Fractures and their geometrical patterns are usually required to analyze the mechanical and flow properties of porous media in the subsurface. Fracture characterization is therefore regarded of crucial importance for ...
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Fractures and their geometrical patterns are usually required to analyze the mechanical and flow properties of porous media in the subsurface. Fracture characterization is therefore regarded of crucial importance for optimizing production management or achieving maximum storage capacity. In this research, we propose to invert the fracture networks under the Bayesian framework for the uncertainty quantification. In particular, the number of fractures in the modelling system is treated as unknown, leading to a trans-dimensional inverse problem, and the reversible jump Markov chain Monte Carlo algorithm is applied to sample the model space with possible model moves proposed in the sampling process. A deep learning network is further applied as a surrogate model in the sampling process for increasing the computational efficiency, instead of using the physical forward simulator. We apply the proposed methodology to estimate the spatial distribution of fracture networks based on the head measurements from the steady-state flow simulation. The prior distributions of fracture parameters such as position, orientation and length are described using the discrete fracture networks approach that is deeply rooted in stochastic modelling. Due to the high non-uniqueness, the correct spatial distribution of fracture patterns cannot be successfully recovered in this case study, even a good match between observed and simulated head data is reached. More analysis could be performed in the future with the production historical data or more informative priors.
This paper investigates the motion planning problem of planar m-link (m >= 4) closed chains among point obstacles with extension to arbitrary convex 2-D obstacles. The configuration space (C-space) of closed chains...
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This paper investigates the motion planning problem of planar m-link (m >= 4) closed chains among point obstacles with extension to arbitrary convex 2-D obstacles. The configuration space (C-space) of closed chains is embedded into two copies of m-3 dimensional tori. Two structural sets, the C-boundaries and the C-obstacles, are analyzed based upon the C-spaces of recursively constructed lower-dimensional closed chains. They contain essential structural information about the connectivity of the collision-free portion (C-free) of the C-space. By approximating each workspace obstacle by a set of points on the boundary after dilation, its corresponding C-obstacle is guaranteed to be covered by the C-obstacle of the convex hull of the point set. This permits a resolution-complete roadmap algorithm that puts specific bias for sampling the structural sets. Several benchmark examples are presented that compare the performance between our algorithm and the traditional algorithms. Animation videos and source codes are also provided which demonstrate the effectiveness of our method for closed chains of up to 20 links.
Social networks and other sparse data sets pose significant challenges for statistical inference, since many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic stati...
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Social networks and other sparse data sets pose significant challenges for statistical inference, since many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic statistics offers a theoretically justified approach to goodness-of-fit testing that relies on the theory of Markov bases. Most current practices require the computation of the entire basis, which is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models. We demonstrate the approach on the Holland-Leinhardt model for random directed graphs that allows for reciprocation effects.
This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of...
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This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-lime computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence. (C) 1999 Academic Press.
Faced with the challenges of intelligently managing the entire product lifecycle, traditional management techniques no longer meet the complex demands of modern enterprises. To address it, we employ an ontology modeli...
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Faced with the challenges of intelligently managing the entire product lifecycle, traditional management techniques no longer meet the complex demands of modern enterprises. To address it, we employ an ontology modeling method based on a multidimensional view of product information for a knowledge graph, culminating in a comprehensive PLM knowledge system. To better serve PLM users, we propose an intelligent recommendation model based on context and user behavior for knowledge recommendations. This model seamlessly integrates the knowledge storage structure, user preference attributes, and the rich semantics of the knowledge graph. To improve the recommendation capability of the model, we design an improved multi-hop neighbor node sampling algorithm and use a graph convolutional neural network to quantify the target user preference attributes layer by layer. After a series of rigorous validation experiments, our method consistently outperformed competing models across key performance metrics, such as accuracy and recall, underscoring its efficacy and practicality in knowledge recommendation within PLM systems.
Many cases arise in practice where a versatile hardwired pseudorandom number or pseudonoise generator would be extremely useful. General-purpose pseudonoise devices are not available today. We present a new sampling m...
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Many cases arise in practice where a versatile hardwired pseudorandom number or pseudonoise generator would be extremely useful. General-purpose pseudonoise devices are not available today. We present a new sampling method, conditional bit sampling, which is suited for hardwired sampling devices because of its generality, simplicity, and accuracy. Random variables sampled from an arbitrary distribution are generated bit by bit from high- to low-order bits with the conditional bit algorithm. The result of a comparison of a uniform number to a conditional probability determines whether a bit in the sampled random number is set to one. The conditional probabilities are easily calculated for any probability distribution and must be arranged in special order. Simple Fortran programs make all necessary computations. Agreement between actual and theoretical performance of the conditional bit algorithm was excellent when sampling accuracy was evaluated for several examples of continuous and discrete densities. sampling from empirically known, perhaps erratic-shaped, densities presents no problems. Only a small memory containing the conditional probabilities needs to be changed to alter the sampled distribution. The conditional bit algorithmic process always remains the same.
A probabilistic interpretation for hierarchical Archimedean copulas based on Levy subordinators is given. Independent exponential random variables are divided by group-specific Levy subordinators which are evaluated a...
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A probabilistic interpretation for hierarchical Archimedean copulas based on Levy subordinators is given. Independent exponential random variables are divided by group-specific Levy subordinators which are evaluated at a common random time. The resulting random vector has a hierarchical Archimedean survival copula. This approach suggests an efficient sampling algorithm and allows one to easily construct several new parametric families of hierarchical Archimedean copulas. (C) 2009 Elsevier Inc. All rights reserved.
Over the last decades, various "non-linear" MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In t...
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Over the last decades, various "non-linear" MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a non-linear generalization of the Metropolis -Hastings algorithm to a proposal that depends not only on the current state, but also on its law. We propose to simulate this dynamics as the mean field limit of a system of interacting particles, that can in turn itself be understood as a generalisation of the Metropolis-Hastings algorithm to a population of particles. Under the double limit in number of iterations and number of particles we prove that this algorithm converges. Then, we propose an efficient GPU implementation and illustrate its performance on various examples. The method is particularly stable on multimodal exam-ples and converges faster than the classical methods.
Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, ar...
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Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered. The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known. Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited. The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.
The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreove...
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The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreover, inspired by a stochastic interpretation of the members of such a class, a procedure is suggested to check whether the dependence structure of a given data set is truncation invariant. The overall performance of the procedure has been illustrated on both simulated and real data.
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