Computational Methods for Inverse Uncertainty Propagation

Predictive models are central to many aspects of modern society. They support the development of new drugs, help stabilise power grids, and inform political and economic decision-making. Weather forecasts guide agricultural planning, while insurance companies rely on models to assess the risk of natural disasters.

However, such models often depend on parameters that are not directly known. Estimating these parameters from experimental data is therefore a key challenge and typically involves solving an inverse problem—inferring model inputs from observed outputs. This task becomes significantly more difficult when the data are heterogeneous, meaning that repeated experiments under similar conditions yield different results. This is common in biology: for example, individual cells can behave differently due to inherent variability, even in controlled environments.

This project addresses this challenge by developing new mathematical and computational methods for parameter estimation in the presence of heterogeneity. Rather than treating variability solely as measurement error, we explicitly model parameters as distributed quantities. In this view, differences in observations arise not only from noise but also from genuine variability in the underlying system. This leads to a class of problems known as stochastic inverse problems (SIPs), where the goal is to infer a distribution of parameters that, when passed through the model, reproduces the observed distribution of data. 

Despite their potential, existing SIP frameworks are often too restrictive for applications in systems biology. At the same time, advances in experimental techniques increasingly allow researchers to observe variability at the level of individual cells, creating a growing demand for methods that can fully exploit such data. 

To address this gap, this project develops new theoretical and computational approaches to extend the scope of SIPs. In particular, we focus on two key challenges: handling incomplete or partially observed data, and accounting for measurement noise or even inherently non-deterministic models. Our approaches draw on tools from measure theory, continuous optimisation, numerical linear algebra, and differential geometry, combined with algorithmic ideas from computer science.

Overall, this work aims to enable the integration of heterogeneous data into predictive models, providing more accurate and informative representations of complex biological systems.