Parameter Estimation in the Age of Degeneracy and Unidentifiability

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.

Effects of Drugs Reabsorption Time Delays for a Pharmacokinetics Model in Humans

A three-compartmental delay model is formulated to describe the pharmacokinetics of drugs subjected to both intravenous and oral doses with reabsorptions by the central compartment. Model dynamics are analyzed rigorously, and two equilibrium points are obtained to be locally asymptotically stable under certain conditions. Time delays used as lags in reabsorption of drugs by central compartment from other two compartments caused rebounds or peaks and fluctuations in the time profiles for amounts of drug in all the compartments. Sensitivity analysis revealed that elimination rates decrease the amounts in all compartments. Furthermore, reabsorption rates cause superimposition at the initial phases of the drug amount profiles; subsequently, the quantities decrease in compartment one and increase in compartments two and three, respectively.

An idealized 1½-layer isentropic model with convection and precipitation for satellite data assimilation research. Part I: model dynamics

An isentropic 1½-layer model based on modified shallow water equations is presented, including terms mimicking convection and precipitation. This model is an updated version of the isopycnal single-layer modified shallow water model presented in Kent et al. (2017). The clearer link between fluid temperature and model variables together with a double-layer structure make this revised, isentropic model a more suitable tool to achieve our future goal: to conduct idealized experiments for investigating satellite data assimilation. The numerical model implementation is verified against an analytical solution for stationary waves in a rotating fluid, based on Shrira’s methodology for the isopycnal case. Recovery of the equivalent isopycnal model is also verified, both analytically and numerically. With convection and precipitation added, we show how complex model dynamics can be achieved exploiting rotation and relaxation to a meridional jet in a periodic domain. This solution represents a useful reference simulation or “truth” in conducting future (satellite) data-assimilation experiments, with additional atmospheric conditions and data. A formal analytical derivation of the isentropic 1½-layer model from an isentropic 2-layer model without convection and precipitation is shown in a companion paper (Part II).

Parameter Learning and Change Detection Using a Particle Filter with Accelerated Adaptation

This paper presents the construction of a particle filter, which incorporates elements inspired by genetic algorithms, in order to achieve accelerated adaptation of the estimated posterior distribution to changes in model parameters. Specifically, the filter is designed for the situation where the subsequent data in online sequential filtering does not match the model posterior filtered based on data up to a current point in time. The examples considered encompass parameter regime shifts and stochastic volatility. The filter adapts to regime shifts extremely rapidly and delivers a clear heuristic for distinguishing between regime shifts and stochastic volatility, even though the model dynamics assumed by the filter exhibit neither of those features.

Minimizing IL-6 and IL-10 signalling pathway elements using lumping species and parameters

There are many cell signalling pathways that include a higher set of elements. Understanding the dynamics of such systems becomes a difficult issue in systems biology. Mathematical approaches with computational simulations provide a wide range to simplify such complex models and to predicate their dynamics. A powerful technique for reducing the complexity of cell signalling pathways is lumping variables and parameters. In this work, we suggest this technique to reduce the number of elements of IL-6 and IL-10 signalling pathways. The reduced model given in this work provides one a better understanding and predicting some model dynamics, and gives accurate approximate solutions. Computational results show that there is a good agreement between the model dynamics for the original and the simplified models.

Robust output regulation of the linearized Boussinesq equations with boundary control and observation

We study a temperature and velocity output tracking problem for a two-dimensional room model with the fluid dynamics governed by the linearized translated Boussinesq equations. Additionally, the room model includes finite-dimensional models for actuation and sensing dynamics; thus, the complete model dynamics are governed by an ODE–PDE–ODE cascade. As the main contribution, we design a low-dimensional internal model-based controller for robust output tracking of the room model. The controller’s performance is demonstrated through a numerical example.

Correction of the model dynamics for the Northern seas using observational altimetry data

The earlier derived data assimilation method called Generalized Kalman filter (GKF) is applied in conjunction with the Nucleus for European Modelling of the Ocean (NEMO) circulation model to the calculation of the dynamics in the North Seas of Russia. By assimilating the satellite altimetry data from archive AVISO (Archiving, validating and interpolating of satellite observations) this method corrects the direct model calculations and improves the ocean state. The model fields, in particular, sea level and sea surface temperature with and without assimilation are constructed and compared with each other. The brief analysis of the results is also performed.

The Dynamic Business Model Framework—Illustrated with Renewable Energy Company Cases from Indonesia

It is important for companies to be able to make their business models dynamic. This enables them to adapt to changing circumstances and remain viable. The aim of this paper is to combine insights from the literature on business models and business model dynamics into a comprehensive dynamic business model framework. The framework that is developed in this paper takes into account various origins of changes in business models (internal or external to the company) and various types of changes in business models (primary or secondary changes and forced changes or strategic choices) and also includes the issue of business model consistency. In order to combine different origins and different types of business model change into one dynamic business model framework, some simplifications of reality were needed. The framework is described in text and shown in a comprehensive picture. The application of the framework to two cases of renewable energy companies in Indonesia shows that the framework is able to capture business model dynamics in a simplified and comprehensive way and that it allows for case study comparison. In a thorough discussion, it is shown how the framework can be adapted to make it better able to represent more complex dynamics.

Exploring the uncertainties in the aviation soot–cirrus effect

A global aerosol–climate model, including a two-moment cloud microphysical scheme and a parametrization for aerosol-induced ice formation in cirrus clouds, is applied in order to quantify the impact of aviation soot on natural cirrus clouds. Several sensitivity experiments are performed to assess the uncertainties in this effect related to (i) the assumptions on the ice nucleation abilities of aviation soot, (ii) the representation of vertical updrafts in the model, and (iii) the use of reanalysis data to relax the model dynamics (the so-called nudging technique). Based on the results of the model simulations, a radiative forcing from the aviation soot–cirrus effect in the range of −35 to 13 mW m−2 is quantified, depending on the assumed critical saturation ratio for ice nucleation and active fraction of aviation soot but with a confidence level below 95 % in several cases. Simple idealized experiments with prescribed vertical velocities further show that the uncertainties on this aspect of the model dynamics are critical for the investigated effect and could potentially add a factor of about 2 of further uncertainty to the model estimates of the resulting radiative forcing. The use of the nudging technique to relax model dynamics is proved essential in order to identify a statistically significant signal from the model internal variability, while simulations performed in free-running mode and with prescribed sea-surface temperatures and sea-ice concentrations are shown to be unable to provide robust estimates of the investigated effect. A comparison with analogous model studies on the aviation soot–cirrus effect show a very large model diversity, with a conspicuous lack of consensus across the various estimates, which points to the need for more in-depth analyses on the roots of such discrepancies.