Fast Approximate Method Research Articles

A fast approximate method for simulating thermal pile heat exchangers

Ground source heat pump systems, operating in conjunction with vertical ground heat exchangers, will play a key role in decarbonising heating and cooling of buildings. Design of traditional borehole heat exchangers relies on tools which implement routine analytical relationships between heat transferred and the temperature change in the ground and circulating thermal fluid. However, for novel piled foundations used as ground heat exchangers, there are few such analytical solutions available that are practical for routine implementation. This paper examines the use of a radial approximation to simulate the dynamic thermal behaviour of pile heat-exchangers. Originally developed for small diameter and high aspect ratio borehole heat exchangers, the approach is more challenging for piles since unsteady heat transfer within the pile material is more significant over typical timescales. Nonetheless, we demonstrate that for pile diameters between 300 mm and 1200 mm, generally the error is <1 °C with centrally placed heat transfer pipes or four or more pipes placed near the edge with circumferential spacing less than 550 mm. The radial model is therefore practical for most pile configurations. The strong performance of the model is demonstrated for a year of hypothetical heating and cooling cycles, and also against a field-scale thermal response test.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation.

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.

Efficient direct position determination using Frobenius norm approximation

To eliminate the bottleneck of computation and communication capability in classic direct position determination, recently several fast approximation methods have been proposed. However, the estimation accuracy of these methods is not satisfactory. In this letter, the common theoretical principle behind these fast approximation methods is analysed in depth. It is demonstrated that the maximum eigenvalue of a matrix can be approximated by the matrix norm. The performance of several commonly used matrix norms is then compared, and the Frobenius norm is preferable because of its great potential inferred from the analysis in this letter. Numerical simulations indicate that, compared with conventional methods, the proposed method can achieve better estimation accuracy with less computational complexity.

Multipactor Threshold Estimation Techniques Based on Circuit Models, Electromagnetic Fields, and Particle Simulators

Multipactor has become a keylimiting factor of the final performance of satellite communication systems, due to the increase in power levels and/or operating frequency bands. As a result, the critical components of these systems must meet demanding multipactor specifications which should be considered during the design process. This paper describes the different techniques available to predict the multipactor threshold power for radio frequency (RF) and microwave passive hardware under continuous wave (CW) excitation, from cumbersome particle simulations to fast approximate methods based on circuit models. All these techniques have been described and compared together for the first time, including also a detailed description of the configuration issues of commercial particle simulators required to obtain accurate multipactor threshold predictions. The techniques are applied to both wideband and narrowband application examples. The predictions have been compared with measured thresholds of manufactured samples obtained with a novel multipactor test bed, thus allowing to highlight the advantages and limitations of each technique and particle simulator. From this paper, it will be possible to choose the most suitable procedure (and an appropriate simulator, if needed) to obtain multipactor threshold prediction of passive hardware.

Fast IQ Amplitude Approximation Method for ASIC Digital System

In some modules of digital systems, such as Fast Fourier Transform (FFT), Discrete Fourier transform (DFT), IQ (in-phase and quadrature components) modulation/ demodulation, the outputs use the complex data formed , and the calculation of its magnitude value √ are required. In software digital signal processing platform, the multiplication and square root operations are executed by using its math library; however, in Application specific integrated circuit (ASIC) digital system design, the implementation of those operators via Coordinate Rotation Digital Computer (CORDIC) algorithm requires the numerous resources and delays. So, in this paper, we present a fast approximation method for above problem which takes a small delay but acceptable accuracy for AISC digital system design. Keywords—ASIC, Digital system design, FFT, DFT, Fast amplitude approximation, Max-Min approximation.

A Fast Approximate Method for Predicting the Behavior of Auditory Nerve Fibers and the Evoked Compound Action Potential (ECAP) Signal.

Background:The goal of the current research is to develop a model based on computer simulations which describes both the behavior of the auditory nerve fibers and the cochlear implant system as a rehabilitation device.Methods:The approximate method was proposed as a low error and fast tool for predicting the behavior of auditory nerve fibers as well as the evoked compound action potential (ECAP) signal. In accurate methods every fiber is simulated; whereas, in approximate method information related to the response of every fiber and its characteristics such as the activation threshold of cochlear fibers are saved and interpolated to predict the behavior of a set of nerve fibers.Results:The approximate model can predict and analyze different stimulation techniques. Although precision is reduced to <1.66% of the accurate method, the required execution time for simulation is reduced by more than 98%.Conclusion:The amplitudes of the ECAP signal and the growth function were investigated by changing the parameters of the approximate model including geometrical parameters, electrical, and temporal parameters. In practice, an audiologist can tune the stimulation parameters to reach an effective restoration of the acoustic signal.

Multi-model Markov decision processes

Markov decision processes (MDPs) have found success in many application areas that involve sequential decision making under uncertainty, including the evaluation and design of treatment and screening protocols for medical decision making. However, the data used to parameterize the model can influence what policies are recommended, and multiple competing data sources are common in many application areas, including medicine. In this article, we introduce the Multi-model Markov decision process (MMDP) which generalizes a standard MDP by allowing for multiple models of the rewards and transition probabilities. Solution of the MMDP generates a single policy that maximizes the weighted performance over all models. This approach allows the decision maker to explicitly trade-off conflicting sources of data while generating a policy of the same level of complexity for models that only consider a single source of data. We study the structural properties of this problem and show that it is at least NP-hard. We develop exact methods and fast approximation methods supported by error bounds. Finally, we illustrate the effectiveness and the scalability of our approach using a case study in preventative blood pressure and cholesterol management that accounts for conflicting published cardiovascular risk models.

UAV Formation Shape Control via Decentralized Markov Decision Processes

In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region where the swarm must form a three-dimensional shape (e.g., surface of a sphere). As most decision-theoretic formulations suffer from the curse of dimensionality, we adapt an existing fast approximate dynamic programming method called nominal belief-state optimization (NBO) to approximately solve the formation control problem. We perform numerical studies in MATLAB to validate the performance of the above control algorithms.

A Fast and Accurate Reliability Approximation Method for Heterogeneous Cold Standby Sparing Systems

Cold standby sparing is a widely-used fault-tolerant technique where spare units are unpowered and non-operational before being activated to replace a malfunctioned on-line unit. The dynamic failure rate behavior of cold standby units poses unique challenges to the reliability analysis of cold standby systems (CSSs). The existing reliability analysis methods developed for CSSs have various limitations, such as being applicable to only the exponential component time-to-failure distribution, CSSs with identical components, and small-scale systems due to high computational complexity. In this paper, we advance the state of the art by proposing a fast and accurate reliability approximation method based on the Lyapunov central limit theorem for heterogeneous 1-out-of-n cold standby systems with non-identical components. The Lyapunov's conditions are proved for CSSs with exponential, Weibull, normal, and mixed component time-to-failure distributions. The accuracy and efficiency of the proposed method are verified and compared with the existing methods through comprehensive case studies on CSSs with different sizes and different types of distributions. The results show that the proposed method can estimate the reliability of large-scale CSSs efficiently and accurately.

Fast Approximation for Sparse Coding with Applications to Object Recognition.

Sparse Coding (SC) has been widely studied and shown its superiority in the fields of signal processing, statistics, and machine learning. However, due to the high computational cost of the optimization algorithms required to compute the sparse feature, the applicability of SC to real-time object recognition tasks is limited. Many deep neural networks have been constructed to low fast estimate the sparse feature with the help of a large number of training samples, which is not suitable for small-scale datasets. Therefore, this work presents a simple and efficient fast approximation method for SC, in which a special single-hidden-layer neural network (SLNNs) is constructed to perform the approximation task, and the optimal sparse features of training samples exactly computed by sparse coding algorithm are used as ground truth to train the SLNNs. After training, the proposed SLNNs can quickly estimate sparse features for testing samples. Ten benchmark data sets taken from UCI databases and two face image datasets are used for experiment, and the low root mean square error (RMSE) results between the approximated sparse features and the optimal ones have verified the approximation performance of this proposed method. Furthermore, the recognition results demonstrate that the proposed method can effectively reduce the computational time of testing process while maintaining the recognition performance, and outperforms several state-of-the-art fast approximation sparse coding methods, as well as the exact sparse coding algorithms.

Fast pricing of American options under variance gamma

We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it a time-changed Brownian motion. In general, the finite difference method and the simulation method can be used for pricing under this model, but their speed is not satisfactory. So there is a need for fast but accurate approximation methods. In the case of Black-Merton-Scholes model, there are fast approximation methods, but they cannot be utilized for the variance gamma model. We develop a new fast method inspired by the quadratic approximation method, while reducing the error by making use of a machine learning technique on pre-calculated quantities. We compare the performance of our proposed method with those of the existing methods and show that this method is efficient and accurate for practical use.

Accelerating patch-based low-rank image restoration using kd-forest and Lanczos approximation

Patch-based low-rank approximation (PLRA) via truncated singular value decomposition is a powerful and effective tool for recovering the underlying low-rank structure in images. Generally, it first performs an approximate nearest neighbors (ANN) search algorithm to group similar patches into a collection of matrices with reshaping them as vectors. The inherent correlation among similar patches makes these matrices have a low-rank structure. Then the singular value decomposition (SVD) is used to derive a low-rank approximation of each matrix by truncating small singular values. However, the conventional implementation of patch-based low-rank image restoration suffers from high computational cost of the ANN search and full SVD. To address this limitation, we propose a fast approximation method that accelerates the computation of PLRA using multiple kd-trees and Lanczos approximation. The basic idea of this method is to exploit an index kd-tree built from patch samples of the observed image and several small kd-trees built from overlapping regions of the image to accelerate the search for similar patches, and apply the Lanczos bidiagonalization procedure to obtain a fast low-rank approximation of patch matrix without computing the full SVD. Experimental results on image denoising and inpainting tasks demonstrate the efficiency and accuracy of our method.

Orthogonal polynomials in and on a quadratic surface of revolution

We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution, generalizing spherical harmonics to the surface of a cone, hyperboloid, and paraboloid. We use this construction to develop cubature and fast approximation methods.

Ultra-Scalable Spectral Clustering and Ensemble Clustering

This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for K-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669.

A comparison between fully-unsteady and quasi-steady approach for the prediction of the propeller performance in waves

Maritime transport is the most energy-effective mode to move large amounts of goods around the world. Hauling cargo via waterway produces an enormous quantity of greenhouse gas emissions. Vessel fuel efficiency directly influences ship emissions by affecting the amount of burnt fuel. Optimizing ships operating in waves rather than in calm water conditions could decrease the fuel consumption of vessels. In particular, ship propellers are traditionally designed neglecting dynamic conditions such as time-varying wake distribution and propulsion factors, propeller speed fluctuations, ship motions, and speed loss.The effect of waves on the propeller performance can be evaluated using both a quasi-steady and a fully-unsteady approach. The former is a fast computational approximation method based on the assumption that the ratio of propeller angular frequency to wave encounter frequency is sufficiently large. The latter provides a complete representation of the propeller dynamics, but it is computationally expensive.The purpose of this paper is to compare the propeller performance in the presence of waves using the quasi-steady and the fully unsteady approach. This analysis is performed by observing the differences in unsteady propeller forces, cavitation volume, and hull pressure pulses between the two approaches. The full-scale KVLCC2 propeller is utilized for the investigation.Results show a good agreement between the quasi-steady and the fully-unsteady approach in the prediction of the temporal mean and the fluctuation amplitude of KT and KQ, the cavity volume variation, and the hull pressure pulses. Therefore, for the considered operating conditions, the quasi-steady approach can be used to compute the propeller performance in waves.

Numerical methods to find the slope at a point on map using level curves. Application in road designing

The problem of determining the slope at a point on a map using level curves has practical applicability in designing the roads. This problem is reduced to the problem of finding the shortest length segment through a point that connects two coplanar lines. Two methods to solve this problem are presented: a fast approximate method and a slower but exact algorithmic method. The results are compared at the end.

Fast approximate methods for modified gravity cosmological simulations

ABSTRACT The accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives. Predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly non-linear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we find that these methods can indeed be used to explore the region around the baryon acoustic oscillation scale, $k\sim 0.1~h\, \text{Mpc}^{-1}$ but not much further.

A hybrid data-driven method for fast approximation of practical dynamic security region boundary of power systems

In the context of high-level integration of stochastic renewable energy resources such as wind and solar power, the practical dynamic security region (PDSR) with hyper-plane expression is a powerful tool for power system situational awareness and stability-constrained operation. In this paper, a hybrid data-driven method is proposed to fast approximating the PDSR boundary with hyper-plane expression. Firstly, the operating point data in the high-dimension nodal injection space is analyzed by the RELIEF algorithm to identify the key generators, active output of which has relatively great effect on transient angle stability. Then, based on the orthogonal point selection method and key generators, the equivalent search space and critical points inside it are determined with high accuracy and high speed. The hyper-plane expression of the PDSR boundary, which matches the critical points best, is finally fitted by the least square approach. Test results obtained using the IEEE 39-bus test system show the efficiency of the proposed method.

MetaStyle: Three-Way Trade-off among Speed, Flexibility, and Quality in Neural Style Transfer

An unprecedented booming has been witnessed in the research area of artistic style transfer ever since Gatys et al. introduced the neural method. One of the remaining challenges is to balance a trade-off among three critical aspects—speed, flexibility, and quality: (i) the vanilla optimization-based algorithm produces impressive results for arbitrary styles, but is unsatisfyingly slow due to its iterative nature, (ii) the fast approximation methods based on feed-forward neural networks generate satisfactory artistic effects but bound to only a limited number of styles, and (iii) feature-matching methods like AdaIN achieve arbitrary style transfer in a real-time manner but at a cost of the compromised quality. We find it considerably difficult to balance the trade-off well merely using a single feed-forward step and ask, instead, whether there exists an algorithm that could adapt quickly to any style, while the adapted model maintains high efficiency and good image quality. Motivated by this idea, we propose a novel method, coined MetaStyle, which formulates the neural style transfer as a bilevel optimization problem and combines learning with only a few post-processing update steps to adapt to a fast approximation model with satisfying artistic effects, comparable to the optimization-based methods for an arbitrary style. The qualitative and quantitative analysis in the experiments demonstrates that the proposed approach achieves high-quality arbitrary artistic style transfer effectively, with a good trade-off among speed, flexibility, and quality.

Discrete Lagrangian algorithm for finding geodesics on triangular meshes

• The fast approximation method for finding open geodesics on polygonal surfaces. • A demonstration of the performance of the method and comparison with several existing methods. • a straightforward implementation. • an application in a real-world civil engineering problem. The present paper introduces an approximation method for finding open geodesics on triangular surfaces. The algorithm is specifically designed to be able to solve real world problems where geodesic paths are needed. We use the model of geodesic curvature flow for open curves in the Lagrangian formulation . The model is enriched with a tangential term in order to have a control over the quality of the discretization grid during the computation. The governing equation of the flow is solved by a numerical method based on a semi-implicit time discretization and a finite difference space discretization. The paper presents the numerical scheme and various implementation details as well as numerous experiments to demonstrate the performance of the method and to provide comparison with several other well known methods. We also present a Grasshopper component for Rhinoceros for finding optimal paths on surface meshes that we developed and that includes our algorithm.