相关论文: Scalable matrix-free adaptive product-convolution …
Spike deconvolution is the problem of recovering the point sources from their convolution with a known point spread function, which plays a fundamental role in many sensing and imaging applications. In this paper, we investigate the local…
In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
The transparent boundary condition for the free Schr\"{o}dinger equation on a rectangular computational domain requires implementation of an operator of the form $\sqrt{\partial_t-i\triangle_{\Gamma}}$ where $\triangle_{\Gamma}$ is the…
Roll-to-roll (R2R) manufacturing requires precise tension and velocity control under operational constraints. Model predictive control demands gradient computation, while sampling-based methods like MPPI struggle with hard constraint…
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
We consider the nonlinear inverse problem of learning a transition operator $\mathbf{A}$ from partial observations at different times, in particular from sparse observations of entries of its powers…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
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.…
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of…
We study an abstract family of asymptotically degenerating variational problems. Those are natural generalisations of families of problems emerging upon application of a rescaled Floquet-Bloch-Gelfand transform to resolvent problems for…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an updated greedy algorithm for the minimization of a suitable…
Adaptive sampling with interpolation-based trust regions or ASTRO-DF is a successful algorithm for stochastic derivative-free optimization with an easy-to-understand-and-implement concept that guarantees almost sure convergence to a…
Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g. the Helmholtz…
This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…
In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…