The objective of this paperwork is the development of a crystal lattice parameter identification algorithm, which allows obtaining a more accurate solution compared to the Bravais unit cell estimation algorithm. To achieve the objective, we suggest solving the parameter identification problem using the steepest descent gradient method. The study of the parameter identification accuracy was cond...

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g. through a measurement, by connecting it to Bayes’s theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a descript...

The paper is devoted to the parameter identification of the axial dispersion model in the closed–open canal. It is oriented to the identification precision for the two variants of the flow model with various variance levels. The identification method is based on the transfer function application for the solution of given model PDE. When the impulse function g(t) is obtained, the characteristics...

For many inverse problems which arise in contributing to real-world decision-making, such as formulating policy objectives for freshwater fish health, only an indicative understanding of the global structure of the solution is all that is required for the associated decision-support. Examples include: (i) Situations where only some linear functional of the solution is required. As noted in vari...

This work studies the parameter identification problem for the Markov chain choice model of Blanchet, Gallego, and Goyal used in assortment planning. In this model, the product selected by a customer is determined by a Markov chain over the products, where the products in the offered assortment are absorbing states. The underlying parameters of the model were previously shown to be identifiable...

Many physical systems can be adequately modelled using a second order approximation. The problem of plant identification reduces to the problem of estimating the position of a single pair of complex conjugate poles. One approach to the problem is to apply the method of least squares to the time domain data. This type of computation is best carried out in "batch" mode and applies to an entire da...

Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...

Many physical systems exhibiting nonlinear spatiotemporal dynamics can be modeled by partial differential equations. Although information about the physical properties for many of these systems is available, normally not all dynamical parameters are known and, therefore, have to be estimated from experimental data. We analyze two prominent approaches to solve this problem and describe advantage...

-One-dimensional cable theory provides the theoretical framework to evaluate the role of linear electrical membrane properties and dendritic geometry in neuronal signal reception and processing. This article presents the basic physical principles as well as mathematical problems arising in neuronal modelling. The main types of passive dendritic neuron models are reviewed and their use in explor...

Understanding the constitutive behavior of the human brain is critical to interpret the physical environment during neurodevelopment, neurosurgery, and neurodegeneration. A wide variety of constitutive models has been proposed to characterize the brain at different temporal and spatial scales. Yet, their model parameters are typically calibrated with a single loading mode and fail to predict th...