Wednesday 4th of March. Async questions here.
Universal Differential Equations (UDEs) augment mechanistic differential-equation models with neural networks to represent unknown processes, balancing structural interpretability with data-adaptive dynamics. However, UDEs face challenges in efficient and reliable training due to stiff dynamics and noisy, sparse data, as well as in ensuring the interpretability of the mechanistic model parameters. We investigate these challenges and evaluate UDE performance on biologically motivated benchmarks. Our results demonstrate the versatility of UDEs and show that optimisation stability and parameter interpretability are improved by combining key aspects of each methodological field, such as regularisation, multi-start methods, and hyperparameter optimisation. In the second part, we build on these results and develop a UDE framework for wastewater-based epidemiology, where translating viral-load measurements into actionable insights remains challenging. We formulate a susceptible-exposed-infectious-recovered (SEIR) UDE to link wastewater viral loads to case counts while learning time-varying parameters via neural networks, enabling non-stationary drivers to be captured without abandoning epidemiological constraints. We assess the method using newly collected SARS-CoV-2 data for Bonn, Germany, as well as published data for five cities in Rhineland-Palatinate, Germany. The proposed approach produces realistic, city-specific out-of-sample projections over a test horizon of up to 50 weeks. Accordingly, it facilitates scalable interpretation and exploitation of wastewater data for monitoring infectious diseases.
We will also introduce new co-organisers at this week’s talk.