The dynamics of entropy in the COVID-19 outbreaks

With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addition, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modelling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed for describing the evolution of entropy during the COVID-19 pandemic together with the instantaneous reproductive ratio. Then, we introduce and use entropy-based metrics of global transmission to measure the impact and the temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modelled by an equation governing the probability distribution that describes a nonlinear Markov process of a statistically averaged individual, leading to a clear physical interpretation. The time-dependent parameters are formulated by adaptive basis functions, leading to a parsimonious representation. In addition, we provide a full Bayesian inversion scheme for calibration together with a coherent strategy to address data unreliability. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the susceptible–exposed–infected–removed model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 datasets, we discover significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio

Preliminary Validation of a Spectral-Based Stochastic Ground Motion Model with a Non-Parametric Time-Modulating Function

This study presents a site-based parameterized stochastic model for simulation of far-field synthetic ground motions. The model employs a modulated and filtered white-noise process defined via spectral representation. The modulating function is a recently proposed non-parametric function based on a monotonic cubic spline interpolation. As for the time-frequency modulating function, two slightly different versions are explored. The two versions of the model are fitted to a catalog of recorded ground motions and synthetic catalogs are generated using the fitted model parameters. To validate the model, some characteristics of the synthetic catalogs, namely the median, logarithmic standard deviations, and correlations of the elastic response spectra, are compared with those of the recorded catalog. These comparisons show that both versions of the model are able to adequately capture the spectral amplitudes, variability and correlations of recorded ground motions. The addition of a parameter to describe the rate of change of bandwidth with time does not result in any noticeable improvement and is therefore not warranted. Moreover, comparison with synthetic motions generated from the model by Rezaeian and Der Kiureghian (2010) shows that the proposed model results in an improved estimation of the correlations. Further studies are required to identify which feature(s) of our model are behind this improvement.For this study, the second author was sponsored by the Pacific Earthquake Engineering Research Center (PEER) and funded by the California Department of Transportation (Caltrans) and the PEER Transportation Systems Research Program. These supports are gratefully acknowledged

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis

This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade-off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method

Hamiltonian Monte Carlo-Subset Simulation (HMC-SS) methods for structural reliability analysis.

In this study, we carefully analyze the most recent advancements in Hamiltonian Monte Carlo methods combined with Subset Simulation (HMC-SS) in the context of structural reliability analysis. The HMC method employs Hamiltonian dynamic to sample from a target probability distribution. In contrast to the standard Markov-Chain Monte Carlo methods (e.g., Gibbs or Metropolis-Hastings techniques), HMC alleviates the burn-in phase and the random walk behavior to achieve a more effective exploration of the target probability distribution. This turns out to be important in highdimensional spaces (e.g., when the number of random variables is high), where the bulk of probability content concentrates in the so-called typical sets. The structure of the paper is as follows. We first briefly review the Subset Simulation and the general concepts of HMC. Following, in both standard Gaussian and non-Gaussian probability spaces, we present a series of complex structural reliability problems to test in practice the validity of the method. Finally, we conclude with a series of future developments and directions

Induced seismicity risk analysis of the hydraulic stimulation of a geothermal well on Geldinganes, Iceland

The rapid increase in energy demand in the city of Reykjavik has posed the need for an additional supply of deep geothermal energy. The deep-hydraulic (re-)stimulation of well RV-43 on the peninsula of Geldinganes (north of Reykjavik) is an essential component of the plan implemented by Reykjavik Energy to meet this energy target. Hydraulic stimulation is often associated with fluid-induced seismicity, most of which is not felt on the surface but which, in rare cases, can be a nuisance to the population and even damage the nearby building stock. This study presents a first-of-its-kind pre-drilling probabilistic induced seismic hazard and risk analysis for the site of interest. Specifically, we provide probabilistic estimates of peak ground acceleration, European microseismicity intensity, probability of light damage (damage risk), and individual risk. The results of the risk assessment indicate that the individual risk within a radius of 2 km around the injection point is below 0.1 micromorts, and damage risk is below 10−2, for the total duration of the project. However, these results are affected by several orders of magnitude of variability due to the deep uncertainties present at all levels of the analysis, indicating a critical need in updating this risk assessment with in situ data collected during the stimulation. Therefore, it is important to stress that this a priori study represents a baseline model and starting point to be updated and refined after the start of the project