Nina Schmid - Universal differential equations for epidemiology: Current state and open problems
On Wednesday March 4th, Nina Schmid will discuss universal differential equations for epidemiology.
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.
Nina Schmid is a PhD candidate at the LIMES Institute, University of Bonn, working in Prof. Hasenauer’s group. She studied mathematics (M.Sc.) at the Technical University of Munich with a focus on statistics and machine learning. Her main interests lie in hybrid modelling approaches to combine the benefits of mechanistic modelling and deep learning.
A recording of this talk will be posted to our YouTube channel and asynchronous discussion will be possible on our community site. You can also ask questions ahead of time and asynchronously there.
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