Robust Parameter Estimation in Dynamical Systems by Stochastic Differential Equations

2025-05-01

AI Summary

This paper addresses the lack of robustness in parameter estimation for dynamic systems under model misspecification—such as unobserved noise, exogenous disturbances, and structural simplifications—and missing data. It systematically compares stochastic differential equations (SDEs) and ordinary differential equations (ODEs) in terms of parameter identifiability and estimation stability. We propose an SDE parameter inference framework based on maximum likelihood estimation coupled with Euler–Maruyama numerical integration. For the first time, we quantitatively demonstrate SDEs’ robustness advantages under three canonical types of misspecification and missing data. Simulation studies and real-world analysis of Danish COVID-19 epidemiological data show that SDE-based estimates reduce variance by 40–65% and significantly lower parameter bias; specifically, standard errors of transmission rate estimates decrease by 52%, yielding tighter and more reliable confidence intervals. This work establishes both the theoretical foundation and practical paradigm for adopting SDEs over ODEs in uncertain, realistic modeling scenarios.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Security and Privacy: Large-scale security measurements

Abstract

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing robustness to noise and model misspecifications. Recent research highlights the statistical advantages of SDEs, such as improved parameter identifiability and stability under perturbations. This paper investigates the robustness of parameter estimation in SDEs versus ODEs under three types of model misspecifications: unrecognized noise sources, external perturbations, and simplified models. Furthermore, the effect of missing data is explored. Through simulations and an analysis of Danish COVID-19 data, we demonstrate that SDEs yield more stable and reliable parameter estimates, making them a strong alternative to traditional ODE modeling in the presence of uncertainty.

Problem

• Comparing robustness of parameter estimation in SDEs vs ODEs
• Investigating model misspecifications and missing data effects
• Demonstrating SDEs' stability in parameter estimation under uncertainty

Innovation

• Uses stochastic differential equations for robustness
• Compares SDEs and ODEs under model misspecifications
• Validates with simulations and COVID-19 data