Using Neural Networks to Model Conditional Multivariate Densities

1996 ◽  
Vol 8 (4) ◽  
pp. 843-854 ◽  
Author(s):  
Peter M. Williams
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Multivariate Data ◽  
Time Dependent ◽  
Local Error ◽  
Statistical Distributions ◽  
Conditional Distributions ◽  
Conditional Correlation ◽  
Univariate Case ◽  
Error Bars

Neural network outputs are interpreted as parameters of statistical distributions. This allows us to fit conditional distributions in which the parameters depend on the inputs to the network. We exploit this in modeling multivariate data, including the univariate case, in which there may be input-dependent (e.g., time-dependent) correlations between output components. This provides a novel way of modeling conditional correlation that extends existing techniques for determining input-dependent (local) error bars.

scholarly journals Harnessing Deep Neural Networks to Solve Inverse Problems in Quantum Dynamics: Machine-Learned Predictions of Time-Dependent Optimal Control Fields

2020 ◽  
Author(s):  
Xian Wang ◽  
Anshuman Kumar ◽  
Christian Shelton ◽  
Bryan Wong
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Optimal Control ◽  
Quantum Dynamics ◽  
Deep Neural Networks ◽  
Time Dependent ◽  
Learning Approaches ◽  
Quantum Dynamical ◽  
Quantum Dynamical Systems

Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, <i>E(t)</i>, that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain (i.e., the Fourier transform of <i>E(t)</i>), and (2) a cross-correlation neural network approach for directly predicting <i>E(t)</i> in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning approaches, particularly deep neural networks, can be employed as a cost-effective statistical approach for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems.

scholarly journals Harnessing Deep Neural Networks to Solve Inverse Problems in Quantum Dynamics: Machine-Learned Predictions of Time-Dependent Optimal Control Fields

2020 ◽  
Author(s):  
Xian Wang ◽  
Anshuman Kumar ◽  
Christian Shelton ◽  
Bryan Wong
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Optimal Control ◽  
Quantum Dynamics ◽  
Deep Neural Networks ◽  
Time Dependent ◽  
Learning Approaches ◽  
Quantum Dynamical ◽  
Quantum Dynamical Systems

Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, <i>E(t)</i>, that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain (i.e., the Fourier transform of <i>E(t)</i>), and (2) a cross-correlation neural network approach for directly predicting <i>E(t)</i> in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning approaches, particularly deep neural networks, can be employed as a cost-effective statistical approach for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems.

NEURAL NETWORKS TO COMPUTE MOLECULAR DYNAMICS

1994 ◽  
Vol 02 (02) ◽  
pp. 193-228 ◽  
Author(s):  
LARRY S. LIEBOVITCH ◽  
NIKITA D. ARNOLD ◽  
LEV Y. SELECTOR
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Molecular Dynamics ◽  
Small Molecule ◽  
Efficient Method ◽  
Hopfield Network ◽  
Time Dependent ◽  
Energy Structure ◽  
Conformational States ◽  
Large Molecules

Large molecules such as proteins have many of the properties of neural networks. Hence, neural networks may serve as a natural and thus efficient method to compute the time dependent changes of the structure in large molecules. We describe how to encode the spatial conformation and energy structure of a molecule in a neural network. The dynamics of the molecule can then be computed from the dynamics of the corresponding neural network. As a detailed example, we formulated a Hopfield network to compute the molecular dynamics of a small molecule, cyclohexane. We used this network to determine the distribution of times spent in the twist and chair conformational states as the cyclohexane thermally switches between these two states.

TIME-DEPENDENT PROPERTIES FOR NEURAL NETWORKS WITH CONTINUOUS SPIN VARIABLES

1995 ◽  
Vol 09 (10) ◽  
pp. 1159-1169 ◽  
Author(s):  
VARSHA BANERJEE ◽  
SANJAY PURI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Relaxation Time ◽  
Continuous Time ◽  
Storage Capacity ◽  
Time Dependent ◽  
Input Output ◽  
Computationally Efficient ◽  
Continuous Spin ◽  
Target Pattern

We present a continuous-time neural network model which consists of neurons with a continuous input-output relation. We use a computationally efficient discrete-time equivalent of this model to study its time-dependent properties. Detailed numerical results are presented for the behavior of the relaxation time to a target pattern as a function of the storage capacity of the network.

SCORING MODELING BASED ON NEURAL NETWORKS FOR DETERMINING A BANK BORROWER'S RATING

2020 ◽  
Vol 2020 (10) ◽  
pp. 54-62
Author(s):  
Oleksii VASYLIEV ◽  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Network Architecture ◽  
Statistical Data ◽  
Activation Function ◽  
Decision Making Process ◽  
Neural Network Architecture ◽  
Acceptable Accuracy ◽  
The Neural Network ◽  
Sigmoid Activation Function

The problem of applying neural networks to calculate ratings used in banking in the decision-making process on granting or not granting loans to borrowers is considered. The task is to determine the rating function of the borrower based on a set of statistical data on the effectiveness of loans provided by the bank. When constructing a regression model to calculate the rating function, it is necessary to know its general form. If so, the task is to calculate the parameters that are included in the expression for the rating function. In contrast to this approach, in the case of using neural networks, there is no need to specify the general form for the rating function. Instead, certain neural network architecture is chosen and parameters are calculated for it on the basis of statistical data. Importantly, the same neural network architecture can be used to process different sets of statistical data. The disadvantages of using neural networks include the need to calculate a large number of parameters. There is also no universal algorithm that would determine the optimal neural network architecture. As an example of the use of neural networks to determine the borrower's rating, a model system is considered, in which the borrower's rating is determined by a known non-analytical rating function. A neural network with two inner layers, which contain, respectively, three and two neurons and have a sigmoid activation function, is used for modeling. It is shown that the use of the neural network allows restoring the borrower's rating function with quite acceptable accuracy.

Color Space Transformation using Neural Networks

2019 ◽  
Vol 2019 (1) ◽  
pp. 153-158
Author(s):  
Lindsay MacDonald
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Color Space ◽  
Reflectance Spectra ◽  
Network Architectures ◽  
Color Spaces ◽  
Natural Materials ◽  
Space Transformation ◽  
Color Space Transformation

We investigated how well a multilayer neural network could implement the mapping between two trichromatic color spaces, specifically from camera R,G,B to tristimulus X,Y,Z. For training the network, a set of 800,000 synthetic reflectance spectra was generated. For testing the network, a set of 8,714 real reflectance spectra was collated from instrumental measurements on textiles, paints and natural materials. Various network architectures were tested, with both linear and sigmoidal activations. Results show that over 85% of all test samples had color errors of less than 1.0 ΔE2000 units, much more accurate than could be achieved by regression.

Estimating Pigment Concentrations from Spectral Images Using an Encoder‐Decoder Neural Network

2020 ◽  
Vol 64 (3) ◽  
pp. 30502-1-30502-15
Author(s):  
Kensuke Fukumoto ◽  
Norimichi Tsumura ◽  
Roy Berns
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Absorption Coefficient ◽  
Spectral Data ◽  
High Accuracy ◽  
Pigment Concentration ◽  
Scattering Coefficient ◽  
A Value ◽  
Input And Output ◽  
Pigment Concentrations

Abstract A method is proposed to estimate the concentration of pigments mixed in a painting, using the encoder‐decoder model of neural networks. The model is trained to output a value that is the same as its input, and its middle output extracts a certain feature as compressed information about the input. In this instance, the input and output are spectral data of a painting. The model is trained with pigment concentration as the middle output. A dataset containing the scattering coefficient and absorption coefficient of each of 19 pigments was used. The Kubelka‐Munk theory was applied to the coefficients to obtain many patterns of synthetic spectral data, which were used for training. The proposed method was tested using spectral images of 33 paintings, which showed that the method estimates, with high accuracy, the concentrations that have a similar spectrum of the target pigments.

Neural Network Techniques for Time Series Prediction: A Review

2019 ◽  
Vol 3 (3) ◽  
Author(s):  
Muhammad Faheem Mushtaq ◽  
Urooj Akram ◽  
Muhammad Aamir ◽  
Haseeb Ali ◽  
Muhammad Zulqarnain
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Time Series ◽  
Time Series Data ◽  
Weather Prediction ◽  
Time Series Prediction ◽  
Series Data ◽  
Prediction Problem ◽  
Neural Network Models ◽  
Physical Time

It is important to predict a time series because many problems that are related to prediction such as health prediction problem, climate change prediction problem and weather prediction problem include a time component. To solve the time series prediction problem various techniques have been developed over many years to enhance the accuracy of forecasting. This paper presents a review of the prediction of physical time series applications using the neural network models. Neural Networks (NN) have appeared as an effective tool for forecasting of time series.  Moreover, to resolve the problems related to time series data, there is a need of network with single layer trainable weights that is Higher Order Neural Network (HONN) which can perform nonlinearity mapping of input-output. So, the developers are focusing on HONN that has been recently considered to develop the input representation spaces broadly. The HONN model has the ability of functional mapping which determined through some time series problems and it shows the more benefits as compared to conventional Artificial Neural Networks (ANN). The goal of this research is to present the reader awareness about HONN for physical time series prediction, to highlight some benefits and challenges using HONN.

Neural networks approached for modelling river suspended sediment concentration due to tropical storms

2013 ◽  
Vol 11 (4) ◽  
pp. 457-466
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Suspended Sediment ◽  
Suspended Sediment Concentration ◽  
Time Series Data ◽  
Water Discharge ◽  
Sediment Concentration ◽  
Series Data ◽  
Generalized Regression Neural Network ◽  
Event Based

Artificial neural networks are one of the advanced technologies employed in hydrology modelling. This paper investigates the potential of two algorithm networks, the feed forward backpropagation (BP) and generalized regression neural network (GRNN) in comparison with the classical regression for modelling the event-based suspended sediment concentration at Jiasian diversion weir in Southern Taiwan. For this study, the hourly time series data comprised of water discharge, turbidity and suspended sediment concentration during the storm events in the year of 2002 are taken into account in the models. The statistical performances comparison showed that both BP and GRNN are superior to the classical regression in the weir sediment modelling. Additionally, the turbidity was found to be a dominant input variable over the water discharge for suspended sediment concentration estimation. Statistically, both neural network models can be successfully applied for the event-based suspended sediment concentration modelling in the weir studied herein when few data are available.

Squeak and rattle noise classification using radial basis function neural networks

2020 ◽  
Vol 68 (4) ◽  
pp. 283-293
Author(s):  
Oleksandr Pogorilyi ◽  
Mohammad Fard ◽  
John Davy ◽  
Mechanical and Automotive Engineering, School ◽  
Mechanical and Automotive Engineering, School ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
High Accuracy ◽  
Training Method ◽  
Vehicle Interior ◽  
Trained Classifier ◽  
Different Types ◽  
Noise Classification ◽  
Automatic Tool ◽  
Multi Class Classification

In this article, an artificial neural network is proposed to classify short audio sequences of squeak and rattle (S&R) noises. The aim of the classification is to see how accurately the trained classifier can recognize different types of S&R sounds. Having a high accuracy model that can recognize audible S&R noises could help to build an automatic tool able to identify unpleasant vehicle interior sounds in a matter of seconds from a short audio recording of the sounds. In this article, the training method of the classifier is proposed, and the results show that the trained model can identify various classes of S&R noises: simple (binary clas- sification) and complex ones (multi class classification).

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