Related papers: Exploiting Extended Krylov Subspace for the Reduct…
Krylov quantum diagonalization methods have emerged as a promising use case for quantum computers. However, many existing implementations rely on controlled operations, which pose challenges to near-term quantum hardware. We introduce a…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy…
An efficient and robust linear scaling method is presented for large scale {\it ab initio} electronic structure calculations of a wide variety of materials including metals. The detailed short range and the effective long range…
Interpolatory methods offer a powerful framework for generating reduced-order models (ROMs) for non-parametric or parametric systems with time-varying inputs. Choosing the interpolation points adaptively remains an area of active interest.…
Classical model reduction techniques project the governing equations onto linear subspaces of the high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, however,…
Linear reduced-order modeling (ROM) simplifies complex simulations by approximating the behavior of a system using a simplified kinematic representation. Typically, ROM is trained on input simulations created with a specific spatial…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
Model order reduction aims to determine a low-order approximation of high-order models with least possible approximation errors. For application to physical systems, it is crucial that the reduced order model (ROM) is robust to any…
A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the…
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid…
This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…
A new method for data-driven interpolatory model reduction is presented in this paper. Using the so-called data informativity perspective, we define a framework that enables the computation of moments at given (possibly complex)…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…
The hybrid LSMR algorithm is proposed for large-scale general-form regularization. It is based on a Krylov subspace projection method where the matrix $A$ is first projected onto a subspace, typically a Krylov subspace, which is implemented…
It is shown in this paper that, almost all current prevalent iterative \mbox{methods} for solving linear system of equations can be classified as what we called extended Krylov subspace methods. In this paper a new type of iterative methods…
Phase type (PH) distributions are widely used in modeling and simulation due to their generality and analytical properties. In such settings, it is often necessary to construct a PH distribution that aligns with real-world data by matching…
We study numerical approaches to computation of spectral properties of composition operators. We provide a characterization of Koopman Modes in Banach spaces using Generalized Laplace Analysis. We cast the Dynamic Mode-Decomposition type…
Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends…