Multidimensional Hyper-Reduction of Large Mechanical Models Involving Internal Variables

2012 ◽  
Author(s):  
David Ryckelynck
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
A Priori ◽  
Functional Space ◽  
Weak Form ◽  
Point Of View ◽  
Internal Variables ◽  
Equilibrium Equations ◽  
Mechanical Models ◽  
Reduced Integration Domain

We propose to incorporate a Response Surface (RS) approximation of variables over a parametric domain into a weak form of parametric Partial Differential Equations (PDEs). Hence a multidimensional model-reduction can be achieved. We propose a multidimensional a priori model reduction method to generate or to enrich RSs. It is coined multidimensional because the fields to forecast are defined over an augmented domain in term of dimension. They are functions of both space variables and parameters that simultaneously evolve in time. This changes the functional space related to the weak form of the PDEs and the definition of the reduced bases. It has a significant impact on the proposed model reduction method. In particular, a new point of view on interpolation of variables has to be addressed. A Multidimensional Reduced Integration Domain (MRID) is proposed to reduce the complexity of the reduced formulation. A multidimensional Hyper-Reduction method extract from the MRID truncated equilibrium equations, truncated residuals and a truncated error indicator.

scholarly journals Incorrect Simulation Results in OpenModelica

2020 ◽  
pp. 43-51
Author(s):  
V. A. Ovchinnikov ◽  
V. A. Trudonoshin ◽  
V. G. Fedoruk
Keyword(s):  
Mathematical Modelling ◽  
A Priori ◽  
Point Of View ◽  
Correct Result ◽  
Simple Test ◽  
Equilibrium Equations ◽  
Technical Object ◽  
Simulation Results ◽  
Inexperienced User ◽  
Object Dynamics

An adequacy of mathematical modelling of the technical object dynamics is always a challenge, and a user can make up his mind about the modelling package using simple test schemes. The article presents the schemes that are quite common from the point of view of an inexperienced user, but have specifics in mathematical modelling. The features of the schemes are that therein failures of equilibrium equations (such as the first Kirchhoff law) and continuity (such as the second Kirchhoff law) can occur. These features can lead to incorrect results when using the OpenModelica package, while the domestic PA9 and PRADIS packages used in modelling these schemes give the correct result. The article presents two simple schemes, the simulation result of which can be a priori estimated, and provides simulation results for three packages - OpenModelica, PA9, and PRADIS.

scholarly journals Cross-Gramian-based dominant subspaces

2019 ◽  
Vol 45 (5-6) ◽  
pp. 2533-2553 ◽  
Author(s):  
Peter Benner ◽  
Christian Himpe
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
A Priori ◽  
Balanced Truncation ◽  
Efficient Computation ◽  
Projection Model ◽  
Numerical Examples ◽  
Error Indicator ◽  
System Properties ◽  
Controllability And Observability

AbstractA standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work, we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

A Fatal Error of Locke’s?

2017 ◽  
Author(s):  
Galen Strawson
Keyword(s):  
Personal Identity ◽  
John Locke ◽  
A Priori ◽  
Point Of View ◽  
Radical Theory ◽  
Single Person

This chapter argues that the unqualified attribution of the radical theory to John Locke is mistaken if we are to take into account the fact that the theory allows for freaks like [Sₓ]. It first considers [I]-transfer without [P]-transfer—that is, [I]-transfer preserving personal identity—before discussing Locke's response to the idea that personal identity might survive [I]-transfer from an a priori point of view. It suggests that [I]-transfer is possible in such a way that the existence of a single Person [P₁] from t₁ to t₂ can successively (and non-overlappingly) involve the existence of two immaterial substances. It also explains how Locke's claim that [I]-transfer is possible opens up the possibility that it could go wrong, in such a way as to lead to injustice. Finally, it examines Locke's notion of “sensible creature,” which refers to a subject of experience who is a person.

scholarly journals Iterative Variable Selection for High-Dimensional Data: Prediction of Pathological Response in Triple-Negative Breast Cancer

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 222
Author(s):  
Juan C. Laria ◽  
M. Carmen Aguilera-Morillo ◽  
Enrique Álvarez ◽  
Rosa E. Lillo ◽  
Sara López-Taruella ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Variable Selection ◽  
Triple Negative Breast Cancer ◽  
Triple Negative ◽  
A Priori ◽  
Simulated Data ◽  
Point Of View ◽  
High Dimensional ◽  
Whole Genome ◽  
Genome Context

Over the last decade, regularized regression methods have offered alternatives for performing multi-marker analysis and feature selection in a whole genome context. The process of defining a list of genes that will characterize an expression profile remains unclear. It currently relies upon advanced statistics and can use an agnostic point of view or include some a priori knowledge, but overfitting remains a problem. This paper introduces a methodology to deal with the variable selection and model estimation problems in the high-dimensional set-up, which can be particularly useful in the whole genome context. Results are validated using simulated data and a real dataset from a triple-negative breast cancer study.

Sign in / Sign up

Export Citation Format

Share Document