Article
Engineering, Mechanical
Earl Dowell
Summary: This paper provides a personal account of the importance and significance of reduced-order models (ROM) in computational modeling. ROMs reduce the size and cost of the original model without losing accuracy. The motivation for creating a ROM is not only to reduce computational cost, but also to study a wider range of parameters and facilitate the interpretation of results, advancing our understanding of the model and the physical phenomena it describes.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Multidisciplinary
P. Solan-Fustero, J. L. Gracia, A. Navas-Montilla, P. Garcia-Navarro
Summary: In this study, a Roe-based reduced-order model is developed to efficiently solve the shallow water equations with source terms, compared to the Roe-based full-order model. The augmented Riemann solvers are used to consider the well-balanced property, entropy fix, and wet-dry treatment in constructing the Roe-based full-order model. Additionally, a time averaging approach is necessary for developing the Roe-based reduced-order model. The approach is validated through solving test cases and comparing the computed solutions with those of Lax-Friedrichs-based reduced-order models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Clement Vella, Serge Prudhomme
Summary: In this paper, a Proper Generalized Decomposition (PGD) approach for problems in linear elastodynamics is proposed. The novelty lies in the development of weak formulations based on Lagrangian and Hamiltonian Mechanics, aiming to devise numerically stable and energy conservative methods. The Galerkin-based version of PGD is considered and it is shown that the PGD solver based on the Hamiltonian formulation offers better stability and energy conservation properties compared to the Lagrangian formulation. The performance of the two formulations is illustrated and compared on several numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Geochemistry & Geophysics
Liliana Borcea, Josselin Garnier, Alexander V. Mamonov, Jorn Zimmerling
Summary: We propose a novel approach to waveform inversion using a data-driven reduced order model (ROM). This method can be applied to acoustic, elastic, or electromagnetic waves. By minimizing the misfit between the ROM computed from recorded data and the ROM computed from modeled data, we solve the inverse problem of velocity estimation. We demonstrate the effectiveness of the ROM misfit objective function compared to the least-squares data fit objective function, which displays multiple local minima even with a poor initial guess.
Article
Computer Science, Interdisciplinary Applications
Murat Uzunca, Buelent Karasoezen
Summary: Reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schrodinger equation (NLSE) with and without damping. The full-order solutions are obtained using different numerical methods for the conservative and dissipative ALE. The reduced-order solutions are constructed intrusively using proper orthogonal decomposition (POD) with Galerkin projection, and the computation is accelerated by the use of tensor techniques and discrete empirical interpolation method (DEIM).
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mechanics
AmirPouya Hemmasian, Amir Barati Farimani
Summary: Reduced-order modeling (ROM) is an active area of research in fluid flows, where more efficient alternative methods like ROMs and surrogate models have been developed to overcome the high computational cost of direct numerical simulations. Machine learning and data-driven methods, similar to other application areas, have played an important role in the development of novel models for fluid dynamics. In this study, the capability of the state-of-the-art deep learning architecture, transformer, is investigated for learning the dynamics of fluid flows in a ROM framework. A convolutional autoencoder is used for dimensionality reduction, and a transformer model is trained to learn the system's dynamics in the encoded state space. The model shows competitive results even for turbulent datasets.
Article
Computer Science, Interdisciplinary Applications
Quincy A. Huhn, Mauricio E. Tano, Jean C. Ragusa, Youngsoo Choi
Summary: Dynamic Mode Decomposition (DMD) is a model-order reduction technique that extracts spatial modes of fixed temporal frequencies from numerical or experimental data. This paper presents two novel approaches to parametric DMD: one based on interpolation of the reduced-order DMD eigen-pair and the other based on interpolation of the reduced DMD (Koopman) operator. Numerical results are provided for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. The three parametric DMD approaches are compared.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Zhong Du, Yan-Peng Ma
Summary: This paper investigates beak-shaped rogue waves in a higher-order coupled nonlinear Schrodinger system, obtaining corresponding solutions through the construction of Lax pairs and Darboux transformations, and observes changes in the characteristics of beak-shaped rogue waves along the space axis with increasing real parameters.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Multidisciplinary
David R. Brandyberry, Xiang Zhang, Philippe H. Geubelle
Summary: This paper proposes a two-step optimization method for the design of multiscale heterogeneous materials with nonlinear macroscopic response driven by volumetric and interfacial damage at the microstructural level. The method includes a reduced-order design phase using Eigendeformation-based reduced-order Homogenization Method (EHM) and a high-fidelity optimization phase using Interface-Enriched Generalized Finite Element Method (IGFEM).
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Mengwu Guo, Shane A. McQuarrie, Karen E. Willcox
Summary: This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. The study formulates the task of learning a reduced-order model as a Bayesian inverse problem, with a Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, enabling predictions with uncertainty. The method estimates statistical moments of the predictions through efficient Monte Carlo sampling.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
R. Reyes, O. Ruz, C. Bayona-Roa, E. Castillo, A. Tello
Summary: This paper presents a parametrized projection-based model reduction approach for time-dependent generalized Newtonian fluids in a computational framework. The authors use an offline-online setting with proper orthogonal and Tucker decompositions, along with finite element method and finite differences for discretization, and variational multiscale approach for stabilization. The reduced method is evaluated through numerical tests.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics
Ahmed B. Khoshaim, Muhammad Naeem, Ali Akgul, Nejib Ghanmi, Shamsullah Zaland
Summary: In this study, the rho-homotopy perturbation transformation method was applied to analyze fifth-order nonlinear fractional KdV equations, demonstrating its validity and efficiency, as well as showing that the solutions for fractional and integer orders converge to the exact results. The technique was successfully utilized for various engineering and science models, proving to be accurate and easy to use.
JOURNAL OF MATHEMATICS
(2022)
Article
Physics, Applied
Li Chen, Shu-Fang Deng
Summary: The study investigates the Darboux transformation for the supersymmetric nonisospectral KdV equation. Using the Lax pair, the one-fold, two-fold, and three-fold Darboux transformations for the equation are successfully constructed. Furthermore, the n-fold Darboux transformation is presented in the form of a superdeterminant.
MODERN PHYSICS LETTERS B
(2021)
Article
Engineering, Aerospace
Brandon M. Lowe, David W. Zingg
Summary: This paper introduces a model order reduction framework for flutter-constrained aircraft optimization. By linearizing the Euler equations around a steady-state solution, a linear reduced-order model with fewer degrees of freedom is constructed and coupled with a linear structural model to form a monolithic aeroelastic system. The onset of flutter is determined by analyzing the eigenvalues of the resulting system, and the use of a stabilizing inner product is demonstrated to ensure the stability of the model.
Article
Chemistry, Physical
Nathan J. Szymanski, Zhengyan Lun, Jue Liu, Ethan C. Self, Christopher J. Bartel, Jagjit Nanda, Bin Ouyang, Gerbrand Ceder
Summary: Pair distribution function (PDF) analysis is a powerful technique for characterizing short-range order (SRO) in disordered materials. This study outlines an approach to model SRO using first-principles calculations based on the cluster-expansion formalism and validates it on neutron scattering data from two disordered rocksalt oxyfluorides. The results demonstrate the importance of considering local variations in site occupancies and bond lengths in accurately interpreting experimental PDF data.
CHEMISTRY OF MATERIALS
(2023)
Article
Computer Science, Interdisciplinary Applications
Ludovic Boilevin-Kayl, Miguel A. Fernandez, Jean-Frederic Gerbeau
COMPUTERS & FLUIDS
(2019)
Article
Engineering, Biomedical
Fabien Raphel, Muriel Boulakia, Nejib Zemzemi, Yves Coudiere, Jean-Michel Guillon, Philippe Zitoun, Jean-Frederic Gerbeau
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING
(2018)
Meeting Abstract
Gastroenterology & Hepatology
C. Audebert, P. Bucur, M. Bekheit, N. Boissier, D. Drasdo, J. -F. Gerbeau, E. Vibert, I. Vignon-Clementel
JOURNAL OF HEPATOLOGY
(2018)
Article
Biology
Jean-Frederic Gerbeau, Damiano Lombardi, Eliott Tixier
MATHEMATICAL BIOSCIENCES
(2018)
Article
Mathematics, Applied
Jean-Frederic Gerbeau, Damiano Lombardi, Eliott Tixier
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2018)
Article
Physiology
Eliott Tixier, Fabien Raphel, Damiano Lombardi, Jean-Frederic Gerbeau
FRONTIERS IN PHYSIOLOGY
(2018)
Meeting Abstract
Pharmacology & Pharmacy
Eliott Tixier, Fabien Raphel, Damiano Lombardi, Philippe Zitoun, Jean-Frederic Gerbeau
JOURNAL OF PHARMACOLOGICAL AND TOXICOLOGICAL METHODS
(2018)
Article
Engineering, Biomedical
Alexandre This, Ludovic Boilevin-Kayl, Miguel A. Fernandez, Jean-Frederic Gerbeau
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
(2020)
Article
Mathematics, Applied
Annabelle Collin, Sebastien Imperiale, Philippe Moireau, Jean-Frederic Gerbeau, Dominique Chapelle
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2019)
Meeting Abstract
Hematology
Nguyen-Peyre Kim-Anh, Laurene Lenoir, Valentin Amar, Frederic Segonds, Nuriye Akcay, Seguin Marion, Philippe Connes, France Pirenne, Jean-Frederic Gerbeau, Irene Vignon-Clementel, Suzanne Verlhac, Pablo Bartolucci
Article
Engineering, Multidisciplinary
Alexandre This, Hernan G. Morales, Odile Bonnefous, Miguel A. Fernandez, Jean-Frederic Gerbeau
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Cardiac & Cardiovascular Systems
Julien Ratelade, Nicholas R. Klug, Damiano Lombardi, Monara Kaelle Servulo Cruz Angelim, Fabrice Dabertrand, Valerie Domenga-Denier, Rustam Al-Shahi Salman, Colin Smith, Jean-Frederic Gerbeau, Mark T. Nelson, Anne Joutel
Article
Biochemical Research Methods
Fabien Raphel, Tessa De Korte, Damiano Lombardi, Stefan Braam, Jean-Frederic Gerbeau
PLOS COMPUTATIONAL BIOLOGY
(2020)
Article
Engineering, Multidisciplinary
Felipe Galarce, Jean-Frederic Gerbeau, Damiano Lombardi, Olga Mula
Summary: This paper discusses the problem of reconstructing blood flows using Doppler ultrasound measurements and introduces a fast and reliable method. The study found that constructing reduced spaces better adapted to the reconstruction task can improve the performance of the algorithm.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Ludovic Boilevin-Kayl, Miguel A. Fernandez, Jean-Frederic Gerbeau
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2019)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
