On the use of the data- and physics-driven approaches for quasi-geostrophic double-gyre problem: application of Genetic Programming

In this study, we investigate Genetic Programming as a data-driven approach to reconstruct eddy-resolved simulations of the double-gyre problem. Stemming from Genetic Algorithms, Genetic Programming is a method of symbolic regression which can be used to extract temporal or spatial functionalities from simulation snapshots. &#160;The double-gyre circulation is simulated by a stratified quasi-geostrophic model which is solved using high-resolution CABARET scheme. The simulation results are compressed using proper orthogonal decomposition and the time variant coefficients of the reduced-order model are fed into a Genetic Programming code. Due to the multi-scale nature of double-gyre problem, we decompose the time signal into a meandering and a fluctuating component. We next explore the parameter space of objective functions in Genetic Programming to capture the two components separately. The data-driven predictions are cross-compared with original double-gyre signal in terms of statistical moments such as variance and auto-correlation function.&#160;

Download Full-text

A Gaussian Process Regression approach within a data-driven POD framework for engineering problems in fluid dynamics

Mathematics in Engineering ◽

10.3934/mine.2022021 ◽

2021 ◽

Vol 4 (3) ◽

pp. 1-16

Author(s):

Giulio Ortali ◽

◽

Nicola Demo ◽

Gianluigi Rozza ◽

Keyword(s):

Gaussian Process ◽

Stokes Problem ◽

Gaussian Process Regression ◽

Engineering Problem ◽

Data Driven ◽

Regression Approach ◽

Data Driven Approach ◽

Naval Engineering ◽

Proper Orthogonal ◽

Industrial Problem

<abstract>This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR). This approach is applied initially to a literature case, the simulation of the Stokes problem, and in the following to a real-world industrial problem, within a shape optimization pipeline for a naval engineering problem.</abstract>

Download Full-text

Multi-scale proper orthogonal decomposition of complex fluid flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.212 ◽

2019 ◽

Vol 870 ◽

pp. 988-1036 ◽

Cited By ~ 21

Author(s):

M. A. Mendez ◽

M. Balabane ◽

J.-M. Buchlin

Keyword(s):

Proper Orthogonal Decomposition ◽

Correlation Matrix ◽

Feature Detection ◽

Orthogonal Decomposition ◽

Data Driven ◽

Dynamic Mode ◽

Time Frequency ◽

Multi Scale ◽

Detection Capabilities ◽

Proper Orthogonal

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low-order models of complex phenomena. In this work, we analyse the main limits of two popular decompositions, namely the proper orthogonal decomposition (POD) and the dynamic mode decomposition (DMD), and we propose a novel decomposition which allows for enhanced feature detection capabilities. This novel decomposition is referred to as multi-scale proper orthogonal decomposition (mPOD) and combines multi-resolution analysis (MRA) with a standard POD. Using MRA, the mPOD splits the correlation matrix into the contribution of different scales, retaining non-overlapping portions of the correlation spectra; using the standard POD, the mPOD extracts the optimal basis from each scale. After introducing a matrix factorization framework for data-driven decompositions, the MRA is formulated via one- and two-dimensional filter banks for the dataset and the correlation matrix respectively. The validation of the mPOD, and a comparison with the discrete Fourier transform (DFT), DMD and POD are provided in three test cases. These include a synthetic test case, a numerical simulation of a nonlinear advection–diffusion problem and an experimental dataset obtained by the time-resolved particle image velocimetry (TR-PIV) of an impinging gas jet. For each of these examples, the decompositions are compared in terms of convergence, feature detection capabilities and time–frequency localization.

Download Full-text

A data-driven approach for multi-scale GIS-based building energy modeling for analysis, planning and support decision making

Applied Energy ◽

10.1016/j.apenergy.2020.115834 ◽

2020 ◽

Vol 279 ◽

pp. 115834

Author(s):

Usman Ali ◽

Mohammad Haris Shamsi ◽

Mark Bohacek ◽

Karl Purcell ◽

Cathal Hoare ◽

...

Keyword(s):

Decision Making ◽

Building Energy ◽

Energy Modeling ◽

Data Driven ◽

Building Energy Modeling ◽

Multi Scale ◽

Data Driven Approach ◽

Support Decision Making

Download Full-text

Model order reduction using sparse coding exemplified for the lid-driven cavity

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.616 ◽

2016 ◽

Vol 808 ◽

pp. 189-223 ◽

Cited By ~ 8

Author(s):

Rohit Deshmukh ◽

Jack J. McNamara ◽

Zongxian Liang ◽

J. Zico Kolter ◽

Abhijit Gogulapati

Keyword(s):

Unsteady Flow ◽

Proper Orthogonal Decomposition ◽

Sparse Coding ◽

Flow Fields ◽

Orthogonal Decomposition ◽

Driven Cavity ◽

Reduced Order ◽

Multi Scale ◽

Small Set ◽

Proper Orthogonal

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

Download Full-text

Data-Driven Genetic Programming-Based Symbolic Regression Metamodels for EDM Process

Advances in Civil and Industrial Engineering - Data-Driven Optimization of Manufacturing Processes ◽

10.4018/978-1-7998-7206-1.ch009 ◽

2021 ◽

pp. 128-150

Author(s):

Kanak Kalita ◽

Ranjan Kumar Ghadai ◽

Dinesh S. Shinde ◽

Xiao-Zhi Gao

Keyword(s):

Genetic Programming ◽

Polynomial Regression ◽

Removal Rate ◽

Symbolic Regression ◽

Data Driven ◽

Electrode Wear ◽

Machining Processes ◽

Testing Data ◽

Data Driven Approach ◽

Pulse On Time

In this research, a data-driven approach to metamodeling of manufacturing/machining processes is developed. Instead of the conventionally used second-order polynomial regression metamodels, a non-predefined form-free approach is discussed. The highly adaptive metamodeling strategy, called symbolic regression, is carried out by using genetic programming. A central composite design based experimental dataset on electric discharge machining is used as the training and the testing data. Four different process parameters namely (voltage, pulse on time, pulse off time, and current) are used as the independent parameters to quantify three different responses (material removal rate, electrode wear rate, and surface roughness). The performance of the metamodels are evaluated by using various statistical metrics like R2, MAE, MSE. The performance of the metamodels on the training and testing data is found to be adequate for all the responses.

Download Full-text