MATRIX Research Program: From Agent Based Models to Nonlinear PDEs in Life and Social Sciences

Mathematical models have become an important tool to understand and predict complex phenomena in the life and social sciences. Applied mathematics is an integral part of model development and analysis. However, various approaches have been developed within communities that focus on different aspects of model development, analysis and calibration. The proposed workshop will bring together applied mathematicians working on mathematical modelling, analysis and simulations. It aims at advancing different methodological approaches and connecting them with available data. Among other challenges, we will focus on the connection between agent-based models and their respective continuum models, which arise in suitable scaling limits. We will be particularly interested in developing continuum approaches, which preserve important microscopic properties of the underlying microscopic system such as entropy decay. Another focus will lie on model calibration and the quantification of uncertainty in parameter estimates.

During our stay at the Matrix Institute we will bring together leading experts and junior researchers with strong interests in PDEs, models for collective dynamics and many-agent systems. The proposed program will pursue the following scientific goals

1. Present new models and methods in IBMs defining interactions between minimal entities in life and social sciences.
2. Reconciling IBMs and continuum models by means of suitable scaling regimes and convergence analysis.
3. Connect mathematical models with available data.

Mathematical modelling with differential equations is becoming a crucial technique in modern research in developmental biology or epidemiology, for instance. Parameter estimation and model selection are fundamental challenges with impact in real-world applications in the life and social sciences. The cross-pollination of different communities working towards the goal of understanding the rigorous upscaling of microscopic models to macroscopic models and their use in real-life applications is therefore the main aim of our research program.

Organisers:

This MATRIX Research Program is partially supported by AMSI and AustMS through the AMSI-AustMS Workshop Funding program, and benefits from the SMRI International Visitor Program.

Registration:

• Deadline: 7 December 2025
• Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
• Arrival date: 5 July 2026

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ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 7 July 2026
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.