Model Selection by Balanced Identification: the Interplay of Optimization and Distributed Computing

AbstractThe technology of formal quantitative estimation of the conformity of mathematical models to the available dataset is presented. The main purpose of the technology is to make the model selection decision-making process easier for the researcher. The method is a combination of approaches from the areas of data analysis, optimization and distributed computing including: cross-validation and regularization methods, algebraic modeling in optimization and methods of optimization, automatic discretization of differential and integral equations, and optimization REST-services. The technology is illustrated by a demo case study. A general mathematical formulation of the method is presented. It is followed by a description of the main aspects of algorithmic and software implementation. The list of success stories of the presented approach is substantial. Nevertheless, the domain of applicability and important unresolved issues are discussed.

Download Full-text

Simultaneous Joint Inversion of Gravity and Self-Potential Data Measured Along Profile: Theory, Numerical Examples, and a Case Study From Mineral Exploration With Cross Validation From Electromagnetic Data

IEEE Transactions on Geoscience and Remote Sensing ◽

10.1109/tgrs.2021.3071973 ◽

2021 ◽

pp. 1-20

Author(s):

Salah A. Mehanee

Keyword(s):

Cross Validation ◽

Joint Inversion ◽

Mineral Exploration ◽

Numerical Examples ◽

Electromagnetic Data ◽

Self Potential

Download Full-text

Computational Modeling of Music Cognition: A Case Study on Model Selection

Music Perception An Interdisciplinary Journal ◽

10.1525/mp.2006.23.5.365 ◽

2006 ◽

Vol 23 (5) ◽

pp. 365-376 ◽

Cited By ~ 21

Author(s):

Henkjan Honing

Keyword(s):

Model Selection ◽

Strong Evidence ◽

Goodness Of Fit ◽

Computational Models ◽

Recent Literature ◽

Music Cognition ◽

Kinematic Model ◽

Music Performance ◽

Limited Range

While the most common way of evaluating a computational model is to see whether it shows a good fit with the empirical data, recent literature on theory testing and model selection criticizes the assumption that this is actually strong evidence for the validity of a model. This article presents a case study from music cognition (modeling the ritardandi in music performance) and compares two families of computational models (kinematic and perceptual) using three different model selection criteria: goodness-of-fit, model simplicity, and the degree of surprise in the predictions. In the light of what counts as strong evidence for a model’s validity—namely that it makes limited range, nonsmooth, and relatively surprising predictions—the perception-based model is preferred over the kinematic model.

Download Full-text

The Use of Photogrammetry in Piping Design

Proceedings of the Institution of Mechanical Engineers Part A Power and Process Engineering ◽

10.1243/pime_proc_1983_197_014_02 ◽

1983 ◽

Vol 197 (2) ◽

pp. 125-138 ◽

Cited By ~ 1

Author(s):

P A Bracewell ◽

U R Klement

Keyword(s):

Information Retrieval ◽

Mathematical Formulation ◽

Three Dimensional ◽

Cost Effective ◽

Process Industry ◽

Process Plant ◽

Definition Of ◽

High Degree ◽

Positional Data

Piping design for ‘revamp’ projects in the process industry requires the retrieval of large amounts of ‘as-built’ data from existing process plant installations. Positional data with a high degree of accuracy are required. Photogrammetry, the science of measurement from photographs, was identified in Imperial Chemical Industries plc (ICI) as a suitable tool for information retrieval. The mathematical formulation enabling the definition of three-dimensional positions from photographic information is described. The process of using ICI's photogrammetric system for the definition of complete objects such as structures and pipes is illustrated. The need for specialized photogrammetric software for design purposes is explained. A case study describing how the photogrammetric system has been applied is described and graphical outputs from this exercise are shown. It is concluded that this particular photogrammetric system has proved to be a cost effective and accurate tool for the retrieval of ‘as-built’ information.

Download Full-text

Assessment of Mineral Potential Using Cross-Validation Techniques and Statistical Analysis: A Case Study from the Paleoproterozoic of West Greenland

Economic Geology ◽

10.2113/gsecongeo.101.7.1397 ◽

2006 ◽

Vol 101 (7) ◽

pp. 1397-1413 ◽

Cited By ~ 11

Author(s):

B. M. Stensgaard ◽

C.-J. Chung ◽

T. M. Rasmussen ◽

H. Stendal

Keyword(s):

Statistical Analysis ◽

Cross Validation ◽

West Greenland ◽

Mineral Potential

Download Full-text

Topology, Shape, and Size Optimization of Additively Manufactured Lattice Structures Based on the Superformula

Volume 2A: 44th Design Automation Conference ◽

10.1115/detc2018-86191 ◽

2018 ◽

Cited By ~ 2

Author(s):

Andrea Nessi ◽

Tino Stanković

Keyword(s):

Lattice Structure ◽

Lightweight Design ◽

Mathematical Formulation ◽

Lattice Structures ◽

Structural Synthesis ◽

Normal Surface ◽

Technical Problems ◽

Wide Range ◽

Tetrahedral Meshing

This paper investigates the application of Superformula for structural synthesis. The focus is set on the lightweight design of parts that can be realized using discrete lattice structures. While the design domain will be obtained using the Superformula, a tetrahedral meshing technique will be applied to this domain to generate the topology of the lattice structure. The motivation for this investigation stems from the property of the Superformula to easily represent complex biological shapes, which opens a possibility to directly link a structural synthesis to a biomimetic design. Currently, numerous results are being reported showing the development of a wide range of design methods and tools that first study and then utilize the solutions and principles from the nature to solve technical problems. However, none of these methods and tools quantitatively utilizes these principles in the form of nature inspired shapes that can be controlled parametrically. The motivation for this work is also in part due to the mathematical formulation of the Superformula as a generalization of a superellipse, which, in contrast to the normal surface modeling offers a very compact and easy way to handle set of rich shape variants with promising applications in structural synthesis. The structural synthesis approach is organized as a volume minimization using Simulated Annealing (SA) to search over the topology and shape of the lattice structure. The fitness of each of candidate solutions generated by SA is determined based on the outcome of lattice member sizing for which an Interior Point based method is applied. The approach is validated with a case study involving inline skate wheel spokes.

Download Full-text