| Abstract: |
| In this talk, I will introduce a data-driven method to identify a comprehensive second-order particle-based model, which integrates numerous advanced models for simulating aggregation and collective behaviors of agents with comparable sizes and shapes. The model is represented as a high-dimensional set of ordinary differential equations, parameterized by dual interaction kernels that evaluate the coordination of positions and velocities. We propose a Gaussian Process (GP)-based methodology for estimating the model parameters, employing two separate GP priors for the latent interaction kernels, which are calibrated against both dynamical and observational data. This approach yields a nonparametric model for interacting dynamical systems, incorporating uncertainty quantification. Additionally, we provide a theoretical analysis to elucidate our method and assess conditions necessary for kernel recovery. The efficacy of our approach is validated through applications to various prototype systems, emphasizing system order and interaction type selection. |
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