Inverse Problems in Agent-Based Models of Spatial Phenomena

Learning individual (agent) behaviours from aggregate summary statistics constitutes a fundamental inverse problem in the study of socio-physical systems. This thesis examines a key facet of this problem that involves inferring the discrete origin-destination matrix (ODM) of agent trip counts between spatial locations, given low-resolution summary statistic data. This problem is ill-posed, as the space of ODMs consistent with the observed data is combinatorially large. In its continuous mean-field limit, the ODM is governed by a stochastic mechanistic force of spatial interaction. As a result, solving the inverse problem requires inverting both the summary statistic and the underlying mechanistic operators. Existing approaches resort to inferring this mean-field ODM approximation and subsequent ad-hoc discretisation thereof. This impedes conditioning on partially observed summary statistics, fails to explore the discrete combinatorial support of the ODM, and incurs discretisation errors. In this thesis I offer three key methodological contributions to address these challenges in a probabilistic manner. First, the proposed frameworks operate directly on the discrete combinatorial space of ODMs subject to any summary statistic constraint. Full exploration of this space is guaranteed via connectivity induced by Markov bases. Second, the discrete ODM is inferred jointly with its continuous counterpart, allowing mechanistic models of spatial interaction to guide and regularise the solution. Third, a computationally efficient framework is developed, scaling linearly with the number of origin-destination pairs. This acts as a low-cost surrogate for a broad class of mechanistic simulators of agent dynamics. The frameworks developed are empirically evaluated through extensive synthetic and real-world ablation studies, demonstrating improved ODM reconstruction error and uncertainty quantification compared to existing approaches.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Zachos, Ioannis

Advisor dc:contributor.advisor

• Girolami, Mark

• machine learning
• multiagent systems
• computational statistics
• agent-based modelling

Licence

• https://www.repository.cam.ac.uk/bitstreams/f8e912e5-801f-4f17-b91a-e71193dabad1/download
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

eng

Author Identifier

0000-0002-7503-2117

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/393680