This repository contains code for the paper: "Enabling Local Neural Operators to perform Equation-Free System-Level Analysis" G. Fabiani, H. Vandecasteele, S. Goswami, C. Siettos, I.G. Kevrekidis ...
Abstract: Neural operators, such as graph neural operators (GNOs) and Fourier neural operators (FNOs), directly learn the mapping from any functional parametric dependence to the solution and have ...
ABSTRACT: In this study, we investigate a mathematical model that describes the growth dynamics of glial cells in glioma, formulated as a nonlinear partial differential equation with a ...
The parabolic equation (PE) serves as a fundamental methodology for modeling underwater acoustic propagation. The computational efficiency of this approach derives from the far-field approximation of ...
Abstract: Solving partial differential equations is a key focus of research in scientific computing. Traditional neural operator methods often face challenges in capturing both global features and ...
Most AI providers try to enhance their products by training them with both public information and user data. However, the latter method puts a privacy-conscious company like Apple in a difficult ...
Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...
Researchers have made a breakthrough in the ability to solve engineering problems. In a new paper published in Nature entitled, “A scalable framework for learning the geometry-dependent solution ...
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