# Neural parameter calibration for large-scale multi-agent models

arXiv: https://arxiv.org/abs/2209.13565 · HTML: https://mlsanity.com/paper/2209.13565/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 62 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Mean Field Analysis of Neural Networks: A Central Limit Theorem](https://mlsanity.com/paper/1808.09372/) (2018)
- [Learning interaction kernels in heterogeneous systems of agents from multiple trajectories](https://mlsanity.com/paper/1910.04832/) (2019)
- [Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories](https://mlsanity.com/paper/2007.15174/) (2020)
- [Black-box Bayesian inference for economic agent-based models](https://mlsanity.com/paper/2202.00625/) (2022)
- [Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data](https://mlsanity.com/paper/2007.11048/) (2020)
- [Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation](https://mlsanity.com/paper/2106.13751/) (2021)
- [Saving Human Lives: What Complexity Science and Information Systems can Contribute](https://mlsanity.com/paper/1402.7011/) (2014)
- [Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture](https://mlsanity.com/paper/1511.02975/) (2015)
- [Stochastic Modelling of Urban Structure](https://mlsanity.com/paper/1805.03567/) (2018)

## Built on by (most cited first, 14 of 14)

- [Inferring networks from time series: a neural approach](https://mlsanity.com/paper/2303.18059/) (2023)
- [Identifiable learning of dissipative dynamics](https://mlsanity.com/paper/2510.24160/) (2025)
- [Neural parameter calibration and uncertainty quantification for epidemic forecasting](https://mlsanity.com/paper/2312.03147/) (2023)
- [Modelling Global Trade with Optimal Transport](https://mlsanity.com/paper/2409.06554/) (2024)
- [Generating Origin-Destination Matrices in Neural Spatial Interaction Models](https://mlsanity.com/paper/2410.07352/) (2024)
- [Fully Data-driven but Interpretable Human Behavioural Modelling with Differentiable Discrete Choice Model](https://mlsanity.com/paper/2412.19403/) (2024)
- [MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data](https://mlsanity.com/paper/2604.00333/) (2026)
- [Neural Parameter Estimation of RC Thermal Building Models for Model Predictive Control](https://mlsanity.com/paper/2604.05904/) (2026)
- [Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation](https://mlsanity.com/paper/2410.04299/) (2024)
- [Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2504.13228/) (2025)
- [Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning (ME-EQL)](https://mlsanity.com/paper/2506.08916/) (2025)
- [Deep learning four decades of human migration](https://mlsanity.com/paper/2506.22821/) (2025)
- [A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models](https://mlsanity.com/paper/2507.10714/) (2025)
- [Neural Parameter Calibration for Finite-State Mean Field Games](https://mlsanity.com/paper/2606.23155/) (2026)

## Abstract (arXiv)

Computational models have become a powerful tool in the quantitative sciences to understand the behaviour 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 multi-agent 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 non-convex 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.