Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly ...

The study of chemotaxis, the directed movement of cells or organisms in response to chemical gradients, is fundamentally linked to the development and analysis of partial differential equations (PDEs) ...

A partial differential equation (PDE) is a mathematical equation that involves multiple independent variables, an unknown function that is dependent on those variables, and partial derivatives of the ...

We were always taught that the fundamental passive components were resistors, capacitors, and inductors. But in 1971, [Leon Chua] introduced the idea of a memristor — a sort of resistor with memory.

Engineers at the University of Pennsylvania have introduced 'Mollifier Layers,' an AI-based method to solve inverse partial differential equations (PDEs), enabling scientists to infer hidden system ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

We consider a specific type of nonlinear partial differential equation (PDE) that appears in mathematical finance as the result of solving some optimization problems. We review some examples of such ...

SIAM Journal on Numerical Analysis, Vol. 44, No. 5 (2006), pp. 1801-1828 (28 pages) ...