Parameter calibration with stochastic gradient descent for interacting particle systems driven by neural networks

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