In the context of complex biological applications, numerical simulations suffer from the extremely high computational demand request for high-fidelity (and accurate) methods in multi-query regimes, e.g. when tackling optimal control, inverse and uncertainty quantification problems. In this talk, we will present some recent contributions regarding high-performance surrogate models, specifically designed to mitigate the bottlenecks of data scarcity and epistemic noise.

We first discuss the formalization of Kernel Operator Learning (KOL) schemes within mathematical epidemiology. We demonstrate their efficacy in retrieving reliable scenario analyses for non-pharmaceutical interventions and solving optimal control problems to determine minimum eradication times [1]. Furthermore, we present a hybrid end-to-end framework designed to infer transmission dynamics conditioned on exogenous parameters. This model’s robustness is validated in the influenza testcase in Italy [2].

The second part of the talk focuses on operator learning techniques in cardiac electrophysiology. We evaluate the performance of KOL and Fourier Neural Operators (FNOs) (adapted for unstructured domains) in reconstructing activation and repolarization maps, providing a computationally efficient tool for simulating clinical ablation procedures in patients with ectopic arrhythmias [3]. Finally, we tackle the inverse problem in electrophysiology, aimed at detecting ischemic regions from ECG signals by leveraging Latent Dynamics networks for approximating the forward problem.

[1] Ziarelli, G., Parolini, N., Verani, M. (2025). Learning epidemic trajectories through Kernel Operator Learning: from modelling to optimal control. Numerical Mathematics: Theory, Methods and Applications, 18, 2:pp. 285–324
[2] Ziarelli, G., Pagani, S., Parolini, N., Regazzoni, F., Verani, M. (2025). A model learning framework for inferring the dynamics of transmission rate depending on exogenous variables for epidemic forecasts. Computer Methods in Applied Mechanics and Engineering, 437, 117796
[3] Ziarelli, G., Centofanti, E., Parolini, N., Scacchi, S., Verani, M., Pavarino, L. F. (2025). Learning cardiac activation and repolarization times with operator learning. PLOS Computational Biology, 22(1), e1013920


Contatto:
andrea1.manzoni@polimi.it