Deep learning-based estimation of time-dependent parameters in Markov models with application to nonlinear regression and SDEs

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network-derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.

On automatic calibration of the SIRD epidemiological model for COVID-19 data in Poland

We propose a novel methodology for estimating the epidemiological parameters of a modified SIRD model (acronym of Susceptible, Infected, Recovered and Deceased individuals) and perform a short-term forecast of SARS-CoV-2 virus spread. We mainly focus on forecasting number of deceased. The procedure was tested on reported data for Poland. For some short-time intervals we performed numerical test investigating stability of parameter estimates in the proposed approach. Numerical experiments confirm the effectiveness of short-term forecasts (up to 2 weeks) and stability of the method. To improve their performance (i.e. computation time) GPU architecture was used in computations.