models.

Contribution

This paper introduces empirical mode modeling, a novel data-driven approach that enhances state-space analysis of noisy nonlinear systems by integrating empirical mode decomposition with dynamic modeling.

Findings

Improves state-space representations in noisy conditions

Effective in mathematical and geophysical applications

Enhances data-driven forecasting accuracy

Abstract

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated from available observations. Since observational data are frequently sampled with noise, it is possible that noise can corrupt the state-space representation degrading analytical performance. Here, we evaluate the synthesis of empirical mode decomposition with empirical dynamic modeling, which we term empirical mode modeling, to increase the information content of state-space representations in the presence of noise. Evaluation of a mathematical, and, an ecologically important geophysical application across three different state-space representations suggests that empirical mode modeling may be a useful technique for data-driven, model-free, state-space analysis in the presence of noise.