Parameter Estimation of Nonlinear Systems using Neural ODEs and Multiple Shooting Methods

This paper presents a data-driven framework for modeling nonlinear ordinary differential equations using Neural ODEs combined with Multiple Shooting methods. The proposed approach partitions the time domain into subintervals, trains Neural ODEs within each segment, and enforces continuity constraints across boundaries, improving accuracy, stability, and scalability. By integrating simulated data with physical priors, the framework jointly estimates system states and unknown parameters, making it suitable for systems with limited or noisy data. To demonstrate its effectiveness, we apply it to the van der Pol oscillator and a pharmacokinetic model, recovering key parameters with relative errors below 1.67%. Numerical experiments highlight its robustness in handling stiff and highly nonlinear systems, showcasing its potential for real-world applications in science and engineering.