A Tree-Structured Algorithm for Reducing Computation in Networks with Separable Basis Functions

1991 ◽  
Vol 3 (1) ◽  
pp. 67-78 ◽  
Author(s):  
Terence D. Sanger
Keyword(s):  
Input Data ◽  
Continuous Functions ◽  
Basis Functions ◽  
Tree Structure ◽  
High Dimensional ◽  
Efficient Computation ◽  
Variable Size ◽  
Differential Delay Equation ◽  
Differential Delay ◽  
The Individual

I describe a new algorithm for approximating continuous functions in high-dimensional input spaces. The algorithm builds a tree-structured network of variable size, which is determined both by the distribution of the input data and by the function to be approximated. Unlike other tree-structured algorithms, learning occurs through completely local mechanisms and the weights and structure are modified incrementally as data arrives. Efficient computation in the tree structure takes advantage of the potential for low-order dependencies between the output and the individual dimensions of the input. This algorithm is related to the ideas behind k-d trees (Bentley 1975), CART (Breiman et al. 1984), and MARS (Friedman 1988). I present an example that predicts future values of the Mackey-Glass differential delay equation.

scholarly journals Design of Multi Standard Near Field Communication Outphasing Transmitter with Modulation Wave Shaping

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 188
Author(s):  
Žiga Korošak ◽  
Nejc Suhadolnik ◽  
Anton Pleteršek
Keyword(s):  
Radio Frequency Identification ◽  
High Efficiency ◽  
Near Field ◽  
Cmos Technology ◽  
Near Field Communication ◽  
Differential Delay ◽  
Fully Differential ◽  
Delay Locked Loop ◽  
Modulation Wave ◽  
The Individual

The aim of this work is to tackle the problem of modulation wave shaping in the field of near field communication (NFC) radio frequency identification (RFID). For this purpose, a high-efficiency transmitter circuit was developed to comply with the strict requirements of the newest EMVCo and NFC Forum specifications for pulse shapes. The proposed circuit uses an outphasing modulator that is based on a digital-to-time converter (DTC). The DTC based outphasing modulator supports amplitude shift keying (ASK) modulation, operates at four times the 13.56 MHz carrier frequency and is made fully differential in order to remove the parasitic phase modulation components. The accompanying transmitter logic includes lookup tables with programmable modulation pulse wave shapes. The modulator solution uses a 64-cell tapped current controlled fully differential delay locked loop (DLL), which produces a 360° delay at 54.24 MHz, and a glitch-free multiplexor to select the individual taps. The outphased output from the modulator is mixed to create an RF pulse width modulated (PWM) output, which drives the antenna. Additionally, this implementation is fully compatible with D-class amplifiers enabling high efficiency. A test circuit of the proposed differential multi-standard reader’s transmitter was simulated in 40 nm CMOS technology. Stricter pulse shape requirements were easily satisfied, while achieving an output linearity of 0.2 bits and maximum power consumption under 7.5 mW.

A Back Allocation Methodology to Estimate the Real-Time Flow and Assist Production Monitoring

2021 ◽  
Author(s):  
Gabriela Chaves ◽  
Danielle Monteiro ◽  
Virgilio José Martins Ferreira
Keyword(s):  
Real Time ◽  
Input Data ◽  
Oil Field ◽  
Well Testing ◽  
Well Test ◽  
Time Data ◽  
Time Flow ◽  
Well Model ◽  
Operational Information ◽  
The Individual

Abstract Commingle production nodes are standard practice in the industry to combine multiple segments into one. This practice is adopted at the subsurface or surface to reduce costs, elements (e.g. pipes), and space. However, it leads to one problem: determine the rates of the single elements. This problem is recurrently solved in the platform scenario using the back allocation approach, where the total platform flowrate is used to obtain the individual wells’ flowrates. The wells’ flowrates are crucial to monitor, manage and make operational decisions in order to optimize field production. This work combined outflow (well and flowline) simulation, reservoir inflow, algorithms, and an optimization problem to calculate the wells’ flowrates and give a status about the current well state. Wells stated as unsuited indicates either the input data, the well model, or the well is behaving not as expected. The well status is valuable operational information that can be interpreted, for instance, to indicate the need for a new well testing, or as reliability rate for simulations run. The well flowrates are calculated considering three scenarios the probable, minimum and maximum. Real-time data is used as input data and production well test is used to tune and update well model and parameters routinely. The methodology was applied using a representative offshore oil field with 14 producing wells for two-years production time. The back allocation methodology showed robustness in all cases, labeling the wells properly, calculating the flowrates, and honoring the platform flowrate.

Polynomial Representation of the Gaussian Process

2018 ◽  
Author(s):  
Jesper Kristensen ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Gaussian Process ◽  
Basis Functions ◽  
Training Data ◽  
Computational Time ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Analysis Tool ◽  
Sobol Indices ◽  
Robust Fitting ◽  
Uncertainty Estimates

Gaussian Process (GP) regression is a well-established probabilistic meta-modeling and data analysis tool. The posterior distribution of the GP parameters can be estimated using, e.g., Markov Chain Monte Carlo (MCMC). The ability to make predictions is a key aspect of using such surrogate models. To make a GP prediction, the MCMC chain as well as the training data are required. For some applications, GP predictions can require too much computational time and/or memory, especially for many training data points. This motivates the present work to represent the GP in an equivalent polynomial (or other global functional) form called a portable GP. The portable GP inherits many benefits of the GP including feature ranking via Sobol indices, robust fitting to non-linear and high-dimensional data, accurate uncertainty estimates, etc. The framework expands the GP in a high-dimensional model representation (HDMR). After fitting each HDMR basis function with a polynomial, they are all added together to form the portable GP. A ranking of which basis functions to use in the fitting process is automatically provided via Sobol indices. The uncertainty from the fitting process can be propagated to the final GP polynomial estimate. In applications where speed and accuracy are paramount, spline fits to the basis functions give very good results. Finally, portable BHM provides an alternative set of assumptions with regards to extrapolation behavior which may be more appropriate than the assumptions inherent in GPs.

scholarly journals Scalable hierarchical clustering by composition rank vector encoding and tree structure

2020 ◽  
Author(s):  
Xiao Lai ◽  
Pu Tian
Keyword(s):  
Machine Learning ◽  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
High Dimensional Data ◽  
Machine Learning Algorithms ◽  
Tree Structure ◽  
Supervised Machine Learning ◽  
High Dimensional ◽  
Rank Vector ◽  
Nonlinear Correlations

AbstractSupervised machine learning, especially deep learning based on a wide variety of neural network architectures, have contributed tremendously to fields such as marketing, computer vision and natural language processing. However, development of un-supervised machine learning algorithms has been a bottleneck of artificial intelligence. Clustering is a fundamental unsupervised task in many different subjects. Unfortunately, no present algorithm is satisfactory for clustering of high dimensional data with strong nonlinear correlations. In this work, we propose a simple and highly efficient hierarchical clustering algorithm based on encoding by composition rank vectors and tree structure, and demonstrate its utility with clustering of protein structural domains. No record comparison, which is an expensive and essential common step to all present clustering algorithms, is involved. Consequently, it achieves linear time and space computational complexity hierarchical clustering, thus applicable to arbitrarily large datasets. The key factor in this algorithm is definition of composition, which is dependent upon physical nature of target data and therefore need to be constructed case by case. Nonetheless, the algorithm is general and applicable to any high dimensional data with strong nonlinear correlations. We hope this algorithm to inspire a rich research field of encoding based clustering well beyond composition rank vector trees.

scholarly journals A consensus-based global optimization method for high dimensional machine learning problems

2020 ◽  
Author(s):  
Jose Carrillo ◽  
Shi Jin ◽  
Lei Li ◽  
Yuhua Zhu
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Weighted Average ◽  
Planck Equation ◽  
Optimization Method ◽  
Learning Problems ◽  
High Dimensional ◽  
Nonconvex Functions ◽  
The Individual ◽  
Parameter Constraints

We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183{204, 2017], which is a gradient-free optimization method for general nonconvex functions. We rst replace the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems. Secondly, we utilize the random mini-batch ideas to reduce the computational cost of calculating the weighted average which the individual particles tend to relax toward. For its mean- eld limit{a nonlinear Fokker-Planck equation{we prove, in both time continuous and semi-discrete settings, that the convergence of the method, which is exponential in time, is guaranteed with parameter constraints independent of the dimensionality. We also conduct numerical tests to high dimensional problems to check the success rate of the method.

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