相关论文: Optimal transfer operators in algebraic two-level …

We systematically study the parity- and time-reversal (PT) symmetric non-Hermitian version of a quantum network proposed in the paper of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)]. The nature of this model shows that it is a…

In this paper we introduce general transfer operators between high-order and low-order refined finite element spaces that can be used to couple high-order and low-order simulations. Under natural restrictions on the low-order refined space…

Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the operators map between Banach or Hilbert spaces. In this work,…

Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…

This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose new non-linear operators that preserve dynamic symmetries…

This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…

We study certain linear and antilinear symmetry generators and involution operators associated with pseudo-Hermitian Hamiltonians and show that the theory of pseudo-Hermitian operators provides a simple explanation for the recent results of…

Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric…

A general strategy is provided to identify the most general metric for diagonalizable pseudo-Hermitian and anti-pseudo-Hermitian Hamilton operators represented by two-dimensional matrices. It is investigated how a permutation of the…

In this paper, we consider the optimal design of photonic crystal band structures for two-dimensional square lattices. The mathematical formulation of the band gap optimization problem leads to an infinite-dimensional Hermitian eigenvalue…

The paper treats pseudodifferential operators $P=Op(p(\xi ))$ with homogeneous complex symbol $p(\xi )$ of order $2a>0$, generalizing the fractional Laplacian $(-\Delta )^a$ but lacking its symmetries, and taken to act on the halfspace…

While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…

We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition methods. The diffusion coefficient can be arbitrarily rough in…

We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…

We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the…

This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…

Hyperbolic-spaces are better suited to represent data with underlying hierarchical relationships, e.g., tree-like data. However, it is often necessary to incorporate, through alignment, different but related representations meaningfully.…

Motivated by the successful use of greedy algorithms for Reduced Basis Methods, a greedy method is proposed that selects N input data in an asymptotically optimal way to solve well-posed operator equations using these N data. The operator…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…

The development of fast numerical methods for multilevel radiative transfer (RT) applications often leads to important breakthroughs in astrophysics, because they allow the investigation of problems that could not be properly tackled using…