Learning Collective Behaviors from Observation
This work addresses the challenge of modeling complex agent systems for researchers in fields like physics or biology, but it appears incremental as it builds on existing variational inverse problem approaches.
The paper tackles the problem of learning collective behaviors from observational data by developing methods for structural identification of dynamical systems, achieving theoretical convergence guarantees and computational efficiency with high-dimensional data.
We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents. Our approach not only ensures theoretical convergence guarantees but also exhibits computational efficiency when handling high-dimensional observational data. The methods adeptly reconstruct both first- and second-order dynamical systems, accommodating observation and stochastic noise, intricate interaction rules, absent interaction features, and real-world observations in agent systems. The foundational aspect of our learning methodologies resides in the formulation of tailored loss functions using the variational inverse problem approach, inherently equipping our methods with dimension reduction capabilities.