Related papers: Robust Matrix-Free Newton-Krylov Solvers via Autom…
In this work, we consider a class of dynamical systems described by ordinary differential equations under the assumption that the global asymptotic stability (GAS) of equilibrium points is established based on the Lyapunov stability theory…
We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of…
We introduce a quadratically convergent semismooth Newton method for nonlinear semidefinite programming that eliminates the need for the generalized Jacobian regularity, a common yet stringent requirement in existing approaches. Our…
With the steady advance of high performance computing systems featuring smaller and smaller hardware components, the systems and algorithms used for numerical simulations increasingly contend with disruptions caused by hardware failures and…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
This project aims to advance differentiable fluid dynamics for hypersonic coupled flow over porous media, demonstrating the potential of automatic differentiation (AD)-based optimization for end-to-end solutions. Leveraging AD efficiently…
Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the…
We present \texttt{DR-DAQP}, an open-source solver for strongly monotone affine variational inequaliries that combines Douglas-Rachford operator splitting with an active-set acceleration strategy. The key idea is to estimate the active set…
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in…
A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in…
Understanding why gradient-based training in deep networks exhibits strong implicit bias remains challenging, in part because tractable singular-value dynamics are typically available only for balanced deep linear models. We propose an…
We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as…
We show that, under certain circumstances, it is possible to automatically compute Jacobian-inverse-vector and Jacobian-inverse-transpose-vector products about as efficiently as Jacobian-vector and Jacobian-transpose-vector products. The…
In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza…
Training recurrent neural networks (RNNs) remains a challenge due to the instability of gradients across long time horizons, which can lead to exploding and vanishing gradients. Recent research has linked these problems to the values of…