Introduction to ABM

Aggregate v.s. Individual

'Traditional' modelling methods work at an aggregate level, from the top-down

E.g. Regression, spatial interaction modelling, location-allocation, etc.

Aggregate models work very well in some situations

Homogeneous individuals

Interactions not important

Very large systems (e.g. pressure-volume gas relationship)

Introduction to ABM

Aggregate v.s. Individual

But they miss some important things:

Low-level dynamics, i.e. “smoothing out” (Batty, 2005)

Interactions and emergence

Individual heterogeneity

Unsuitable for modelling complex systems

Why ABM?

Emergence

"The whole is greater than the sum of its parts." (Aristotle?)

Simple rules → complex outcomes

E.g. who plans the air-conditioning in termite mounds?

Hard to anticipate, and cannot be deduced from analysis of an individual

ABM uses simulation to (try to) understand how macro-level patterns emerge from micro-level behaviours

Why ABM?

Better Representations of Theory

Example: Crime theories emphasise importance of ...

Individual behaviour (offenders, victims, guardians)

Individual geographical awareness

Environmental backcloth

Why ABM?

Better Representations of Space

Micro-level environment is very important

Can richly define the space that agents inhabit

More Natural Description of a System

Describe the entities directly, rather than using aggregate equations

Why ABM?

History of the Model Evolution

Rather than returning a single result, the model evolves

The evolution itself can be interesting

Analyse why certain events occurred

Agent-Based Modelling - Difficulties

Tendency towards minimal behavioural complexity

Stochasticity

Computationally expensive (not amenable to optimisation)

Complicated agent decisions, lots of decisions, multiple model runs

Modelling "soft" human factors

Need detailed, high-resolution, individual-level data

Individual-level data

Data assimilation v.s. calibration

Challenges for using DA with ABMs

Model size

10,000 agents * 5 variables = 50,000 distinct parameters

Agent behaviour

Agent's have goals, needs, etc., so can't be arbitrarily adjusted

Assumptions and parameter types

Maths typically developed for continuous parameters and assume normal distributions

Categorical parameters can be a big problem

... but, at least, some of these problems are shared by climate models

Some DA Methods

Basic idea: estimate the posterior model state

Particle Filter

Create loads of individual model 'particles' run them simultaneously.

Remove those that don't represent the observations well; duplicate those that do

Advantage: very few assumptions (Gaussian distributions etc.)

Kalman Filter

Many flavours: Ensemble, Unscented, ...

Maintain a smaller ensemble and update the particles more intelligently

Efficient but has stronger assumptions (although they might work OK anyway...)

4DVar

This is popular in meteorology but I don't know anything about it...

Case study 1:

Real Time Crowd Modelling

We can track individuals (anonymously?) as they move through busy public spaces

We can simulate crowds quite well, but our simulated crowd will inevitably diverge from the real one

Scenario: can we use data assimmilathion to update our crowd model in response to real-time data?

Lots of potential applications for crowd management etc.

Attempt 1: Particle Filter

Particle Filter & Categorical Parameters

Filtering makes it worse!

(video)

Solution 1

Categorical-Noise PF Step

Solution 1

Categorical-Noise PF Step

Solution 2: Use an EnKF

More complicated, and has stronger assuptions, but can update the model state (including categorical parameters) directly

\( \hat{X} = X + K \left( D - H X \right) \)

Current state estimate (\(X\)) updated with new information (\(\hat{X}\))

\(K\) (Kalman gain) balances importance of new data (\(D\)) v.s. current prediction.

\(H X\): prediction transformed into the same space as the observed data (e.g. arrregate observations and individual agents)

Pedestrian simulation: EnKF Results

Conclusions

Real Time Crowd Modelling

Particle filter struggled (so many agents with so many destination choices)

But there is an opportunity to develop more neuanced filters

EnKF performed very well

Next steps: scale up to larger/more complicated crowds and use a more advanced crowd model.

Case Study 2:

International Policy Diffusion

ABM simulates COVID-19 policy diffusion via peer mimicry

Particle filter enhances prediction accuracy with real-time data.

Frequent filtering improves results.

Y. Oswald, N. Malleson and K. Suchak (2024). An Agent-Based Model of the 2020 International Policy Diffusion in Response to the COVID-19 Pandemic with Particle Filter. Journal of Artificial Societies and Social Simulation 27(2) 3. DOI: 10.18564/jasss.5342

International Policy Diffusion

Global challenges hinge on international coordination of policy

COVID-19 lockdown: compelling example of almost unanimous global response

Aim: Develop a parsimonious ABM to explore mechanisms of international lockdown diffusion and improve prediction accuracy through data assimilation.

Methods

Agent-Based Model (ABM)

Agents: countries, with binary lockdown states ("lockdown" or "not in lockdown").

Behaviour: Peer mimicry based on similarity (income, democracy index, geography).

Secondary mechanism: Autonomous lockdown adoption based on internal thresholds (e.g., population density).

Calibration

Based on real-world lockdown data (March 2020) and parameters like social thresholds, peer group size, and adoption probabilities.

Data assimilation with a particle filter

Updates model predictions in real time using observed data (e.g., lockdown status of countries).

Improves model alignment with real-world dynamics by filtering poorly performing simulations.

Results

After calibration, base model performance is adequate, but exhibits large variance, especially during 'critical' phase (when most countries are going in to lockdown).

Macro performance better than macro performance

An accurate lockdown percentage doesn't mean the right countries are in lockdown

Particle filter narrows confidence intervals and reduces MSE by up to 75%; up to 40% in the critical phase

Performance during the critical few days is crucial if the model is going to be useful

Conclusions

International Policy Diffusion

Proof-of-concept: social / political A-B diffusion models can be combined with data assimilation.

Particle filter improves lockdown predictions, particularly in the 'critical phase'

But the model still incorrectly predicts many countries

Undoubtedly need a more nuanced model to improve predictions further (beyond peer mimicry).

Case Study 3

Wealth Diffusion with an EnKF

Significant wealth inequality in the U.S.

The top 1% hold ~35% of wealth, while the bottom 50% hold almost none.

(Near) real-time predictions are essential, particularly during crises

Paper explores the integration of ABMs with data assimilation to improve prediction accuracy.

Wealth Diffusion: Context

Methods (i)

Wealth Diffusion with an EnKF

Developed two agent-based models of U.S. wealth distribution:

Model 1:

Adapted from literature, focused on wealth accumulation through proportional allocation of growth.

Agents' wealth grows as a function of their initial wealth, reflecting the compounding effect of wealth.

Limited agent interaction; growth is largely independent of network effects.

Model 2:

Developed from scratch, includes network-based agent interactions and adaptive behaviours (more akin to a 'true' ABM)

Methods (ii)

Wealth Diffusion with an EnKF

Integrated the ABMs with an Ensemble Kalman Filter (EnKF):

EnKF adjusted agent-specific variables (e.g., wealth per agent) dynamically to match observed data.

Calibrated to U.S. wealth data (1990–2022) and tested them against real-time wealth estimates.

Results

EnKF improved model accuracy significantly (20–50% error reduction).

Corrected disparities in predicted wealth shares for different economic groups (observe the jagged lines).

Filter still exhibited some unexpected behaviour

Conclusions

Wealth Diffusion with an EnKF

We show that a marco-economic ABM can be optimised with an EnKF

Improved short-term predictions, especially during a crisis

Essential during crises; models cannot include everything

Additional opportunity for improved understanding

E.g. through examining evolution of the Kalman Gain matrix and contrasting the observation v.s. model weights -- which become more or less certain over time?

Summary and Challenges

This talk has outlined some of the opportunities offered by DA for improving empirical ABMs

Case studies: crowding; international policy response; wealth dynamics

Computational complexity

Examples here use models that are parsimonious. Will it be possible with more complex models, e.g. those use to to build city digital twins??

Methodological

Non-trivial to adapt meteorological methods, e.g. handling categorical parameters

Data

Availability of high-quality, high-resolution data

Privacy & ethical issues