Related papers: Lagrange approximation of transfer operators assoc…
This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale,…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
This paper presents reconstructions of homogeneous targets from the 2D and 3D Fresnel databases by one-step imaging methods based on the computation of topological derivative and topological energy fields. The electromagnetic inverse…
The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…
The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
A random phase property establishing a link between quasi-one-dimensional random Schroedinger operators and full random matrix theory is advocated. Briefly summarized it states that the random transfer matrices placed into a normal system…
Machine learning interatomic potentials trained on first-principles reference data are becoming valuable tools for computational physics, biology, and chemistry. Equivariant message-passing neural networks, including transformers, achieve…
We propose a data-driven interpolation method for approximating real-valued functions on smooth manifolds, based on the Laplace--Beltrami operator and Voronoi tessellations. Given pointwise evaluations, the method constructs a continuous…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
A method for solving spectral problems for the Sturm-Liouville equation $(pv^{\prime})^{\prime}-qv+\lambda rv=0$ based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The…
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential…
We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…
An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of…
We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two…
This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…
Motivated by the success of Sinkhorn's algorithm for entropic optimal transport, we study convergence properties of iterative proportional fitting procedures (IPFP) used to solve more general information projection problems. We establish…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
Motivated by Fredholm theory, we develop a framework to establish the convergence of spectral methods for operator equations $\mathcal L u = f$. The framework posits the existence of a left-Fredholm regulator for $\mathcal L$ and the…
Holographic representations of data encode information in packets of equal importance that enable progressive recovery. The quality of recovered data improves as more and more packets become available. This progressive recovery of the…