Article
Engineering, Multidisciplinary
Gil -Yong Lee, K. C. Park, Yong-Hwa Park
Summary: This paper proposes a new reduced-order modeling methodology for frequency response analysis of linear dynamical systems with parametric uncertainty. The methodology consists of offline and online stages, utilizing progressive Galerkin approach and statistical ROM model to accelerate computational efficiency.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Xiang Sun, Xiaomin Pan, Jung-Il Choi
Summary: The proposed method utilizes POD and PCE to construct an efficient stochastic representation model through non-intrusive methods, significantly reducing computational costs and storage requirements for high-dimensional physical and random spaces, while demonstrating similar accuracy in predicting statistical quantities as classical sparse PCE.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Xiang Sun, Jung-Il Choi
Summary: The proposed method utilizes POD and PCE to model spacetime-dependent parameterized problems, effectively estimating low-order moments and accuracy loss under uncorrelated or correlated input parameters.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Peter Benner, Jan Heiland
Summary: In this work, a multidimensional Galerkin proper orthogonal decomposition method is proposed to reduce the complexity of quantifying multivariate uncertainties in partial differential equations. The analytical framework and results are provided to define and quantify the low-dimensional approximation. An application for uncertainty modeling using polynomial chaos expansions is illustrated, showing the efficiency of the proposed method.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Elizabeth H. Krath, Forrest L. Carpenter, Paul G. A. Cizmas, David A. Johnston
Summary: This study introduces a novel, more efficient reduced-order model for compressible flows based on proper orthogonal decomposition (POD). By using specific volume instead of density, the coefficients of the system of ODEs in the reduced-order model were pre-computed. Various methods were used to enhance ODE solver stability. Validation was done for two cases, showing a speedup exceeding four orders of magnitude compared to the full-order model.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Philip Pergam, Heiko Briesen
Summary: This study aims to improve the computational efficiency of a complex mathematical cake-filtration model with strong nonlinearities. A hybrid data-driven approach using proper orthogonal decomposition is employed, and optimal, globally defined basis functions are found based on a few sample simulations. The reduced-order model obtained from this approach has a 98% decrease in dimension compared to the full-order model, resulting in a 90% decrease in computational time for solving a benchmark optimization problem. This significant numerical speed-up offers the potential to use the reduced-order model in advanced process control and optimization methods.
COMPUTERS & CHEMICAL ENGINEERING
(2023)
Article
Engineering, Mechanical
Giorgio Gobat, Andrea Opreni, Stefania Fresca, Andrea Manzoni, Attilio Frangi
Summary: In this study, the Proper Orthogonal Decomposition (POD) method is applied to efficiently simulate the nonlinear behavior of Micro-Electro-Mechanical-Systems (MEMS) in various scenarios involving geometric and electrostatic nonlinearities. The POD method reduces the polynomial terms up to cubic order associated with large displacements through exact projection onto a low-dimensional subspace spanned by the Proper Orthogonal Modes (POMs). Electrostatic nonlinearities are modeled using precomputed manifolds based on the amplitudes of the electrically active POMs. The reliability of the assumed linear trial space is extensively tested in challenging applications such as resonators, micromirrors, and arches with internal resonances. Comparisons are made between the periodic orbits computed with POD and the invariant manifold approximated with Direct Normal Form approaches, highlighting the reliability and remarkable predictive capabilities of the technique, particularly in terms of estimating the frequency response function of selected output quantities of interest.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Xi Li, Yan Luo, Minfu Feng
Summary: In this paper, an efficient proper orthogonal decomposition based reduced-order model (POD-ROM) for nonstationary Stokes equations is proposed. The new scheme combines the classical projection method with POD technique, resulting in low computational costs and improved efficiency.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Multidisciplinary
Arash Mohammadi, Koji Shimoyama, Mohamad Sadeq Karimi, Mehrdad Raisee
Summary: An efficient surrogate model based on POD and compressed sensing is developed for affordable representation of high-dimensional stochastic fields, showing potential in engineering applications.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mechanics
Xuyi Jia, Chunna Li, Wen Ji, Chunlin Gong
Summary: This paper proposes a new modeling method based on a hybrid reduced-order model to improve the accuracy and robustness of predicting complex and strongly nonlinear flow structures. The method combines DMD and POD to capture different flow properties and achieves better accuracy and forecasting capability for shock waves and vortex.
Article
Thermodynamics
Jiacheng Ma, Donghun Kim, James E. Braun
Summary: This paper presents a computationally efficient and accurate dynamic modeling approach for vapor compression systems using model order reduction techniques. By reformulating the heat exchanger model and applying POD, reduced order models for evaporator and condenser are constructed with system stability and numerical efficiency in mind. Transient simulations conducted under various operating conditions show that the reduced order model can execute faster with negligible prediction errors compared to the high-fidelity finite volume model.
INTERNATIONAL JOURNAL OF REFRIGERATION
(2021)
Article
Mathematics, Applied
Birgul Koc, Tomas Chacon Rebollo, Samuele Rubino
Summary: In this paper, we provide evidence of uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of the Burgers equation with the inclusion of difference quotients (DQs). Our study focuses on the behavior of DQ ROM error bounds using different POD spaces and error measures. Numerical tests show that DQ ROM errors are significantly smaller than noDQ errors, and the addition of DQs in the POD process leads to an optimality/super-optimality behavior.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Azzedine Abdedou, Azzeddine Soulaimani
Summary: The POD-BSBEM method is proposed as a non-intrusive reduced-order model for uncertainty propagation in stochastic time-dependent problems, utilizing proper orthogonal decomposition and B-splines approximation. Experimental results confirm its accuracy and efficiency in predicting statistical moments of output quantities of interest.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Stefania Fresca, Andrea Manzoni
Summary: DL-ROMs are proposed to overcome limitations of conventional ROMs, but require expensive training. The proposed method combines POD and multi-fidelity pretraining to avoid the costly training stage of DL-ROMs.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Michel Onori, Nicholas J. Hills
Summary: This paper presents a Reduced Order Modelling (ROM) approach for turbulent flow in a rotor-stator cavity commonly found in aircraft engine secondary air systems. The method uses Proper Orthogonal Decomposition (POD) with data from Large Eddy Simulations (LES) to predict turbulence phenomena accurately, introducing two novel techniques in the process.
COMPUTERS & FLUIDS
(2021)
Article
Engineering, Civil
Muzammil Hussain Rammay, Ahmed H. Elsheikh, Yan Chen
JOURNAL OF HYDROLOGY
(2019)
Article
Engineering, Multidisciplinary
Alexadner Tarakanov, Ahmed H. Elsheikh
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Computer Science, Interdisciplinary Applications
Muzammil Hussain Rammay, Ahmed H. Elsheikh, Yan Chen
Summary: Iterative ensemble smoothers are commonly used for calibrating simulators of physical systems, but model errors are often present in imperfect models. This paper proposes a flexible iterative ensemble smoother that can reduce the impact of model bias, improving the quality of parameter estimation and prediction capacity in imperfect physical models.
COMPUTATIONAL GEOSCIENCES
(2021)
Article
Engineering, Petroleum
Caroline Johnson, Morteza Haghighat Sefat, Ahmed H. Elsheikh, David Davies
Summary: In the next few decades, there will be a significant increase in well plugging and abandonment operations globally, particularly in the North Sea region. This will require new design tools and technologies to ensure the safe and cost-effective decommissioning of hydrocarbon production wells.
Article
Water Resources
Mark Ashworth, Ahmed H. Elsheikh, Florian Doster
Summary: This paper introduces a machine learning-based multiscale modelling framework for hierarchical multiscale problems. The framework combines a data-driven model with a macroscale simulator to form a hybrid ML-physics-based approach. The framework is applied to transient phenomena in dual-porosity geomaterials, and the hybrid approach is compared to traditional dual-porosity and microscale models, showing high-quality results without the computational burden of explicit microscale simulations.
ADVANCES IN WATER RESOURCES
(2022)
Article
Geochemistry & Geophysics
Muzammil Hussain Rammay, Sergey Alyaev, Ahmed H. Elsheikh
Summary: This paper explores the challenges of real-time inversion using Bayesian algorithms in the presence of uncertain model parameters, and investigates the effects of the approximate nature and model errors of deep learning models on the inversion results. By utilizing deep neural networks for model evaluation and the flexible iterative ensemble smoother to reduce model bias, the quality of the inversion results for geosteering can be improved. The paper also describes a method for identifying inversion multimodality and proposes possible solutions to alleviate it in real-time.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Automation & Control Systems
Atish Dixit, Ahmed H. ElSheikh
Summary: This study introduces a model-free reinforcement learning framework to address the robust optimal well control problem, utilizing deep RL algorithms to learn optimal action policies based on saturation, pressure values, and valve openings. By introducing a domain randomization scheme to handle model parameter uncertainties, numerical results are presented on two subsurface flow test cases with distinct uncertainty distributions, demonstrating the robustness of the proposed RL approach when applied to unseen samples.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2022)
Article
Computer Science, Interdisciplinary Applications
Kristian Fossum, Sergey Alyaev, Jan Tveranger, Ahmed H. Elsheikh
Summary: This paper proposes a method that uses GANs for parameterization and generation of geomodels, combined with EnRML for rapid updating of subsurface uncertainty. It illustrates the predictive ability of EnRML on assimilating well log data through several examples and verifies the results statistically using MCMC.
JOURNAL OF COMPUTATIONAL SCIENCE
(2022)
Article
Astronomy & Astrophysics
Sergey Alyaev, Ahmed H. Elsheikh
Summary: This study presents a proof-of-concept approach to multi-modal probabilistic inversion of geophysical logs using a deep neural network. The proposed method provides more accurate and realistic solutions for real-time stratigraphic inversion and predicts their probabilities, enabling better real-time decisions under geological uncertainties.
EARTH AND SPACE SCIENCE
(2022)
Article
Geosciences, Multidisciplinary
Atish Dixit, Ahmed H. Elsheikh
Summary: Reinforcement learning is a promising tool for solving robust optimal well control problems. However, the reliance on a large number of simulations for learning robust control policies can be computationally intractable. To address this issue, an adaptive multigrid reinforcement learning framework is proposed, inspired by geometric multigrid methods. The framework starts with computationally efficient low-fidelity simulations and gradually increases the simulation fidelity, resulting in significant gains in computational efficiency. The effectiveness of the framework is demonstrated through case studies.
MATHEMATICAL GEOSCIENCES
(2023)
Article
Computer Science, Software Engineering
Mosayeb Shams, Ahmed H. Elsheikh
Summary: Active flow control (AFC) involves manipulating fluid flow over time to achieve a desired performance or efficiency. Reinforcement Learning (RL) can be utilized for dynamic optimization in AFC as a sequential optimization task. Gym-preCICE is introduced as a Python adapter fully compliant with Gymnasium API to facilitate designing and developing RL environments for single- and multi-physics AFC applications. Gym-preCICE uses preCICE, an open-source coupling library, for information exchange between a controller (actor) and an AFC simulation environment, providing a framework for seamless integration of RL and AFC.
Article
Water Resources
Shing Chan, Ahmed H. Elsheikh
FRONTIERS IN WATER
(2020)
Article
Mathematics, Interdisciplinary Applications
Shing Chan, Ahmed H. Elsheikh
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
(2019)
Article
Environmental Sciences
Nagoor Kani Jabarullah Khan, Ahmed H. Elsheikh
FRONTIERS IN ENVIRONMENTAL SCIENCE
(2019)
Article
Environmental Sciences
Corinna Koepke, Ahmed H. Elsheikh, James Irving
FRONTIERS IN ENVIRONMENTAL SCIENCE
(2019)