Nonparametric inference of interaction laws in systems of agents from trajectory data

Abstract

Inferring the laws of interaction between particles and agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics.

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• Discovery of Dynamics Using Linear Multistep Methods
• Random Feature Models for Learning Interacting Dynamical Systems
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• Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles
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• Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation
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• Numerical Identification of Nonlocal Potential in Aggregation
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• Identifiability of interaction kernels in mean-field equations of interacting particles
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• Machine learning of continuous and discrete variational ODEs with convergence guarantee and uncertainty quantification
• Cluster Prediction for Opinion Dynamics from Partial Observations
• Learning Continuous Network Emerging Dynamics from Scarce Observations via Data-Adaptive Stochastic Processes
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• Learning Interaction Kernels for Agent Systems on Riemannian Manifolds
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• ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems
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• Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction
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