scholarly journals Machine learning of Kondo physics using variational autoencoders and symbolic regression

2021 ◽  
Vol 104 (23) ◽  
Author(s):  
Cole Miles ◽  
Matthew R. Carbone ◽  
Erica J. Sturm ◽  
Deyu Lu ◽  
Andreas Weichselbaum ◽  
...  
Keyword(s):  
Machine Learning ◽  
Symbolic Regression ◽  
Kondo Physics

scholarly journals Control Synthesis as Machine Learning Control by Symbolic Regression Methods

2021 ◽  
Vol 11 (12) ◽  
pp. 5468
Author(s):  
Elizaveta Shmalko ◽  
Askhat Diveev
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Mathematical Formulation ◽  
Small Variation ◽  
Learning Control ◽  
Symbolic Regression ◽  
Control Technique ◽  
Control Synthesis ◽  
Basic Solution ◽  
Regression Methods

The problem of control synthesis is considered as machine learning control. The paper proposes a mathematical formulation of machine learning control, discusses approaches of supervised and unsupervised learning by symbolic regression methods. The principle of small variation of the basic solution is presented to set up the neighbourhood of the search and to increase search efficiency of symbolic regression methods. Different symbolic regression methods such as genetic programming, network operator, Cartesian and binary genetic programming are presented in details. It is shown on the computational example the possibilities of symbolic regression methods as unsupervised machine learning control technique to the solution of MLC problem of control synthesis for obtaining the stabilization system for a mobile robot.

scholarly journals Ensemble modeling approach for rainfall/groundwater balancing

2007 ◽  
Vol 9 (2) ◽  
pp. 95-106 ◽  
Author(s):  
D. Laucelli ◽  
O. Giustolisi ◽  
V. Babovic ◽  
M. Keijzer
Keyword(s):  
Machine Learning ◽  
Genetic Programming ◽  
Empirical Evidence ◽  
Averaging Method ◽  
Total Error ◽  
Ensemble Methods ◽  
Real Data ◽  
Symbolic Regression ◽  
Ensemble Modeling ◽  
Physical Phenomena

This paper introduces an application of machine learning, on real data. It deals with Ensemble Modeling, a simple averaging method for obtaining more reliable approximations using symbolic regression. Considerations on the contribution of bias and variance to the total error, and ensemble methods to reduce errors due to variance, have been tackled together with a specific application of ensemble modeling to hydrological forecasts. This work provides empirical evidence that genetic programming can greatly benefit from this approach in forecasting and simulating physical phenomena. Further considerations have been taken into account, such as the influence of Genetic Programming parameter settings on the model's performance.

scholarly journals Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

2019 ◽  
Vol 104 (2-3) ◽  
pp. 579-603 ◽  
Author(s):  
Martin Schmelzer ◽  
Richard P. Dwight ◽  
Paola Cinnella
Keyword(s):  
Machine Learning ◽  
Model Development ◽  
Turbulence Models ◽  
Symbolic Regression ◽  
Systematic Assessment ◽  
Rans Turbulence Models ◽  
Diverging Channel ◽  
Stress Models ◽  
Separating Flows ◽  
Made In

AbstractA novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.

scholarly journals Fast, accurate, and transferable many-body interatomic potentials by symbolic regression

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Alberto Hernandez ◽  
Adarsh Balasubramanian ◽  
Fenglin Yuan ◽  
Simon A. M. Mason ◽  
Tim Mueller
Keyword(s):  
Machine Learning ◽  
Density Functional ◽  
Computational Cost ◽  
Symbolic Regression ◽  
Machine Learning Algorithms ◽  
Training Data ◽  
Many Body ◽  
Potential Models ◽  
Embedded Atom ◽  
Hypothesis Space

AbstractThe length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine-learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine-learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient many-body potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton-Chen embedded-atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded-atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.

scholarly journals Synthesis of a mobile robot spatial stabilization system based on machine learning control by symbolic regression

2021 ◽  
Vol 22 (2) ◽  
pp. 129-138
Author(s):  
Askhat I. Diveev ◽  
Neder Jair Mendez Florez
Keyword(s):  
Machine Learning ◽  
Mobile Robot ◽  
Initial Conditions ◽  
Symbolic Regression ◽  
Synthesis Problem ◽  
Terminal Point ◽  
Control Synthesis ◽  
Stabilization System ◽  
Nonlinear Feedback ◽  
Regression Methods

The spatial stabilization system synthesis problem of the robot is considered. The historical overview of methods and approaches for solving the problem of control synthesis is given. It is shown that the control synthesis problem is the most important task in the field of control, for which there are no universal numerical methods for solving it. As one of the ways to solve this problem, it is proposed to use the method of machine learning based on the application of modern symbolic regression methods. This allows you to build universal algorithms for solving control synthesis problems. Several most promising symbolic regression methods are considered for application in control tasks. The formal statement of the control synthesis problem for its numerical solution is given. Examples of solving problems of synthesis of system of spatial stabilization of mobile robot by method of network operator and variation Cartesian genetic programming are given. The problem required finding one nonlinear feedback function to move the robot from thirty initial conditions to one terminal point. Mathematical records of the obtained control functions are given. Results of simulation of control systems obtained by symbolic regression methods are given.

scholarly journals Data Analysis and Symbolic Regression Models for Predicting CO and NOx Emissions from Gas Turbines

Computation ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 139
Author(s):  
Olga Kochueva ◽  
Kirill Nikolskii
Keyword(s):  
Machine Learning ◽  
Gas Turbines ◽  
Symbolic Regression ◽  
Monitoring Systems ◽  
Nox Emissions ◽  
Learning Methods ◽  
Machine Learning Methods ◽  
Model Based ◽  
Emission Monitoring ◽  
Electrical Generation

Predictive emission monitoring systems (PEMS) are software solutions for the validation and supplementation of costly continuous emission monitoring systems for natural gas electrical generation turbines. The basis of PEMS is that of predictive models trained on past data to estimate emission components. The gas turbine process dataset from the University of California at Irvine open data repository has initiated a challenge of sorts to investigate the quality of models of various machine learning methods to build a model for predicting CO and NOx emissions depending on ambient variables and the parameters of the technological process. The novelty and features of this paper are: (i) a contribution to the study of the features of the open dataset on CO and NOx emissions for gas turbines, which will enable one to more objectively compare different machine learning methods for further research; (ii) for the first time for the CO and NOx emissions, a model based on symbolic regression and a genetic algorithm is presented—the advantage of this being the transparency of the influence of factors and the interpretability of the model; (iii) a new classification model based on the symbolic regression model and fuzzy inference system is proposed. The coefficients of determination of the developed models are: R2=0.83 for NOx emissions, R2=0.89 for CO emissions.

scholarly journals Data-driven turbulence modelling using symbolic regression

2021 ◽  
Vol 2099 (1) ◽  
pp. 012020
Author(s):  
A Chakrabarty ◽  
S N Yakovenko
Keyword(s):  
Machine Learning ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Learning Algorithm ◽  
Gene Expression Programming ◽  
Turbulent Channel Flow ◽  
Symbolic Regression ◽  
Test Case ◽  
Data Set ◽  
Anisotropy Tensor

Abstract The study is focused on the performance of machine-learning methods applied to improve the velocity field predictions in canonical turbulent flows by the Reynolds-averaged Navier–Stokes (RANS) equation models. A key issue here is to approximate the unknown term of the Reynolds stress (RS) tensor needed to close the RANS equations. A turbulent channel flow with the curved backward-facing step on the bottom has the high-fidelity LES data set. It is chosen as the test case to examine possibilities of GEP (gene expression programming) of formulating the enhanced RANS approximations. Such a symbolic regression technique allows us to get the new explicit expressions for the RS anisotropy tensor. Results obtained by the new model produced using GEP are compared with those from the LES data (serving as the target benchmark solution during the machine-learning algorithm training) and from the conventional RANS model with the linear gradient Boussinesq hypothesis for the Reynolds stress tensor.

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