Parameter estimation using multiparametric programming for implicit Euler’s method based discretization

Parameter estimation by implicit sampling

Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use implicit sampling in parameter estimation problems, where the goal is to find parameters of a numerical model, e.g. a partial differential equation (PDE), such tha...

Determination of Optimal ValveTiming for Internal Combustion Engines Using Parameter Estimation Method

Unsupervised Discretization Using Tree-Based Density Estimation

This paper presents an unsupervised discretization method that performs density estimation for univariate data. The subintervals that the discretization produces can be used as the bins of a histogram. Histograms are a very simple and broadly understood means for displaying data, and our method automatically adapts bin widths to the data. It uses the log-likelihood as the scoring function to se...

Estimation of Discretization Errors using the Method of Nearby Problems

The Method of Nearby Problems (MNP) is developed as an approach for estimating numerical errors due to insufficient mesh resolution. A key aspect of this approach is the generation of accurate, analytic curve fits to an underlying numerical solution. Accurate fits are demonstrated using fifth-order Hermite splines that provide for solution continuity up to the third derivative, which is recomme...

A Novel Discretization for Parameter Learning in Bayesian Network using Dynamic Programming

In AI and machine learning techniques such as decision trees and Bayesian networks, there is a growing need for converting continuous data into discrete form. Several approaches are available for discretization, however finding an appropriate and efficient discretization method is a challenging task. In this paper, we present an impurity based dynamic multi-interval discretization approach for ...