Embedded model discrepancy: A case study of Zika modeling

Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of these simplifications, the model output, of say new cases of a disease over time, or when an epidemic will occur, may be inconsistent with available data. In this case, we must improve the model, especially if we plan to make decisions based on it that could affect human health and safety, but direct improvements are often beyond our reach. In this work, we explore this problem through a case study of the Zika outbreak in Brazil in 2016. We propose an embedded discrepancy operator---a modification to the model equations that requires modest information about the system and is calibrated by all relevant data. We show that the new enriched model demonstrates greatly increased consistency with real data. Moreover, the method is general enough to easily apply to many other mathematical models in epidemiology.Comment: 9 pages, 7 figure

Problemas inversos para identificação de parâmetros em sistemas dinâmicos

International audienc

A data-driven approach for inference of the evolution equation of a Duffing oscillator

International audienceAs more and more data is available on a daily basis, it is natural to seek to infer relevant information embedded in these datasets. In the context of dynamical systems, this idea translates into the use of observations (data) to infer the evolution law. I this sense, machine learning techniques are getting more space in the analysis and synthesis of dynamical systems. This paper uses regularized data-driven regression algorithm to infer the evolution law of a Duffing oscillator, using a library of mathematical functions obtained from a dataset generated from the underlying physical system

Sensitivity Analysis in Zika Virus Dynamics and a Model Discrepancy Approach

International audienc

Ressonância Estocástica em Sistemas Dinâmicos Não Lineares: aplicações a coletores de energia

International audienc

Application of a stochastic version of the restoring force surface method to identify a Duffing oscillator

International audienceThis work deals with the identification of stochastic parameters in a nonlinear single degree-of-freedom system. For this purpose, a stochastic version of the restoring force surface method is proposed and used to identify the parameters of a clamped-free beam, with nonlinear effects induced by the presence of a magnet near to the free extremity. This system recalls a Duffing oscillator, which is used as mechanical-mathematical model. In order to validate the obtained stochastic model, experimental and theoretical responses are compared in time and frequency domains, taking into account a probabilistic band of confidence. The results show that obtained stochastic model adequately predict the beam's vibration responses, which ensure the robustness of identification of a stochastic model

On the classical and fractional control of a nonlinear inverted cart-pendulum system: a comparative analysis

International audienceFractional-order control is based on the fractional calculus and its use is being explored for many researchers in order to improve the performance of control systems. In this paper, fractional integrators are employed in a state-feedback controller and applied to an inverted cart-pendulum system. Faster transient responses and increased (local) attraction domains are achieved when compared to the integer integrator based implementation of the proposed control law

Cross-entropy Method In Structural Optimization with Dynamic Constraints

International audienc

Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling

An inverse problem via cross-entropy method for calibration of a drill string torsional dynamic model

International audienceModel selection and parameter identification are challenging tasks in drill string dynamics due to the high degree of nonlinearity that abound the diverse and complex mechanisms involved. This work explores the application of a stochastic metaheuristic procedure for parameter identification over the torsional mode of drill string vibration. A proposed model is calibrated with data from a validated experimental setup , adjusting stiffness, damping and friction parameters. The resulting simulations display a reasonable fit with almost ideal correlation coefficients even in the presence of stick-slip. The optimization strategy is compared with an Genetic Algorithm, revealing significantly greater efficiency and showcasing how the cross-entropy method may be a viable tool in the demanding context of drill string modeling