SURROGATE MODELING OF STORM RESPONSE

Surrogate models are yielding simple, fast and accurate storm response predictions. Surrogate modelling is being applied to compute regional response or compute thousands of realizations in seconds. These tools are useful for forecasting, scenario analysis and risk assessments. Approaches used for coastal application include artificial neural networks (ANN), Gaussian process regression (Kriging), and response surface techniques (e.g. Kim et al. 2015, Jia et al. 2013,). These previous approaches were limited to hurricane suites that were already optimally preconfigured using joint probability methods. The results were surprisingly effective in large part because the simulation suites were already optimized and the high dimensional parameter space was well correlated in time and space. The kriging method was applied for the study reported here to: 1) Optimize the parameter space and resulting selection of storms for high fidelity modelling, and 2) Construct surrogate models for both extratropical and tropical storm suites and for wave transformation as well as hurricane surge and other hurricane responses. The results were used for forecasting, scenario analysis, and risk assessments.

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Measure of Similarity between GMMs by Embedding of the Parameter Space That Preserves KL Divergence

Mathematics ◽

10.3390/math9090957 ◽

2021 ◽

Vol 9 (9) ◽

pp. 957

Author(s):

Branislav Popović ◽

Lenka Cepova ◽

Robert Cep ◽

Marko Janev ◽

Lidija Krstanović

Keyword(s):

Computational Complexity ◽

Parameter Space ◽

Recognition Accuracy ◽

Gaussian Mixture Models ◽

Gaussian Mixture ◽

Dimensional Manifold ◽

Dimensional Parameter ◽

Trade Off ◽

Measure Of Similarity ◽

Lower Dimensional

In this work, we deliver a novel measure of similarity between Gaussian mixture models (GMMs) by neighborhood preserving embedding (NPE) of the parameter space, that projects components of GMMs, which by our assumption lie close to lower dimensional manifold. By doing so, we obtain a transformation from the original high-dimensional parameter space, into a much lower-dimensional resulting parameter space. Therefore, resolving the distance between two GMMs is reduced to (taking the account of the corresponding weights) calculating the distance between sets of lower-dimensional Euclidean vectors. Much better trade-off between the recognition accuracy and the computational complexity is achieved in comparison to measures utilizing distances between Gaussian components evaluated in the original parameter space. The proposed measure is much more efficient in machine learning tasks that operate on large data sets, as in such tasks, the required number of overall Gaussian components is always large. Artificial, as well as real-world experiments are conducted, showing much better trade-off between recognition accuracy and computational complexity of the proposed measure, in comparison to all baseline measures of similarity between GMMs tested in this paper.

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Searching bifurcations in high-dimensional parameter space via a feedback loop breaking approach

International Journal of Systems Science ◽

10.1080/00207720902957269 ◽

2009 ◽

Vol 40 (7) ◽

pp. 769-782 ◽

Cited By ~ 10

Author(s):

Steffen Waldherr ◽

Frank Allgöwer

Keyword(s):

Parameter Space ◽

Feedback Loop ◽

High Dimensional ◽

Dimensional Parameter

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COMPLEX BIFURCATION STRUCTURES IN THE HINDMARSH–ROSE NEURON MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018877 ◽

2007 ◽

Vol 17 (09) ◽

pp. 3071-3083 ◽

Cited By ~ 71

Author(s):

J. M. GONZÀLEZ-MIRANDA

Keyword(s):

Phase Diagram ◽

Bifurcation Diagram ◽

Parameter Space ◽

Neuron Model ◽

Two Dimensional ◽

Dimensional Parameter ◽

Rapid Responses ◽

Bifurcation Structures

The results of a study of the bifurcation diagram of the Hindmarsh–Rose neuron model in a two-dimensional parameter space are reported. This diagram shows the existence and extent of complex bifurcation structures that might be useful to understand the mechanisms used by the neurons to encode information and give rapid responses to stimulus. Moreover, the information contained in this phase diagram provides a background to develop our understanding of the dynamics of interacting neurons.

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Searching for the interesting stuff in a multi-dimensional parameter space

Proceedings of the 2016 Symposium on Digital Production - DigiPro '16 ◽

10.1145/2947688.2947690 ◽

2016 ◽

Author(s):

Andy Lomas

Keyword(s):

Parameter Space ◽

Dimensional Parameter

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TERBIUM MOLYBDATE: GROUP THEORY AND FLUCTUATIONS

Modern Physics Letters B ◽

10.1142/s0217984987000338 ◽

1987 ◽

Vol 01 (05n06) ◽

pp. 239-244

Author(s):

SERGE GALAM

Keyword(s):

Fixed Point ◽

Group Theory ◽

Parameter Space ◽

Landau Theory ◽

Two Dimensional ◽

Stable Fixed Point ◽

Theory Analysis ◽

Continuous Transition ◽

Dimensional Parameter ◽

First Order

A new mechanism to explain the first order ferroelastic—ferroelectric transition in Terbium Molybdate (TMO) is presented. From group theory analysis it is shown that in the two-dimensional parameter space ordering along either an axis or a diagonal is forbidden. These symmetry-imposed singularities are found to make the unique stable fixed point not accessible for TMO. A continuous transition even if allowed within Landau theory is thus impossible once fluctuations are included. The TMO transition is therefore always first order. This explanation is supported by experimental results.

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Bifurcation Diagrams and Quotient Topological Spaces Under the Action of the Affine Group of a Family of Planar Quadratic Vector Fields

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127415501503 ◽

2015 ◽

Vol 25 (11) ◽

pp. 1550150 ◽

Cited By ~ 1

Author(s):

Oxana Cerba Diaconescu ◽

Dana Schlomiuk ◽

Nicolae Vulpe

Keyword(s):

Parameter Space ◽

Group Action ◽

Sufficient Conditions ◽

Phase Portraits ◽

Topological Spaces ◽

Canonical Forms ◽

Affine Transformations ◽

Bifurcation Diagrams ◽

Dimensional Parameter ◽

Quotient Spaces

In this article, we consider the class [Formula: see text] of all real quadratic differential systems [Formula: see text], [Formula: see text] with gcd (p, q) = 1, having invariant lines of total multiplicity four and two complex and one real infinite singularities. We first construct compactified canonical forms for the class [Formula: see text] so as to include limit points in the 12-dimensional parameter space of this class. We next construct the bifurcation diagrams for these compactified canonical forms. These diagrams contain many repetitions of phase portraits and we show that these are due to many symmetries under the group action. To retain the essence of the dynamics we finally construct the quotient spaces under the action of the group G = Aff(2, ℝ) × ℝ* of affine transformations and time homotheties and we place the phase portraits in these quotient spaces. The final diagrams retain only the necessary information to capture the dynamics under the motion in the parameter space as well as under this group action. We also present here necessary and sufficient conditions for an affine line to be invariant of multiplicity k for a quadratic system.

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