Pore network modeling is widely applied to investigate transport phenomena in porous media, as this approach allows for efficient and accurate pore-scale simulation. However, the direct extraction of the pore network ...
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Pore network modeling is widely applied to investigate transport phenomena in porous media, as this approach allows for efficient and accurate pore-scale simulation. However, the direct extraction of the pore network (PN) from three-dimensional pore structure images can often not be achieved, due to the conflict between the wide pore size range of many porous materials and the limited image size inherent to many imaging techniques. This obstacle is typically overcome by stochastic PN generation, and this paper proposes and assesses improved stochastic algorithms to generate such statistically similar PNs. Four algorithms for geometry generation as well as two algorithms for topology generation are investigated, both qualitatively and quantitatively, for four porous materials with different degrees of complexity. Particularly, with each algorithm, the materials' unsaturated moisture storage and transport properties are simulated and compared. The results demonstrate that, as the pore structure's complexity increases, the basic stochastic algorithms available in the literature do not suffice for an accurate and dependable PN generation. The improved geometry and topology generation algorithms put forward in this paper, on the other hand, highly enhance the reliability of the generated PNs, by reducing the deviations for specific moisture contents and permeabilities by 67-98% on average. The improved stochastic algorithms also set the stage for generating PNs of porous materials with (very) wide pore size ranges, and future research can build on these algorithms to generate full-scale PNs using multiple 3D image sets with different resolutions.
stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. ...
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stochastic optimization has experienced significant growth in recent decades, with the increasing prevalence of variance reduction techniques in stochastic optimization algorithms to enhance computational efficiency. In this paper, we introduce two projection-free stochastic approximation algorithms for maximizing diminishing return (DR) submodular functions over convex constraints, building upon the stochastic Path Integrated Differential EstimatoR (SPIDER) and its variants. Firstly, we present a SPIDER Continuous Greedy (SPIDER-CG) algorithm for the monotone case that guarantees a (1- e(-1))OPT- epsilon approximation after O(epsilon(-1)) iterations and O(epsilon(-2)) stochastic gradient computations under the mean-squared smoothness assumption. For the non-monotone case, we develop a SPIDER Frank-Wolfe (SPIDER-FW) algorithm that guarantees a 1/4 (1- minx (x is an element of C)||x||(infinity))OPT- epsilon approximation withO(epsilon(-1)) iterations and O(epsilon (-2)) stochastic gradient estimates. To address the practical challenge associated with a large number of samples per iteration, we introduce a modified gradient estimator based on SPIDER, leading to a Hybrid SPIDER-FW (Hybrid SPIDER-CG) algorithm, which achieves the same approximation guarantee as SPIDER-FW (SPIDER-CG) algorithm with only O(1) samples per iteration. Numerical experiments on both simulated and real data demonstrate the efficiency of the proposed methods.
For minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space we propose a stochastic incremental mirror descent algorithm constructed ...
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For minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space we propose a stochastic incremental mirror descent algorithm constructed by means of the Nesterov smoothing. Further, we modify the algorithm in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions composed with linear operators. Next, a stochastic incremental mirror descent Bregman-proximal scheme with Nesterov smoothing is proposed in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions and a prox-friendly proper, convex and lower semicontinuous function. Different to the previous contributions from the literature on mirror descent methods for minimizing sums of functions, we do not require these to be (Lipschitz) continuous or differentiable. Applications in Logistics, Tomography and Machine Learning modelled as optimization problems illustrate the theoretical achievements
The multi-objective optimization (MOO) of ethylene glycol (EG) production in a hydrogenation tubular reactor focuses on two main objectives: increasing yield and reducing energy cost. A model-based optimization approa...
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The multi-objective optimization (MOO) of ethylene glycol (EG) production in a hydrogenation tubular reactor focuses on two main objectives: increasing yield and reducing energy cost. A model-based optimization approach using the ASPEN Plus simulator was employed to simulate the reactions. In addition, an inequality constraint was imposed on the reactor temperature to prevent a runaway condition. To solve the optimization problems, three multi-objective stochastic optimization algorithms, which are the multi-objective stochastic paint optimizer (MOSPO), multi-objective slime mold algorithm (MOSMA), and multi-objective dragonfly algorithm (MODA), were utilized along with MATLAB and ASPEN Plus simulator. In addition, performance metrics including hypervolume (H), pure diversity (PD), and spacing (S) were employed to evaluate and decide the most effective MOO approach. The results show that the most effective MOO approach for EG production in a hydrogenation tubular reactor is MODA. Its solution set provides precise, diverse, and well-distributed allocation of ND points along the Pareto Front (PF). Also, the results indicate that the highest productivity, lowest energy cost, and highest yield achieved are RM41.3499 million/year, RM0.1667 million/year, and 95.5249%, respectively. Furthermore, the plots of decision variables demonstrate that the reactor pressure highly impacts the optimal solution.
Sparse learning is essential in mining high-dimensional data. Iterative hard thresholding (IHT) methods are effective for optimizing nonconvex objectives for sparse learning. However, IHT methods are vulnerable to adv...
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Sparse learning is essential in mining high-dimensional data. Iterative hard thresholding (IHT) methods are effective for optimizing nonconvex objectives for sparse learning. However, IHT methods are vulnerable to adversary attacks that infer sensitive data. Although pioneering works attempted to relieve such vulnerability, they confront the issue of high computational cost for large-scale problems. We propose two differentially private stochastic IHT: one based on the stochastic gradient descent method (DP-SGD-HT) and the other based on the stochastically controlled stochastic gradient method (DP-SCSG-HT). The DP-SGD-HT method perturbs stochastic gradients with small Gaussian noise rather than full gradients, which are computationally expensive. As a result, computational complexity is reduced from O(nlog(n)) to a lower O(blog(n)), where n is the sample size and b is the mini-batch size used to compute stochastic gradients. The DP-SCSG-HT method further perturbs the stochastic gradients controlled by largebatch snapshot gradients to reduce stochastic gradient variance. We prove that both algorithms guarantee differential privacy and have linear convergence rates with estimation bias. A utility analysis examines the relationship between convergence rate and the level of perturbation, yielding the best-known utility bound for nonconvex sparse optimization. Extensive experiments show that our algorithms outperform existing methods.
In this paper, we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. We explain it...
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In this paper, we develop a novel regularization method for deep neural networks by penalizing the trace of Hessian. This regularizer is motivated by a recent guarantee bound of the generalization error. We explain its benefits in finding flat minima and avoiding Lyapunov stability in dynamical systems. We adopt the Hutchinson method as a classical unbiased estimator for the trace of a matrix and further accel-erate its calculation using a Dropout scheme. Experiments demonstrate that our method outperforms existing regularizers and data augmentation methods, such as Jacobian, Confidence Penalty, Label Smoothing, Cutout, and Mixup. The code is available at https://***/Dean-lyc/Hessian-Regularization.(c) 2023 Elsevier B.V. All rights reserved.
In this brief, a novel stochastic minimum-maximum finite-time consensus protocol is proposed. The stochastic consensus protocol is then applied to a system of agents with continuous high-order dynamics. Based on this ...
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In this brief, a novel stochastic minimum-maximum finite-time consensus protocol is proposed. The stochastic consensus protocol is then applied to a system of agents with continuous high-order dynamics. Based on this protocol, new continuous auxiliary variables are defined, which use only samples of the neighbors' outputs. If those variables are regulated to zero in finite time, it is proven that finite-time output consensus is achieved. This regulation problem is then solved using a standard finite-time control law. Simulations are provided that illustrate the efficiency of this distributed finite-time control scheme.
Background: The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic ...
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Background: The Anaerobic Digestion (AD) processes involve numerous complex biological and chemical reactions occurring simultaneously. Appropriate and efficient models are to be developed for simulation of anaerobic digestion systems. Although several models have been developed, mostly they suffer from lack of knowledge on constants, complexity and weak generalization. The basis of the deterministic approach for modelling the physico and bio-chemical reactions occurring in the AD system is the law of mass action, which gives the simple relationship between the reaction rates and the species concentrations. The assumptions made in the deterministic models are not hold true for the reactions involving chemical species of low concentration. The stochastic behaviour of the physicochemical processes can be modeled at mesoscopic level by application of the stochastic algorithms. Method: In this paper a stochastic algorithm (Gillespie Tau Leap Method) developed in MATLAB was applied to predict the concentration of glucose, acids and methane formation at different time intervals. By this the performance of the digester system can be controlled. The processes given by ADM1 (Anaerobic Digestion Model 1) were taken for verification of the model. Results: The proposed model was verified by comparing the results of Gillespie's algorithms with the deterministic solution for conversion of glucose into methane through degraders. At higher value of 'tau' (timestep), the computational time required for reaching the steady state is more since the number of chosen reactions is less. When the simulation time step is reduced, the results are similar to ODE solver. Conclusion: It was concluded that the stochastic algorithm is a suitable approach for the simulation of complex anaerobic digestion processes. The accuracy of the results depends on the optimum selection of tau value.
When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in ea...
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When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this paper, we present a method requiring only one function measurement value per iteration in the average sense. We prove the strong convergence and asymptotic normality of the new algorithm. Limited experimental results demonstrate the effectiveness and potential of our algorithm for solving low-dimensional problems.
With the help of accurate solar photovoltaic (PV) cell modeling, the PV system's performance can be enhanced. However, PV cell modeling is erroneously caused by inaccurate solar cell parameters. In general, the ma...
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With the help of accurate solar photovoltaic (PV) cell modeling, the PV system's performance can be enhanced. However, PV cell modeling is erroneously caused by inaccurate solar cell parameters. In general, the manufacturers will not provide the required data to model PV cells accurately. Thus, it is essential to get the PV cell parameters effectively. With this primary motivation, this paper presents a new stochastic optimization algorithm for estimating the solar PV cell parameters. Numerous optimization algorithms are discussed in the literature, and nevertheless, due to the convergence towards local minima, the sub-optimal results are produced by most of the algorithms. Thus, in this paper, a new algorithm named as Slime Mould algorithm (SMA) is presented for the solar cell estimation. The proposed algorithm has a new feature called as an exceptional mathematical model with adaptive weights to simulate negative and positive feedback of the propagation wave to find the best path for attaching food with an excellent exploitation tendency and exploratory capacity. The performance of the proposed SMA algorithm is validated by comparing the estimated results with experimental results. The superiority of the SMA algorithm is proved by extensive statistical analysis. In addition, the performance of the proposed algorithm is also compared with the other benchmark meta-heuristics algorithms.
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