Abstract: Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), ...

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 ...

Learn how to classify PDEs,and apply and visualize characteristic and finite difference solution methods. You can use these live scripts as demonstrations in lectures, class activities, or interactive ...

Abstract: Curved spaces, such as surfaces, provide a rich setting for the study of partial differential equations (PDEs). Building upon the extensive research conducted on PDEs in flat spaces, the ...

Differential equations are equations that involve an unknown function and its derivatives with respect to one or more independent variables. They play a fundamental role in various fields of science, ...

The fractional-order nonlinear Gardner and Cahn–Hilliard equations are often used to model ultra-short burst beams of light, complex fields of optics, photonic transmission systems, ions, and other ...

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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.

Our numerical results show the capability of a single neural network as a few-shot operator learner for a diversified type of differential equation problems, including forward and inverse problems of ...