Related papers: Space-filling design for nonlinear models

Computational models are powerful tools for understanding human cognition and behavior. They let us express our theories clearly and precisely, and offer predictions that can be subtle and often counter-intuitive. However, this same…

This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…

Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…

While optimal input design for linear systems has been well-established, no systematic approach exists for nonlinear systems where robustness to extrapolation/interpolation errors is prioritized over minimizing estimated parameter variance.…

Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…

The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this paper, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are…

Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…

The aim of this research is to introduce a novel structural design process that allows architects and engineers to extend their typical design space horizon and thereby promoting the idea of creativity in structural design. The theoretical…

Simulation design is the choice of locations in parameter space at which simulations are to be run and is the first step in building an emulator capable of quickly providing estimates of simulation results for arbitrary locations in the…

Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…

Computer experiments are often performed to allow modeling of a response surface of a physical experiment that can be too costly or difficult to run except using a simulator. Running the experiment over a dense grid can be prohibitively…

Copula modelling has in the past decade become a standard tool in many areas of applied statistics. However, a largely neglected aspect concerns the design of related experiments. Particularly the issue of whether the estimation of copula…

We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act…

Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…

Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…

Empirical research plays a fundamental role in the machine learning domain. At the heart of impactful empirical research lies the development of clear research hypotheses, which then shape the design of experiments. The execution of…