Bias and Coverage Properties of the WENDy-IRLS Algorithm

2025-10-03

AI Summary

This study systematically evaluates the statistical performance of the WENDy-IRLS algorithm for joint parameter and state estimation in nonlinear ordinary differential equations (ODEs), using five benchmark systems: Logistic, Lotka–Volterra, FitzHugh–Nagumo, Hindmarsh–Rose, and Protein Transduction. We conduct large-scale simulations under four nonstandard noise regimes—Gaussian, log-normal, additive censored normal, and additive truncated normal—at high noise levels. As the first comprehensive statistical analysis of WENDy-IRLS, we rigorously assess estimator bias and confidence interval coverage. Results demonstrate that the synergy between the weak-form estimation framework and iterative reweighted least squares (IRLS) substantially enhances robustness against heteroscedasticity, non-Gaussianity, and censoring/truncation effects. Even under severe noise, the algorithm achieves low bias and near-nominal coverage, establishing it as a reliable tool for uncertainty quantification in complex dynamical systems.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Weak form Estimation of Nonlinear Dynamics (WENDy) method is a recently proposed class of parameter estimation algorithms that exhibits notable noise robustness and computational efficiency. This work examines the coverage and bias properties of the original WENDy-IRLS algorithm's parameter and state estimators in the context of the following differential equations: Logistic, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark. The estimators' performance was studied in simulated data examples, under four different noise distributions (normal, log-normal, additive censored normal, and additive truncated normal), and a wide range of noise, reaching levels much higher than previously tested for this algorithm.

Problem

• Analyzes bias and coverage of WENDy-IRLS parameter estimators
• Evaluates algorithm performance under four different noise distributions
• Tests parameter estimation robustness at high noise levels

Innovation

• Weak form estimation of nonlinear dynamics
• IRLS algorithm for parameter estimation
• Noise robustness across multiple distributions