Hessam Babaee
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View article: A CUR Krylov Solver for Large-Scale Linear Matrix Equations
A CUR Krylov Solver for Large-Scale Linear Matrix Equations Open
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for s…
View article: Multi-fidelity framework and uncertainty quantification for thermal conductivities of aluminum alloys
Multi-fidelity framework and uncertainty quantification for thermal conductivities of aluminum alloys Open
Building surrogate models to predict thermal conductivity as a function of composition and temperature is essential for a wide range of applications from material design and optimization to uncertainty quantification. However, experimental…
View article: Optimally time-dependent modes of vortex gust–airfoil interactions
Optimally time-dependent modes of vortex gust–airfoil interactions Open
We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the u…
View article: Optimally time-dependent modes of vortex gust-airfoil interactions
Optimally time-dependent modes of vortex gust-airfoil interactions Open
We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the u…
View article: Time-dependent low-rank input–output operator for forced linearized dynamics with unsteady base flows
Time-dependent low-rank input–output operator for forced linearized dynamics with unsteady base flows Open
Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the…
View article: CUR for Implicit Time Integration of Random Partial Differential Equations on Low-Rank Matrix Manifolds
CUR for Implicit Time Integration of Random Partial Differential Equations on Low-Rank Matrix Manifolds Open
Dynamical low-rank approximation allows for solving large-scale matrix differential equations (MDEs) with significantly fewer degrees of freedom and has been applied to a growing number of applications. However, most existing techniques re…
View article: Reconstructing blood flow in data-poor regimes: a vasculature network kernel for Gaussian process regression
Reconstructing blood flow in data-poor regimes: a vasculature network kernel for Gaussian process regression Open
Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, transcranial Doppler ultrasound is a non-invasive clinical t…
View article: Skeletal Kinetics Reduction for Astrophysical Reaction Networks
Skeletal Kinetics Reduction for Astrophysical Reaction Networks Open
A novel methodology is developed to extract accurate skeletal reaction models for nuclear combustion. Local sensitivities of isotope mass fractions with respect to reaction rates are modeled based on the forced optimally time-dependent (f-…
View article: Cross Interpolation for Solving High-Dimensional Dynamical Systems on Low-Rank Tucker and Tensor Train Manifolds
Cross Interpolation for Solving High-Dimensional Dynamical Systems on Low-Rank Tucker and Tensor Train Manifolds Open
We present a novel tensor interpolation algorithm for the time integration of nonlinear tensor differential equations (TDEs) on the tensor train and Tucker tensor low-rank manifolds, which are the building blocks of many tensor network dec…
View article: Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression
Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression Open
Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive clini…
View article: A DEIM Tucker Tensor Cross Algorithm and its Application to Dynamical Low-Rank Approximation
A DEIM Tucker Tensor Cross Algorithm and its Application to Dynamical Low-Rank Approximation Open
We introduce a Tucker tensor cross approximation method that constructs a low-rank representation of a $d$-dimensional tensor by sparsely sampling its fibers. These fibers are selected using the discrete empirical interpolation method (DEI…
View article: Time-Dependent Low-Rank Input-Output Operator for Forced Linearized Dynamics with Unsteady Base Flows
Time-Dependent Low-Rank Input-Output Operator for Forced Linearized Dynamics with Unsteady Base Flows Open
Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the…
View article: Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases
Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases Open
Time-dependent basis reduced-order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For many practical problems of interest, discretizing these PDEs…
View article: Oblique projection for scalable rank-adaptive reduced-order modeling of nonlinear stochastic PDEs with time-dependent bases
Oblique projection for scalable rank-adaptive reduced-order modeling of nonlinear stochastic PDEs with time-dependent bases Open
Time-dependent basis reduced order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For many practical problems of interest, discretizing these PDEs…
View article: Learning stiff chemical kinetics using extended deep neural operators
Learning stiff chemical kinetics using extended deep neural operators Open
We utilize neural operators to learn the solution propagator for the challenging chemical kinetics equation. Specifically, we apply the deep operator network (DeepONet) along with its extensions, such as the autoencoder-based DeepONet and …
View article: Constant Diffusion Burgers Code from Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with
Constant Diffusion Burgers Code from Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with Open
MATLAB code to solve the stochastic Burgers equation using TDB-CUR with oversampling
View article: Constant Diffusion Burgers Code from Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with
Constant Diffusion Burgers Code from Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with Open
MATLAB code to solve the stochastic Burgers equation using TDB-CUR with oversampling
View article: Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases
Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases Open
Stochastic reduced-order modeling based on time-dependent bases (TDBs) has proven successful for extracting and exploiting low-dimensional manifold from stochastic partial differential equations (SPDEs). The nominal computational cost of s…
View article: Skeletal Reaction Models for Methane Combustion
Skeletal Reaction Models for Methane Combustion Open
A local-sensitivity-analysis technique is employed to generate new skeletal reaction models for methane combustion from the foundational fuel chemistry model (FFCM-1). The sensitivities of the thermo-chemical variables with respect to the …
View article: Scalable In Situ Compression of Transient Simulation Data Using Time-Dependent Bases
Scalable In Situ Compression of Transient Simulation Data Using Time-Dependent Bases Open
Large-scale simulations of time-dependent problems generate a massive amount of data and with the explosive increase in computational resources the size of the data generated by these simulations has increased significantly. This has impos…
View article: Reduced Order Modeling of Turbulence-Chemistry Interactions using Dynamically Bi-Orthonormal Decomposition
Reduced Order Modeling of Turbulence-Chemistry Interactions using Dynamically Bi-Orthonormal Decomposition Open
The performance of the dynamically bi-orthogonal (DBO) decomposition for the reduced order modeling of turbulence-chemistry interactions is assessed. DBO is an on-the-fly low-rank approximation technique, in which the instantaneous composi…