相关论文: A Preconditioned Multiple Shooting Shadowing Algor…

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…

Model Predictive Control (MPC) has established itself as the primary methodology for constrained control, enabling autonomy across diverse applications. While model fidelity is crucial in MPC, solving the corresponding optimization problem…

The computation of a few singular triplets of large, sparse matrices is a challenging task, especially when the smallest magnitude singular values are needed in high accuracy. Most recent efforts try to address this problem through…

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…

Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…

Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…

This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…

Preconditioning of a linear system obtained from spectral discretization of time-dependent PDEs often results in a full matrix which is expensive to compute and store specially when the problem size increases. A matrix-free implementation…

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…

We propose the use of preconditioning in FCIQMC which, in combination with perturbative estimators, greatly increases the efficiency of the algorithm. The use of preconditioning allows a time step close to unity to be used (without…

Solving systems of Boolean equations is a fundamental task in symbolic computation and algebraic cryptanalysis, with wide-ranging applications in cryptography, coding theory, and formal verification. Among existing approaches, the Boolean…

It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent…

The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the…

This paper presents a novel Sliding Mode Control (SMC) algorithm to handle mismatched uncertainties in systems via a novel Self-Learning Disturbance Observer (SLDO). A computationally efficient SLDO is developed within a framework of…

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their scalability…

We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…