Spatial segregation among life-cycle stages has been observed in many stage-structured species, including species of the flour beetle Tribolium. We investigate density-dependent dispersal of life-cycle stages as a pos...
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Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is frequently a challenging task. ...
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A significant drawback of Lagrangian (particle-tracking) reactive transport models has been their inability to properly simulate interactions between solid and liquid chemical phases, such as dissolution and precipita...
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Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problem...
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Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (∼ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on...
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ISBN:
(数字)9798350370942
ISBN:
(纸本)9798350370959
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on Fréchet means and propose a network regression method using the Wasserstein metric. We show that when representing graphs as multivariate Gaussian distributions, the network regression problem requires the computation of a Riemannian center of mass (i.e., Fréchet means). Fréchet means with non-negative weights translates into a barycenter problem and can be efficiently computed using fixed point iterations. Although the convergence guarantees of fixed-point iterations for the computation of Wasserstein affine averages remain an open problem, we provide evidence of convergence in a large number of synthetic and real-data scenarios. Extensive numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, topology, and sparsity in synthetic experiments. Additionally, real-world experiments using the proposed approach result in higher Coefficient of Determination (R
2
) values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.
The presence of large amounts of data in hyperspectral images makes it very difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction u...
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The presence of large amounts of data in hyperspectral images makes it very difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction using diffusion maps. Diffusion maps interpret the eigenfunctions of Markov matrices as a system of coordinates on the original data set in order to obtain an efficient representation of data geometric descriptions. A neural network clustering theory, Fuzzy ART, is further applied to the reduced data to form clusters of the potential minerals. Experimental results on a subset of hyperspectral core imager data show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals in core samples.
In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence...
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作者：
Darunee HunwisaiPoom KumamWiyada KumamDepartment of Applied Mathematics
Faculty of Science and Technology Valaya Alongkorn Rajabhat University under the Royal Patronage Pathumthani Thailand Science Laboratory Building
Faculty of Science KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA) Theoretical and Computational Science Center (TaCS) King Mongkut's University of Technology Thonburi (KMUTT) Bangkok Thailand Department of Mathematics and Computer Science
Faculty of Science and Technology Rajamangala University of Technology Thanyaburi Pathumthani Thailand
In this paper, we introduce the new method for solving the intuitionistic fuzzy transportation problem (IFTP), by using north-west corner method and modified distribution method to find the optimal solution for IFTP.
In this paper, we introduce the new method for solving the intuitionistic fuzzy transportation problem (IFTP), by using north-west corner method and modified distribution method to find the optimal solution for IFTP.
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which have been proposed to describe the dynamics of a variety of large s...
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