Computational Engineering, Finance, and Science
New submissions
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New submissions for Fri, 10 May 24
- [1] arXiv:2405.05556 [pdf, other]
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Title: Extension of graph-accelerated non-intrusive polynomial chaos to high-dimensional uncertainty quantification through the active subspace methodSubjects: Computational Engineering, Finance, and Science (cs.CE)
The recently introduced graph-accelerated non-intrusive polynomial chaos (NIPC) method has shown effectiveness in solving a broad range of uncertainty quantification (UQ) problems with multidisciplinary systems. It uses integration-based NIPC to solve the UQ problem and generates the quadrature rule in a desired tensor structure, so that the model evaluations can be efficiently accelerated through the computational graph transformation method, Accelerated Model evaluations on Tensor grids using Computational graph transformations (AMTC). This method is efficient when the model's computational graph possesses a certain type of sparsity which is commonly the case in multidisciplinary problems. However, it faces limitations in high-dimensional cases due to the curse of dimensionality. To broaden its applicability in high-dimensional UQ problems, we propose AS-AMTC, which integrates the AMTC approach with the active subspace (AS) method, a widely-used dimension reduction technique. In developing this new method, we have also developed AS-NIPC, linking integration-based NIPC with the AS method for solving high-dimensional UQ problems. AS-AMTC incorporates rigorous approaches to generate orthogonal polynomial basis functions for lower-dimensional active variables and efficient quadrature rules to estimate their coefficients. The AS-AMTC method extends AS-NIPC by generating a quadrature rule with a desired tensor structure. This allows the AMTC method to exploit the computational graph sparsity, leading to efficient model evaluations. In an 81-dimensional UQ problem derived from an air-taxi trajectory optimization scenario, AS-NIPC demonstrates a 30% decrease in relative error compared to the existing methods, while AS-AMTC achieves an 80% reduction.
- [2] arXiv:2405.05790 [pdf, ps, other]
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Title: A Robust eLORETA Technique for Localization of Brain Sources in the Presence of Forward Model UncertaintiesSubjects: Computational Engineering, Finance, and Science (cs.CE); Artificial Intelligence (cs.AI); Quantitative Methods (q-bio.QM)
In this paper, we present a robust version of the well-known exact low-resolution electromagnetic tomography (eLORETA) technique, named ReLORETA, to localize brain sources in the presence of different forward model uncertainties. Methods: We first assume that the true lead field matrix is a transformation of the existing lead field matrix distorted by uncertainties and propose an iterative approach to estimate this transformation accurately. Major sources of the forward model uncertainties, including differences in geometry, conductivity, and source space resolution between the real and simulated head models, and misaligned electrode positions, are then simulated to test the proposed method. Results: ReLORETA and eLORETA are applied to simulated focal sources in different regions of the brain and the presence of various noise levels as well as real data from a patient with focal epilepsy. The results show that ReLORETA is considerably more robust and accurate than eLORETA in all cases. Conclusion: Having successfully dealt with the forward model uncertainties, ReLORETA proved to be a promising method for real-world clinical applications. Significance: eLORETA is one of the localization techniques that could be used to study brain activity for medical applications such as determining the epileptogenic zone in patients with medically refractory epilepsy. However, the major limitation of eLORETA is sensitivity to the uncertainties in the forward model. Since this problem can substantially undermine its performance in real-world applications where the exact lead field matrix is unknown, developing a more robust method capable of dealing with these uncertainties is of significant interest.
Cross-lists for Fri, 10 May 24
- [3] arXiv:2405.05516 (cross-list from q-bio.NC) [pdf, other]
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Title: Deep Learning Models for Atypical Serotonergic Cells RecognitionComments: 34 pagesJournal-ref: Journal of Neuroscience Methods, Volume 407, 2024, 110158Subjects: Neurons and Cognition (q-bio.NC); Computational Engineering, Finance, and Science (cs.CE)
The serotonergic system modulates brain processes via functionally distinct subpopulations of neurons with heterogeneous properties, including their electrophysiological activity. In extracellular recordings, serotonergic neurons to be investigated for their functional properties are commonly identified on the basis of "typical" features of their activity, i.e. slow regular firing and relatively long duration of action potentials. Thus, due to the lack of equally robust criteria for discriminating serotonergic neurons with "atypical" features from non-serotonergic cells, the physiological relevance of the diversity of serotonergic neuron activities results largely understudied. We propose deep learning models capable of discriminating typical and atypical serotonergic neurons from non-serotonergic cells with high accuracy. The research utilized electrophysiological in vitro recordings from serotonergic neurons identified by the expression of fluorescent proteins specific to the serotonergic system and non-serotonergic cells. These recordings formed the basis of the training, validation, and testing data for the deep learning models. The study employed convolutional neural networks (CNNs), known for their efficiency in pattern recognition, to classify neurons based on the specific characteristics of their action potentials.
- [4] arXiv:2405.05626 (cross-list from math.NA) [pdf, other]
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Title: An Uncertainty-aware, Mesh-free Numerical Method for Kolmogorov PDEsComments: 17 pages, 3 figuresSubjects: Numerical Analysis (math.NA); Computational Engineering, Finance, and Science (cs.CE); Optimization and Control (math.OC)
This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods based on the Feynman-Kac formula. The proposed method has two main advantages: 1. uncertainty assessment, which is facilitated by the probabilistic nature of GPR, and 2. mesh-free computation, which allows efficient handling of high-dimensional PDEs. The quality of the solution is improved by adjusting the kernel function and incorporating noise information from the Monte Carlo samples into the GPR noise model. The performance of the method is rigorously analyzed based on a theoretical lower bound on the posterior variance, which serves as a measure of the error between the numerical and true solutions. Extensive tests on three representative PDEs demonstrate the high accuracy and robustness of the method compared to existing methods.
Replacements for Fri, 10 May 24
- [5] arXiv:2311.14228 (replaced) [pdf, other]
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Title: Formulations to select assets for constructing sparse index tracking portfoliosSubjects: Computational Engineering, Finance, and Science (cs.CE)
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