The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Ricardo Baptista - One of the best experts on this subject based on the ideXlab platform.
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some greedy Algorithms for sparse polynomial chaos expansions
Journal of Computational Physics, 2019Co-Authors: Ricardo Baptista, Valentin Stolbunov, Prasanth B NairAbstract:Abstract Compressed sensing Algorithms approximate functions using limited evaluations by searching for a sparse representation among a dictionary of basis functions. Orthogonal matching pursuit (OMP) is a greedy Algorithm for selecting basis functions whose computational cost scales with the size of the dictionary. For polynomial chaos (PC) approximations, the size of the dictionary grows quickly with the number of model inputs and the maximum polynomial degree, making them often prohibitive to use with greedy methods. We propose two new Algorithms for efficiently constructing sparse PC expansions for problems with high-dimensional inputs. The first Algorithm is a parallel OMP method coupled with an Incremental QR factorization scheme, wherein the model construction step is interleaved with a ν-fold cross-validation procedure. The second approach is a randomized greedy Algorithm that leverages a probabilistic argument to only evaluate a subset of basis functions from the dictionary at each iteration of the Incremental Algorithm. The randomized Algorithm is demonstrated to recover model outputs with a similar level of sparsity and accuracy as OMP, but with a cost that is independent of the dictionary size. Both Algorithms are validated with a numerical comparison of their performance on a series of algebraic test problems and PDEs with high-dimensional inputs.
Prasanth B Nair - One of the best experts on this subject based on the ideXlab platform.
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some greedy Algorithms for sparse polynomial chaos expansions
Journal of Computational Physics, 2019Co-Authors: Ricardo Baptista, Valentin Stolbunov, Prasanth B NairAbstract:Abstract Compressed sensing Algorithms approximate functions using limited evaluations by searching for a sparse representation among a dictionary of basis functions. Orthogonal matching pursuit (OMP) is a greedy Algorithm for selecting basis functions whose computational cost scales with the size of the dictionary. For polynomial chaos (PC) approximations, the size of the dictionary grows quickly with the number of model inputs and the maximum polynomial degree, making them often prohibitive to use with greedy methods. We propose two new Algorithms for efficiently constructing sparse PC expansions for problems with high-dimensional inputs. The first Algorithm is a parallel OMP method coupled with an Incremental QR factorization scheme, wherein the model construction step is interleaved with a ν-fold cross-validation procedure. The second approach is a randomized greedy Algorithm that leverages a probabilistic argument to only evaluate a subset of basis functions from the dictionary at each iteration of the Incremental Algorithm. The randomized Algorithm is demonstrated to recover model outputs with a similar level of sparsity and accuracy as OMP, but with a cost that is independent of the dictionary size. Both Algorithms are validated with a numerical comparison of their performance on a series of algebraic test problems and PDEs with high-dimensional inputs.
Diego Gonzalezaguilera - One of the best experts on this subject based on the ideXlab platform.
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road safety evaluation through automatic extraction of road horizontal alignments from mobile lidar system and inductive reasoning based on a decision tree
Isprs Journal of Photogrammetry and Remote Sensing, 2018Co-Authors: Jose Antonio Martinjimenez, Santiago Zazo, Jose Juan Arranz Justel, Pablo Rodriguezgonzalvez, Diego GonzalezaguileraAbstract:Abstract Safe roads are a necessity for any society because of the high social costs of traffic accidents. This challenge is addressed by a novel methodology that allows us to evaluate road safety from Mobile LiDAR System data, taking advantage of the road alignment due to its influence on the accident rate. Automation is obtained through an inductive reasoning process based on a decision tree that provides a potential risk assessment. To achieve this, a 3D point cloud is classified by an iterative and Incremental Algorithm based on a 2.5D and 3D Delaunay triangulation, which apply different Algorithms sequentially. Next, an automatic extraction process of road horizontal alignment parameters is developed to obtain geometric consistency indexes, based on a joint triple stability criterion. Likewise, this work aims to provide a powerful and effective preventive and/or predictive tool for road safety inspections. The proposed methodology was implemented on three stretches of Spanish roads, each with different traffic conditions that represent the most common road types. The developed methodology was successfully validated through as-built road projects, which were considered as “ground truth.”
Hadi Meidani - One of the best experts on this subject based on the ideXlab platform.
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divide and conquer an Incremental sparsity promoting compressive sampling approach for polynomial chaos expansions
Computer Methods in Applied Mechanics and Engineering, 2017Co-Authors: Negin Alemazkoor, Hadi MeidaniAbstract:This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed Algorithm Incrementally explores sub-dimensional expansions for a sparser recovery, and shows success when removal of uninfluential parameters that results in a lower coherence for measurement matrix, allows for a higher order and/or sparser expansion to be recovered. The Incremental Algorithm effectively searches for the sparsest PC approximation, and not only can it decrease the prediction error, but it can also reduce the dimensionality of PCE model. Four numerical examples are provided to demonstrate the validity of the proposed approach. The results from these examples show that the Incremental Algorithm substantially outperforms conventional compressive sampling approaches for PCE, in terms of both solution sparsity and prediction error.
Pablo Rodriguezgonzalvez - One of the best experts on this subject based on the ideXlab platform.
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road safety evaluation through automatic extraction of road horizontal alignments from mobile lidar system and inductive reasoning based on a decision tree
Isprs Journal of Photogrammetry and Remote Sensing, 2018Co-Authors: Jose Antonio Martinjimenez, Santiago Zazo, Jose Juan Arranz Justel, Pablo Rodriguezgonzalvez, Diego GonzalezaguileraAbstract:Abstract Safe roads are a necessity for any society because of the high social costs of traffic accidents. This challenge is addressed by a novel methodology that allows us to evaluate road safety from Mobile LiDAR System data, taking advantage of the road alignment due to its influence on the accident rate. Automation is obtained through an inductive reasoning process based on a decision tree that provides a potential risk assessment. To achieve this, a 3D point cloud is classified by an iterative and Incremental Algorithm based on a 2.5D and 3D Delaunay triangulation, which apply different Algorithms sequentially. Next, an automatic extraction process of road horizontal alignment parameters is developed to obtain geometric consistency indexes, based on a joint triple stability criterion. Likewise, this work aims to provide a powerful and effective preventive and/or predictive tool for road safety inspections. The proposed methodology was implemented on three stretches of Spanish roads, each with different traffic conditions that represent the most common road types. The developed methodology was successfully validated through as-built road projects, which were considered as “ground truth.”
