Massimiliano Ferronato

Institute of Mathematics of the Czech Academy of Sciences

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of governing parameters, and data errors challenge the reliability of predictions. In the absence of direct measurements, inverse modeling and stochastic data assimilation methods can offer reliable solutions, but in complex and large‐scale settings, the computational expense can become prohibitive. To address these challenges, this paper presents a deep learning‐based surrogate model (SurMoDeL) designed for seismic data assimilation in fault activation modeling. The surrogate model leverages neural networks to provide simplified yet accurate representations of complex geophysical systems, enabling faster simulations and analyses essential for uncertainty quantification. The work proposes two different methods to integrate an understanding of fault behavior into the model, thereby enhancing the accuracy of its predictions. The application of the proxy model to integrate seismic data through effective data assimilation techniques efficiently constrains the uncertain parameters, thus bridging the gap between theoretical models and real‐world observations.

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic.