This paper presents In-Context Operator Networks (ICON), a neural network approach that can learn new operators from prompted data during the inference stage without requiring any weight updates.

Inverse problems in spectral theory address the challenge of reconstructing differential operators from observed spectral data. This field, rich in both theoretical and applied mathematics, underpins ...

SIAM Journal on Applied Mathematics, Vol. 42, No. 5 (Oct., 1982), pp. 941-955 (15 pages) Slepian, Landau and Pollak found that a certain finite convolution integral operator on the real line commutes ...

Inverse problems in differential operators and spectral theory constitute a vibrant research area where one seeks to determine unknown parameters within differential equations from observed spectral ...

In this paper, we use the generalized Bernstein operator collocation method to compute weak singular kernel differential integral equations. We reconstruct the differential matrix form according to ...

ABSTRACT: In this paper, the algebraic, geometric and analytic multiplicities of an eigenvalue for linear differential operators are defined and classified. The relationships among three ...

Abstract: This paper presents the development of an operator algebra for differential systems which is useful in that it allows the transmittance methods commonly applied to linear stationary systems ...

Abstract: Using Walsh functions the solution of a linear periodic delay differential equation is approximated. The monodromy operator is then constructed based in the solution obtained. Dominant ...

ABSTRACT: We found in 2016 a few results on the conformal Killing operator in dimension n, in particular the changes of the orders of the successive compatibility conditions for n = 3, 4 or n≥ 5. They ...

https://doi.org/10.21203/rs.3.rs-3524665/v1 PPR: PPR755363 ...

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...