Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

In this paper we introduce a method to estimate a pressure dependent thermal conductivity coefficient arising in a heat diffusion model with applications in food technology. To address the known smoothing effect of the direct problem, we model the uncertainty of the conductivity coefficient as a hierarchical Gaussian Markov random field (GMRF) restricted to uniqueness conditions for the solution of the inverse problem established in Fraguela et al. Furthermore, we propose a Single Variable Exchange Metropolis-Hastings algorithm to sample the corresponding conditional probability distribution of the conductivity coefficient given observations of the temperature. Sensitivity analysis of the direct problem suggests that large integration times are necessary to identify the thermal conductivity coefficient. Numerical evidence indicates that a signal to noise ratio of roughly 1000 suffices to reliably retrieve the thermal conductivity coefficient

On full seismic waveform inversion by descent methods in a lattice

In this work we are concerned with the full waveform inversion problem. The problem is formulated as one of minimizing a nonlinear least squares functional. Assuming Fr\{e}chet differentiability we use the adjoint state approach to compute the gradient. To approximate local minima, we develop a discrete framework for descent methods in a finite difference lattice. We describe the methods of Gradient descent with line search and the positive definite secant update (BFGS) for computation in the lattice. To illustrate the methods numerical solutions of several examples in 1D are presented. In this case we carry out some analysis and provide a simple proof for identifiability of wave speeds using the spread and shrink argument. It is argued that we may build on this work and apply techniques such as regularization or bayesian inference in future investigations

Forecasting hospital demand in metropolitan areas during the current COVID-19 pandemic and estimates of lockdown-induced 2nd waves.

We present a forecasting model aim to predict hospital occupancy in metropolitan areas during the current COVID-19 pandemic. Our SEIRD type model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non-exponential residence times in each latent and infected compartments. Using both hospital admittance confirmed cases and deaths, we infer the contact rate and the initial conditions of the dynamical system, considering breakpoints to model lockdown interventions and the increase in effective population size due to lockdown relaxation. The latter features let us model lockdown-induced 2nd waves. Our Bayesian approach allows us to produce timely probabilistic forecasts of hospital demand. We have applied the model to analyze more than 70 metropolitan areas and 32 states in Mexico