Towards agent-based-model informed neural networks

TL;DR

This article introduces Agent-Based-Model informed Neural Networks (ABM-NNs), which leverage restricted graph neural networks and hierarchical decomposition to learn interpretable, structure-preserving dynamics.

Abstract

In this article, we present a framework for designing neural networks that remain consistent with the underlying principles of agent-based models. We begin by highlighting the limitations of standard neural differential equations in modeling complex systems, where physical invariants (like energy) are often absent but other constraints (like mass conservation, information locality, bounded rationality) must be enforced. To address this, we introduce Agent-Based-Model informed Neural Networks (ABM-NNs), which leverage restricted graph neural networks and hierarchical decomposition to learn interpretable, structure-preserving dynamics. We validate the framework across three case studies of increasing complexity: (i) a generalized Generalized Lotka--Volterra system, where we recover ground-truth parameters from short trajectories in presence of interventions; (ii) a graph-based SIR contagion model, where our method outperforms state-of-the-art graph learning baselines (GCN, GraphSAGE, Graph Transformer) in out-of-sample forecasting and noise robustness; and (iii) a real-world macroeconomic model of the ten largest economies, where we learn coupled GDP dynamics from empirical data and demonstrate counterfactual analysis for policy interventions

Figures (10)

• Figure 1: Comparison between a feed-forward neural network (left) and a physics-informed Hamiltonian neural network (right) Greydanus2019Hamiltonian on an ideal spring system. The HNN preserves energy and yields structure-consistent trajectories, while the unconstrained network can violate physical invariants. The color gradient from blue to red denotes the progression of time from the initial time to the final integration time.
• Figure 2: Out-of-sample (OOS) application of a model learned from a single trajectory. Top row: deployment on a new Erdős--Rényi graph ($n=150$, $p=0.05$) without interventions. Bottom row: identical model evaluated on a larger graph ($n=250$, $p=0.05$) under a social-distancing intervention that disables 90% of links per node during the window $t \in [1.5, 10.0]$ (marked by two red vertical lines). Despite not observing interventions during training, the model accurately predicts the system response with infection rate $\beta=0.3$ and recovery rate $\gamma=0.2$.
• Figure 3: Shared-parameter GLV trained on 1995--2020 GDP and macro data, evaluated out-of-sample through 2024 (top) together with the learned interaction matrix $A$ (bottom). The dashed line marks the 2021 holdout boundary. Full hyperparameters and training configuration are detailed in Appendix \ref{['sec:macro_hyperparams']}.
• Figure 4: Three-body GLV with explicit self/interaction terms. Top: shared-parameter rollout trained only on $t\in[0,50]$ (green) yet evaluated through $t=250$, including highlighted exogenous-shock regimes and the Sophon lock removal marker. Bottom: learned growth-rate parameters $r_i$ converging from random initialization (solid) toward the ground-truth rates (dotted) during optimization.
• Figure 5: Training results for the ABM-informed neural network on SIR dynamics with default parameters ($n=100$, $p=0.05$, $\beta=0.4$, $\gamma=0.2$, $\mathrm{d}t=0.1$). The model fits aggregate trajectories while respecting compartmental structure.