Boosting the Model Discovery of Hybrid Dynamical Systems in an Informed Sparse Regression Approach

2021 ◽  
Author(s):  
Nico Novelli ◽  
Stefano Lenci ◽  
Pierpaolo Belardinelli
Keyword(s):  
Dynamical Systems ◽  
Hybrid Systems ◽  
Vector Fields ◽  
A Priori ◽  
Data Driven ◽  
Governing Equations ◽  
Discontinuity Surfaces ◽  
Efficient Data ◽  
The Many ◽  
Small Clusters

Abstract We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identify discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In our approach, we first focus to identify the switches between the separate vector fields. Then, the dynamics among the manifolds are regressed by making use of the model discovery algorithm of Brunton et al. [1]. The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro-clusters) and a rigid library of models. This allows to identify all the many possible switch points that are clustered to determine the actual discontinuity surfaces. The performances of the method are tested on two numerical examples, namely, a canonical spring–mass hopper and a free/impact electromagnetic energy harvester. These applications are characterized by the presence of a single and double discontinuity, respectively. The analyses demonstrate that in the supervised approach, i.e. where the number of discontinuities is preassigned, we are capable to determine accurately both discontinuities and set of governing equations. It is found a great improvement in time of computation reaching the maximum achievable reliability that outperform existing data-driven identification approaches for hybrid systems.

Boosting the Model Discovery of Hybrid Dynamical Systems in An Informed Sparse Regression Approach

2021 ◽  
Author(s):  
Nico Novelli ◽  
Stefano Lenci ◽  
Pierpaolo Belardinelli
Keyword(s):  
Dynamical Systems ◽  
Hybrid Systems ◽  
Vector Fields ◽  
A Priori ◽  
Data Driven ◽  
Computationally Efficient ◽  
Governing Equations ◽  
Sparse Regression ◽  
Discontinuity Surfaces ◽  
Efficient Data

Abstract We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identifying discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In a two-stages approach, we first locate the switches between separate vector fields. Then, the dynamics among the manifolds are regressed, in this case by making use of the existing algorithm of Brunton et al. [1]. The reconstruction of the discontinuity surfaces comes as the outcome of a statistical analysis implemented via symbolic regression with small clusters (micro-clusters) and a rigid library of models. These allow to classify all the feasible discontinuities that are clustered and to reduce them into the actual discontinuity surfaces. The performances of the sparse regression hybrid model discovery are tested on two numerical examples, namely, a canonical spring-mass hopper and a free/impact electromagnetic energy harvester, engineering archetypes characterized by the presence of a single and double discontinuity, respectively. Results show that a supervised approach, i.e. where the number of discontinuities is preassigned, is computationally efficient and it determines accurately both discontinuities and set of governing equations. A large improvement in the time of computation is found with the maximum achievable reliability. Informed regression-based identification offers the prospect to outperform existing data-driven identification approaches for hybrid systems at the expense of instructing the algorithm for expected discontinuities.

scholarly journals Incorporating radiomics into clinical trials: expert consensus on considerations for data-driven compared to biologically driven quantitative biomarkers

2021 ◽  
Author(s):  
Laure Fournier ◽  
Lena Costaridou ◽  
Luc Bidaut ◽  
Nicolas Michoux ◽  
Frederic E. Lecouvet ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Quantitative Imaging ◽  
A Priori ◽  
External Validation ◽  
Data Driven ◽  
Imaging Biomarkers ◽  
Clinical Validation ◽  
Biological Processes ◽  
Imaging Data ◽  
Selection Of

Abstract Existing quantitative imaging biomarkers (QIBs) are associated with known biological tissue characteristics and follow a well-understood path of technical, biological and clinical validation before incorporation into clinical trials. In radiomics, novel data-driven processes extract numerous visually imperceptible statistical features from the imaging data with no a priori assumptions on their correlation with biological processes. The selection of relevant features (radiomic signature) and incorporation into clinical trials therefore requires additional considerations to ensure meaningful imaging endpoints. Also, the number of radiomic features tested means that power calculations would result in sample sizes impossible to achieve within clinical trials. This article examines how the process of standardising and validating data-driven imaging biomarkers differs from those based on biological associations. Radiomic signatures are best developed initially on datasets that represent diversity of acquisition protocols as well as diversity of disease and of normal findings, rather than within clinical trials with standardised and optimised protocols as this would risk the selection of radiomic features being linked to the imaging process rather than the pathology. Normalisation through discretisation and feature harmonisation are essential pre-processing steps. Biological correlation may be performed after the technical and clinical validity of a radiomic signature is established, but is not mandatory. Feature selection may be part of discovery within a radiomics-specific trial or represent exploratory endpoints within an established trial; a previously validated radiomic signature may even be used as a primary/secondary endpoint, particularly if associations are demonstrated with specific biological processes and pathways being targeted within clinical trials. Key Points • Data-driven processes like radiomics risk false discoveries due to high-dimensionality of the dataset compared to sample size, making adequate diversity of the data, cross-validation and external validation essential to mitigate the risks of spurious associations and overfitting. • Use of radiomic signatures within clinical trials requires multistep standardisation of image acquisition, image analysis and data mining processes. • Biological correlation may be established after clinical validation but is not mandatory.

scholarly journals Quantifying the Impact of a Tsunami on Data-Driven Earthquake Relief Zone Planning in Los Angeles County via Multivariate Spatial Optimization

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 99 ◽  
Author(s):  
Yueqi Gu ◽  
Orhun Aydin ◽  
Jacqueline Sosa
Keyword(s):  
Los Angeles ◽  
A Priori ◽  
Safety Data ◽  
Spatial Optimization ◽  
Optimal Number ◽  
Multidisciplinary Optimization ◽  
Data Driven ◽  
Fault System ◽  
Design Data ◽  
The Impact

Post-earthquake relief zone planning is a multidisciplinary optimization problem, which required delineating zones that seek to minimize the loss of life and property. In this study, we offer an end-to-end workflow to define relief zone suitability and equitable relief service zones for Los Angeles (LA) County. In particular, we address the impact of a tsunami in the study due to LA’s high spatial complexities in terms of clustering of population along the coastline, and a complicated inland fault system. We design data-driven earthquake relief zones with a wide variety of inputs, including geological features, population, and public safety. Data-driven zones were generated by solving the p-median problem with the Teitz–Bart algorithm without any a priori knowledge of optimal relief zones. We define the metrics to determine the optimal number of relief zones as a part of the proposed workflow. Finally, we measure the impacts of a tsunami in LA County by comparing data-driven relief zone maps for a case with a tsunami and a case without a tsunami. Our results show that the impact of the tsunami on the relief zones can extend up to 160 km inland from the study area.

scholarly journals EXTENDED ABSOLUTE PARALLELISM GEOMETRY

2008 ◽  
Vol 05 (07) ◽  
pp. 1109-1135 ◽  
Author(s):  
NABIL. L. YOUSSEF ◽  
A. M. SID-AHMED
Keyword(s):  
Tangent Bundle ◽  
Special Form ◽  
Vector Fields ◽  
A Priori ◽  
Building Blocks ◽  
Absolute Parallelism ◽  
Linearly Independent ◽  
Geometric Objects ◽  
Directional Argument ◽  
Curvature Tensors

In this paper, we study Absolute Parallelism (AP-) geometry on the tangent bundle TM of a manifold M. Accordingly, all geometric objects defined in this geometry are not only functions of the positional argument x, but also depend on the directional argument y. Moreover, many new geometric objects, which have no counterpart in the classical AP-geometry, emerge in this different framework. We refer to such a geometry as an Extended Absolute Parallelism (EAP-) geometry. The building blocks of the EAP-geometry are a nonlinear connection (assumed given a priori) and 2n linearly independent vector fields (of special form) defined globally on TM defining the parallelization. Four different d-connections are used to explore the properties of this geometry. Simple and compact formulae for the curvature tensors and the W-tensors of the four defined d-connections are obtained, expressed in terms of the torsion and the contortion tensors of the EAP-space. Further conditions are imposed on the canonical d-connection assuming that it is of Cartan type (resp. Berwald type). Important consequences of these assumptions are investigated. Finally, a special form of the canonical d-connection is studied under which the classical AP-geometry is recovered naturally from the EAP-geometry. Physical aspects of some of the geometric objects investigated are pointed out and possible physical implications of the EAP-space are discussed, including an outline of a generalized field theory on the tangent bundle TM of M.

scholarly journals A Twenty-First Century Guidebook for Applied Dynamical Systems

2006 ◽  
Vol 1 (4) ◽  
pp. 279-282 ◽  
Author(s):  
A. R. Champneys
Keyword(s):  
Dynamical Systems ◽  
21St Century ◽  
Vector Fields ◽  
Nonlinear Oscillations ◽  
First Century ◽  
Twenty First Century ◽  
The Impact ◽  
Young Researchers

This paper represents the author’s view on the impact of the book Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields by John Guckenheimer and Philip Holmes, first published in 1983 (Springer-Verlag, Berlin). In particular, the questions addressed are: if one were to write a similar book for the 21st century, which topics should be contained and what form should the book take in order to have a similar impact on the modern generation of young researchers in applied dynamical systems?

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

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