84,485 research outputs found
Averaging of kernel functions
In kernel-based machines, the integration of several kernels to build more flexible learning methods is a promising avenue for research. In particular, in Multiple Kernel Learning a compound kernel is build by learning a kernel that is the weighted mean of several sources. We show in this paper that the only feasible average for kernel learning is precisely the arithmetic average. We also show that three familiar means (the geometric, inverse root mean square and harmonic means) for positive
real values actually generate valid kernels.Postprint (published version
An Algorithm to Generate Deep-Layer Temperatures from Microwave Satellite Observations for the Purpose of Monitoring Climate Change
An algorithm for generating deep-layer mean temperatures from satellite-observed microwave observations is presented. Unlike traditional temperature retrieval methods, this algorithm does not require a first guess temperature of the ambient atmosphere. By eliminating the first guess a potentially systematic source of error has been removed. The algorithm is expected to yield long-term records that are suitable for detecting small changes in climate. The atmospheric contribution to the deep-layer mean temperature is given by the averaging kernel. The algorithm computes the coefficients that will best approximate a desired averaging kernel from a linear combination of the satellite radiometer's weighting functions. The coefficients are then applied to the measurements to yield the deep-layer mean temperature. Three constraints were used in deriving the algorithm: (1) the sum of the coefficients must be one, (2) the noise of the product is minimized, and (3) the shape of the approximated averaging kernel is well-behaved. Note that a trade-off between constraints 2 and 3 is unavoidable. The algorithm can also be used to combine measurements from a future sensor (i.e., the 20-channel Advanced Microwave Sounding Unit (AMSU)) to yield the same averaging kernel as that based on an earlier sensor (i.e., the 4-channel Microwave Sounding Unit (MSU)). This will allow a time series of deep-layer mean temperatures based on MSU measurements to be continued with AMSU measurements. The AMSU is expected to replace the MSU in 1996
Bayesian Optimization Approach for Analog Circuit Synthesis Using Neural Network
Bayesian optimization with Gaussian process as surrogate model has been
successfully applied to analog circuit synthesis. In the traditional Gaussian
process regression model, the kernel functions are defined explicitly. The
computational complexity of training is O(N 3 ), and the computation complexity
of prediction is O(N 2 ), where N is the number of training data. Gaussian
process model can also be derived from a weight space view, where the original
data are mapped to feature space, and the kernel function is defined as the
inner product of nonlinear features. In this paper, we propose a Bayesian
optimization approach for analog circuit synthesis using neural network. We use
deep neural network to extract good feature representations, and then define
Gaussian process using the extracted features. Model averaging method is
applied to improve the quality of uncertainty prediction. Compared to Gaussian
process model with explicitly defined kernel functions, the
neural-network-based Gaussian process model can automatically learn a kernel
function from data, which makes it possible to provide more accurate
predictions and thus accelerate the follow-up optimization procedure. Also, the
neural-network-based model has O(N) training time and constant prediction time.
The efficiency of the proposed method has been verified by two real-world
analog circuits
Diffusion-Based Coarse Graining in Hybrid Continuum-Discrete Solvers: Theoretical Formulation and A Priori Tests
Coarse graining is an important ingredient in many multi-scale
continuum-discrete solvers such as CFD--DEM (computational fluid
dynamics--discrete element method) solvers for dense particle-laden flows.
Although CFD--DEM solvers have become a mature technique that is widely used in
multiphase flow research and industrial flow simulations, a flexible and
easy-to-implement coarse graining algorithm that can work with CFD solvers of
arbitrary meshes is still lacking. In this work, we proposed a new coarse
graining algorithm for continuum--discrete solvers for dense particle-laden
flows based on solving a transient diffusion equation. Via theoretical analysis
we demonstrated that the proposed method is equivalent to the statistical
kernel method with a Gaussian kernel, but the current method is much more
straightforward to implement in CFD--DEM solvers. \textit{A priori} numerical
tests were performed to obtain the solid volume fraction fields based on given
particle distributions, the results obtained by using the proposed algorithm
were compared with those from other coarse graining methods in the literature
(e.g., the particle centroid method, the divided particle volume method, and
the two-grid formulation). The numerical tests demonstrated that the proposed
coarse graining procedure based on solving diffusion equations is theoretically
sound, easy to implement and parallelize in general CFD solvers, and has
improved mesh-convergence characteristics compared with existing coarse
graining methods. The diffusion-based coarse graining method has been
implemented into a CFD--DEM solver, the results of which are presented in a
separate work (R. Sun and H. Xiao, Diffusion-based coarse graining in hybrid
continuum-discrete solvers: Application in CFD-DEM solvers for particle laden
flows)
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