Optimal control for interacting particle systems driven by neural networks

TL;DR

This paper introduces a neural network-based method for modeling interaction dynamics in particle systems, formulating it as an optimal control problem and validating it with real traffic and crowd data.

Contribution

It develops a theoretical framework for optimal control of neural network models of particle interactions and proposes a stochastic gradient descent algorithm for parameter calibration.

Findings

Validated approach with real traffic data

Compared neural network model with classical interaction models

Proved existence of optimal controls and derived optimality conditions

Abstract

We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach we use real data sets from traffic and crowd dynamics to fit the parameters. The results are compared to forces corresponding to well-known interaction models such as the Lighthill-Whitham-Richards model for traffic and the social force model for crowd motion.