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A differentiable model of supply-chain shocks

Saad Hamid, José Moran, Luca Mungo, Arnau Quera-Bofarull, Sebastian Towers

TL;DR

The paper tackles the challenge of calibrating agent-based supply-chain models that capture dynamic shock propagation. It introduces a differentiable ABM implemented in JAX, leveraging GPU tensorization and automatic differentiation to enable gradient-based calibration with uncertainty quantification via Generalized Variational Inference. The main findings show speedups exceeding $10^3$x over non-differentiable baselines and the ability to calibrate models with thousands of parameters efficiently, demonstrated on networks with up to 1,000 firms. This scalable, uncertainty-aware framework enhances realism and practical applicability for modeling disruption responses in large-scale supply chains, including price dynamics, logistics, and potential network restructuring.

Abstract

Modelling how shocks propagate in supply chains is an increasingly important challenge in economics. Its relevance has been highlighted in recent years by events such as Covid-19 and the Russian invasion of Ukraine. Agent-based models (ABMs) are a promising approach for this problem. However, calibrating them is hard. We show empirically that it is possible to achieve speed ups of over 3 orders of magnitude when calibrating ABMs of supply networks by running them on GPUs and using automatic differentiation, compared to non-differentiable baselines. This opens the door to scaling ABMs to model the whole global supply network.

A differentiable model of supply-chain shocks

TL;DR

The paper tackles the challenge of calibrating agent-based supply-chain models that capture dynamic shock propagation. It introduces a differentiable ABM implemented in JAX, leveraging GPU tensorization and automatic differentiation to enable gradient-based calibration with uncertainty quantification via Generalized Variational Inference. The main findings show speedups exceeding x over non-differentiable baselines and the ability to calibrate models with thousands of parameters efficiently, demonstrated on networks with up to 1,000 firms. This scalable, uncertainty-aware framework enhances realism and practical applicability for modeling disruption responses in large-scale supply chains, including price dynamics, logistics, and potential network restructuring.

Abstract

Modelling how shocks propagate in supply chains is an increasingly important challenge in economics. Its relevance has been highlighted in recent years by events such as Covid-19 and the Russian invasion of Ukraine. Agent-based models (ABMs) are a promising approach for this problem. However, calibrating them is hard. We show empirically that it is possible to achieve speed ups of over 3 orders of magnitude when calibrating ABMs of supply networks by running them on GPUs and using automatic differentiation, compared to non-differentiable baselines. This opens the door to scaling ABMs to model the whole global supply network.

Paper Structure

This paper contains 7 sections, 1 equation, 2 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Methods
  4. Model
  5. Calibration
  6. Results
  7. Conclusion

Figures (2)

  • Figure 1: A: We model a directed production network where firms produce to serve demand from other firms, households, government, and foreign customers. B: In each period, an exogenous shock may limit each firm's capacity to produce, then firms receive and place orders, produce subject to input inventories and a capacity limit, and update inventories.
  • Figure 2: Two plots showing the advantages of our methodology. A: we compare the speed of SVI calibration on GPU (RTX 5090) vs CPU (Ryzen 9 9950X). B: We show how the accuracy per model evaluation decreases between SVI and ABC.