Intelligent co-simulation: neural network vs. proper orthogonal decomposition applied to a 2D diffusive problem

Berger, Julien; Mazuroski, Walter; Oliveira, Ricardo C. L. F.; Mendes, Nathan

doi:10.1080/19401493.2017.1414879

Cited by 12 publications

(15 citation statements)

References 28 publications

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“…Although the methodology has been demonstrated for a much simpler problem in comparison to what is expected in the context of Digital Twin, we stress the fact that the field of hybrid analytics research is in its infancy and work is currently ongoing to combine more advanced machine learning algorithms like deep neural network and convolutional neural network with physics-based equations. Such hybrid approaches combining data science methods with physics offer promises in diverse application areas of fluids [102][103][104][105][106][107][108][109], and we will continue to advance this new envisioned field of research.…”

Section: Discussionmentioning

confidence: 99%

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

Rahman

Rasheed

San

2018

Fluids

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Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the major component of the computational expense. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the computation of incompressible flows. In our approach, proper orthogonal basis functions are generated to be used in solving the Poisson equation in a reduced order space. Since the time integration of the advection–diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in the full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full order and reduced order spaces. We investigate the feasibility of the proposed method by solving the Taylor–Green vortex decaying problem, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model.

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Section: Discussionmentioning

confidence: 99%

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

Rahman

Rasheed

San

2018

Fluids

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“…Some of the numerical values are inspired from 1D numerical application [2]. The boundary conditions used are presented in the Figure 5.…”

Section: Physical Constants Usedmentioning

confidence: 99%

“…Each problem is solved using a numerical model for each set of governing equations. The whole energy model represents then the aggregation of those several sub-models through a coupling procedure also called co-simulation [2]. Each numerical model exchanges parameters (i.e.…”

Section: Introductionmentioning

confidence: 99%

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

Azam

Berger

Guernouti

et al. 2021

Journal of Building Performance Simulation

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Estimating the temperature field of a building envelope could be a time-consuming task. The use of a reduced-order method is then proposed: the Proper Generalized Decomposition method. The solution of the transient heat equation is then re-written as a function of its parameters: the boundary conditions, the initial condition, etc. To avoid a tremendous number of parameters, the initial condition is parameterized. This is usually done by using the Proper Orthogonal Decomposition method to provide an optimal basis. Building this basis requires data and a learning strategy. As an alternative, the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.

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“…The proper orthogonal decomposition method was first proposed by Kosambi [30], and it has since been successfully applied in a variety of engineering fields, such as image processing, signal analysis, data compression, and recently equally in building physics [26,[31][32][33][34][35]. POD is also known as Karhunen -Loeve decomposition, principal component analysis, or singular value decomposition, and the connections of the methods are provided by [36].…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Model order reduction for efficient deterministic and probabilistic assessment of building envelope thermal performance

Hou

Roels

Janssen

2020

Energy and Buildings

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To lessen the computational expense of building energy simulations, the potential of model order reduction methods for assessing building envelope thermal performance is assessed, through both deterministic and probabilistic case studies of modelling heat transfer through a massive masonry wall. More specifically, two model order reduction methodsproper orthogonal decomposition (POD) and proper generalized decomposition (PGD)are investigated: therefore their calculation accuracies and computational costs are compared with a standard finite element method (FEM). The outcomes show that the POD model strongly outperforms the PGD and FEM models when deterministically simulating wall heat transfer. Additionally, the use of POD to simulate a problem differing from the training simulation can provide an accurate result, and hence the robustness and flexibility of POD is confirmed. This advantage thus expands the application scope of POD for simulating building envelope thermal performance with variable input parameters, rendering it excellent to replace a time-consuming original model in the probabilistic analysis. For the probabilistic case study, it is shown that the sampling errors are much more dominant in the accuracy, implying that the deterministic accuracy of the different models plays a much smaller role, and hence has a very limited effect on the overall convergence behavior of different models. Therefore, the use of POD with a smaller number of modes is strongly suggested in probabilistic analyses to reduce the overall computational expense as much as possible.

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Intelligent co-simulation: neural network vs. proper orthogonal decomposition applied to a 2D diffusive problem

Cited by 12 publications

References 28 publications

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers

Parametric PGD model used with orthogonal polynomials to assess efficiently the building's envelope thermal performance

Model order reduction for efficient deterministic and probabilistic assessment of building envelope thermal performance

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