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Frequent Directions, as a deterministic matrix sketching technique, has been proposed for tackling low-rank approximation problems. This method has a high degree of accuracy and practicality, but experiences a lot of computational cost for…

In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…

Assessing IC manufacturing process fluctuations and their impacts on IC interconnect performance has become unavoidable for modern DSM designs. However, the construction of parametric interconnect models is often hampered by the rapid…

We introduce two novel interpolatory dynamical low-rank (DLR) approximation methods for the efficient time integration of the Boltzmann-BGK equation. Both methods overcome limitations of classic DLR schemes based on orthogonal projections…

New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…

A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…

This work proposes a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations. The proposed…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is…

The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity.…

This paper presents a single-life reinforcement learning (SLRL) approach to adaptively select the dimension of the Krylov subspace during the generalized minimal residual (GMRES) iteration. GMRES is an iterative algorithm for solving large…

This study investigates computationally efficient algorithms for solving discrete-time infinite-horizon single-agent/multi-agent dynamic models with continuous actions. It shows that we can easily reduce the computational costs by slightly…

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…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

We present a reduced basis stochastic Galerkin method for partial differential equations with random inputs. In this method, the reduced basis methodology is integrated into the stochastic Galerkin method, resulting in a significant…

Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…

We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…

The paper introduces CycleIK, a neuro-robotic approach that wraps two novel neuro-inspired methods for the inverse kinematics (IK) task, a Generative Adversarial Network (GAN), and a Multi-Layer Perceptron architecture. These methods can be…