Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

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 ...

Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

The radiative transfer phenomenon is modeled by an integro-differential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the ...

We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a "full" model. We propose a ...

This project demonstrates the implementation of Physics-Informed Neural Networks (PINNs) using TensorFlow to solve differential equations, specifically focusing on the Helmholtz equation. PINNs ...

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential ...

ABSTRACT: It is well known that the system (1 + 1) can be unequal to 2, because this system has both observation error and system error. Furthermore, we must provide ...