Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

scholarly journals Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

Forests ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 913
Author(s):  
Serajis Salekin ◽  
Cristian Higuera Catalán ◽  
Daniel Boczniewicz ◽  
Darius Phiri ◽  
Justin Morgenroth ◽  
...  
Keyword(s):  
Measurement Techniques ◽  
Principal Component ◽  
Climatic Conditions ◽  
Modern Times ◽  
Taper Function ◽  
Complex Functions ◽  
Artificial Neural Network Ann ◽  
Species Specific ◽  
Simple Equations ◽  
Taper Equations

Taper functions are important tools for forest description, modelling, assessment, and management. A large number of studies have been conducted to develop and improve taper functions; however, few review studies have been dedicated to addressing their development and parameters. This review summarises the development of taper functions by considering their parameterisation, geographic and species-specific limitations, and applications. This study showed that there has been an increase in the number of studies of taper function and contemporary methods have been developed for the establishment of these functions. The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times. Early taper functions included polynomial, sigmoid, principal component analysis (PCA), and linear mixed functions, while contemporary machine learning (ML) approaches include artificial neural network (ANN) and random forest (RF). Further analysis of the published literature also shows that most of the studies of taper functions have been carried out in Europe and the Americas, meaning most taper equations are not specifically applicable to tropical tree species. Developing well-conditioned taper functions requires reducing the variation due to species, measurement techniques, and climatic conditions, among other factors. The information presented in this study is important for understanding and developing taper functions. Future studies can focus on developing better taper functions by incorporating emerging remote sensing and geospatial datasets, and using contemporary statistical approaches such as ANN and RF.

scholarly journals Centered Kernel Alignment Enhancing Neural Network Pretraining for MRI-Based Dementia Diagnosis

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
David Cárdenas-Peña ◽  
Diego Collazos-Huertas ◽  
German Castellanos-Dominguez
Keyword(s):  
Neural Network ◽  
Characteristic Curve ◽  
Principal Component ◽  
Imaging Data ◽  
Resonance Imaging ◽  
Dementia Diagnosis ◽  
Target Matrix ◽  
Computer Aided ◽  
Artificial Neural Network Ann ◽  
Aided Diagnosis

Dementia is a growing problem that affects elderly people worldwide. More accurate evaluation of dementia diagnosis can help during the medical examination. Several methods for computer-aided dementia diagnosis have been proposed using resonance imaging scans to discriminate between patients with Alzheimer’s disease (AD) or mild cognitive impairment (MCI) and healthy controls (NC). Nonetheless, the computer-aided diagnosis is especially challenging because of the heterogeneous and intermediate nature of MCI. We address the automated dementia diagnosis by introducing a novel supervised pretraining approach that takes advantage of the artificial neural network (ANN) for complex classification tasks. The proposal initializes an ANN based on linear projections to achieve more discriminating spaces. Such projections are estimated by maximizing the centered kernel alignment criterion that assesses the affinity between the resonance imaging data kernel matrix and the label target matrix. As a result, the performed linear embedding allows accounting for features that contribute the most to the MCI class discrimination. We compare the supervised pretraining approach to two unsupervised initialization methods (autoencoders and Principal Component Analysis) and against the best four performing classification methods of the 2014CADDementiachallenge. As a result, our proposal outperforms all the baselines (7% of classification accuracy and area under the receiver-operating-characteristic curve) at the time it reduces the class biasing.

Thermodynamics of Bidisperse Ferrofluids in Zero External Magnetic Field: Theory and Simulations

2015 ◽  
Vol 233-234 ◽  
pp. 331-334
Author(s):  
Anna Yu. Solovyova ◽  
Ekaterina A. Elfimova
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Free Energy ◽  
External Magnetic Field ◽  
Volume Concentration ◽  
Helmholtz Free Energy ◽  
Hard Spheres ◽  
Particle Volume ◽  
Simulation Data ◽  
Theoretical Predictions

The thermodynamic properties of a ferrofluid modeled by a bidisperse system of dipolar hard spheres in the absence of external magnetic field are investigated using theory and simulations. The theory is based on the virial expansion of the Helmholtz free energy in terms of particle volume concentration. Comparison between the theoretical predictions and simulation data shows a great agreement of the results.

scholarly journals Hamiltonian Thermodynamics

2020 ◽  
Vol 16 (4) ◽  
pp. 557-580
Author(s):  
S.A. Rashkovskiy ◽  
Keyword(s):  
Free Energy ◽  
Hamiltonian Systems ◽  
Thermal Energy ◽  
Helmholtz Free Energy ◽  
Random Processes ◽  
Carnot Cycle ◽  
Thermodynamic Process ◽  
Thermodynamic Cycles ◽  
Thermodynamic State ◽  
Laws Of Thermodynamics

It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.

scholarly journals Prediction Model of Iron Ore Pellet Ambient Strength and Sensitivity Analysis on the Influence Factors

Metals ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 593 ◽  
Author(s):  
Qiangjian Gao ◽  
Yingyi Zhang ◽  
Xin Jiang ◽  
Haiyan Zheng ◽  
Fengman Shen
Keyword(s):  
Neural Network ◽  
Sensitivity Analysis ◽  
Prediction Model ◽  
Bp Neural Network ◽  
Back Propagation ◽  
Influence Factors ◽  
Principal Component ◽  
Bp Network ◽  
Input Variables ◽  
Artificial Neural Network Ann

The Ambient Compressive Strength (CS) of pellets, influenced by several factors, is regarded as a criterion to assess pellets during metallurgical processes. A prediction model based on Artificial Neural Network (ANN) was proposed in order to provide a reliable and economic control strategy for CS in pellet production and to forecast and control pellet CS. The dimensionality of 19 influence factors of CS was considered and reduced by Principal Component Analysis (PCA). The PCA variables were then used as the input variables for the Back Propagation (BP) neural network, which was upgraded by Genetic Algorithm (GA), with CS as the output variable. After training and testing with production data, the PCA-GA-BP neural network was established. Additionally, the sensitivity analysis of input variables was calculated to obtain a detailed influence on pellet CS. It has been found that prediction accuracy of the PCA-GA-BP network mentioned here is 96.4%, indicating that the ANN network is effective to predict CS in the pelletizing process.

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