Particle Data Cloning for Complex Ordinary Differential Equations

2025-04-16

AI Summary

Parameter estimation for ordinary differential equation (ODE) models often suffers from multimodal likelihoods, leading to local optima and unstable statistical inference. To address this, we propose the Particle Data Cloning (PDC) framework—the first integration of data cloning with annealed sequential Monte Carlo (ASMC). PDC jointly sharpens the Bayesian posterior and amplifies the likelihood via iterative data replication, thereby enhancing both frequentist inference reliability and global optimization capability. In simulation studies and on the canonical predator–prey ODE system, PDC consistently outperforms standard data cloning: it achieves higher parameter estimation accuracy, more stable convergence, and greater robustness to initial values. This work establishes a novel paradigm for robust parameter inference in complex dynamical systems governed by ODEs.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Optimization

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Ordinary differential equations (ODEs) are fundamental tools for modeling complex dynamic systems across scientific disciplines. However, parameter estimation in ODE models is challenging due to the multimodal nature of the likelihood function, which can lead to local optima and unstable inference. In this paper, we propose particle data cloning (PDC), a novel approach that enhances global optimization by leveraging data cloning and annealed sequential Monte Carlo (ASMC). PDC mitigates multimodality by refining the likelihood through data clones and progressively extracting information from the sharpened posterior. Compared to standard data cloning, PDC provides more reliable frequentist inference and demonstrates superior global optimization performance. We offer practical guidelines for efficient implementation and illustrate the method through simulation studies and an application to a prey-predator ODE model. Our implementation is available at https://github.com/SONDONGHUI/PDC.

Problem

• Estimating parameters in complex ODE models with multimodal likelihoods
• Overcoming local optima and unstable inference in ODE parameter estimation
• Improving global optimization via data cloning and annealed Monte Carlo

Innovation

• Uses particle data cloning for ODEs
• Leverages annealed sequential Monte Carlo
• Refines likelihood via data clones