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
Meteorology & Atmospheric Sciences
Changhong Mou, Leslie M. Smith, Nan Chen
Summary: In this study, a hybrid data assimilation algorithm is developed for complex dynamical systems and applied to a precipitating quasi-geostrophic (PQG) model. The algorithm combines machine learning with a cheap stochastic parameterized extended Kalman filter (SPEKF) model to efficiently estimate the unobserved state variables. The algorithm shows robustness and low computational cost.
JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS
(2023)
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
Rakesh Halder, Krzysztof J. Fidkowski, Kevin J. Maki
Summary: The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods. However, for some nonlinear problems, linear RB methods are not efficient. Nonlinear manifolds have shown increased performance for certain nonlinear problems over linear methods. In this work, a non-intrusive ROM framework is proposed that uses convolutional autoencoders to provide a nonlinear solution manifold and is augmented by Gaussian process regression (GPR) to approximate the expansion coefficients of the reduced model.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Energy & Fuels
S. Bhavsar, R. Pitchumani, M. A. Ortega-Vazquez
Summary: This work presents a novel and efficient method to generate statistically accurate scenarios from probabilistic forecasts and reduce the number of scenarios using unsupervised machine learning, while preserving the statistical properties of the original set. The approach yields statistically equivalent characteristics as a full set with a substantially reduced cardinality and preserves the temporal correlation in time-series data.
Article
Engineering, Multidisciplinary
Mohammad Hossein Naderi, Hessam Babaee
Summary: Stochastic reduced-order modeling based on time-dependent bases has been successful in capturing low-dimensional manifold from stochastic partial differential equations (SPDEs). A new adaptive sparse interpolation algorithm is proposed to enable stochastic ROMs to achieve computational efficiency for nonlinear SPDEs. The algorithm constructs a low-rank approximation for the SPDE using the DEIM method, and it does not require any offline computation, allowing it to adapt to transient changes on-the-fly. The algorithm achieves computational speedup by adaptive sampling of the state and random spaces, resulting in significant reduction in computational cost for various test cases.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Computer Science, Interdisciplinary Applications
Pia Stammer, Lucas Burigo, Oliver Jaekel, Martin Frank, Niklas Wahl
Summary: Fast and accurate predictions of uncertainties in computed dose are crucial for radiation therapy treatment plans. Monte Carlo methods are commonly used to solve particle transport problems with uncertain parameters, but traditional solution strategies become infeasible due to long run-times. We propose a new non-intrusive approach for uncertainty quantification in dose calculations, which supports almost arbitrary error correlation models.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Yinling Zhang, Nan Chen, Curt A. Bronkhorst, Hansohl Cho, Robert Argus
Summary: This paper presents a data-driven statistical reduced-order modeling framework for predicting the deformation process of porosity-based ductile damage in polycrystalline metallic materials, with uncertainty quantification. The framework computes the time evolution of the leading few moments of specific state variables from full-field polycrystal simulations and utilizes a sparse model identification algorithm to discover the governing equations. The predicted moments are then used to obtain an approximate solution of the time evolution of the probability density function (PDF) using the maximum entropy principle. Numerical experiments demonstrate the effectiveness of the model in characterizing the non-Gaussian PDF and quantifying extreme events.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Computer Science, Interdisciplinary Applications
Pierre Jacquier, Azzedine Abdedou, Vincent Delmas, Azzeddine Soulaimani
Summary: Deep Learning research is rapidly growing and can bring benefits to older fields like Computational Fluid Dynamics. This study compares methods for uncertainty quantification in Deep Neural Networks and applies them to engineering problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yihang Gao, Michael K. Ng
Summary: This paper investigates a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) to quantify uncertainty in solutions of partial differential equations. The network generators learn the uncertainty from the observed initial/boundary data using specific activation functions in the adversarial network discriminators. Numerical results validate the effectiveness of the proposed method, but further research is needed to improve the accuracy of uncertainty quantification.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Wenqian Chen, Qian Wang, Jan S. Hesthaven, Chuhua Zhang
Summary: A reduced basis method based on a physics-informed machine learning framework, using neural networks to model parametrized partial differential equations, achieves more accurate and efficient results compared to traditional methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Geochemistry & Geophysics
John M. Rekoske, Alice-Agnes Gabriel, Dave A. May
Summary: Physics-based simulations of earthquake ground motion can be time-consuming, limiting their applicability to real-time solutions or ensembles of solutions. To address this, we present a reduced-order modeling approach using interpolated proper orthogonal decomposition to predict peak ground velocities (PGVs). Testing against an independent data set, we found that the radial basis function interpolation gives the lowest error (= 0.1 cm/s). The reduced-order model proves to be 10(7)-10(8) times faster than the wave propagation simulations.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2023)
Article
Environmental Sciences
Amir H. Kohanpur, Siddharth Saksena, Sayan Dey, J. Michael Johnson, M. Sadegh Riasi, Lilit Yeghiazarian, Alexandre M. Tartakovsky
Summary: Estimating uncertainty in flood model predictions is crucial for various applications. This study focuses on uncertainty in physics-based urban flooding models, considering model complexity, uncertainty in input parameters, and the effects of rainfall intensity. The ICPR model is used to quantify floodwater depth prediction uncertainty, with results showing localized uncertainties. Model simplifications lead to overconfident predictions, while increasing model resolution reduces uncertainty but increases computational cost. The multilevel MC method is employed to reduce cost when estimating uncertainty in a high-resolution ICPR model. Utilizing ensemble estimates, the proposed framework improves flood depth forecasting accuracy compared to the ICPR model's mean prediction, even with limited measurements.
WATER RESOURCES RESEARCH
(2023)
Article
Computer Science, Interdisciplinary Applications
Christian Perron, Darshan Sarojini, Dushhyanth Rajaram, Jason Corman, Dimitri Mavris
Summary: This work applies a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method to effectively fuse high-dimensional displacements and stress fields in structural analysis. The proposed approach leverages manifold alignment to combine outputs from high- and low-fidelity simulations, achieving higher predictive accuracy at a lower computational cost.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Multidisciplinary
Xinshuai Zhang, Tingwei Ji, Fangfang Xie, Hongyu Zheng, Yao Zheng
Summary: This study proposes a novel compressed sensing reduced-order modeling framework for predicting unsteady flow fields from sparse and noisy sensor measurements. The framework includes an offline learning stage using Long Short Term Memory (LSTM) model and sparsity-promoting Dynamic Mode Decomposition (DMD) algorithm, and an online forecasting stage using Deep Neural Network (DNN) to establish correlations and predict flow fields accurately.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
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)