Neural parameter calibration for large-scale multiagent models

Significance

In this work, we consider multiagent models, widely used across the quantitative sciences to analyze complex systems. These often contain parameters which must be estimated from data. While many methods to do so have been developed, they can be mathematically involved or computationally expensive. We present an alternative using neural networks that addresses both these issues. Our method can make accurate predictions from various kinds of data in seconds where more classical techniques, such as MCMC, take hours, thereby presenting researchers across the quantitative disciplines with a valuable tool to estimate relevant parameters and produce more meaningful simulations at a greatly reduced computational cost.

Abstract

Computational models have become a powerful tool in the quantitative sciences to understand the behavior of complex systems that evolve in time. However, they often contain a potentially large number of free parameters whose values cannot be obtained from theory but need to be inferred from data. This is especially the case for models in the social sciences, economics, or computational epidemiology. Yet, many current parameter estimation methods are mathematically involved and computationally slow to run. In this paper, we present a computationally simple and fast method to retrieve accurate probability densities for model parameters using neural differential equations. We present a pipeline comprising multiagent models acting as forward solvers for systems of ordinary or stochastic differential equations and a neural network to then extract parameters from the data generated by the model. The two combined create a powerful tool that can quickly estimate densities on model parameters, even for very large systems. We demonstrate the method on synthetic time series data of the SIR model of the spread of infection and perform an in-depth analysis of the Harris–Wilson model of economic activity on a network, representing a nonconvex problem. For the latter, we apply our method both to synthetic data and to data of economic activity across Greater London. We find that our method calibrates the model orders of magnitude more accurately than a previous study of the same dataset using classical techniques, while running between 195 and 390 times faster.