Partial Differential Equations (PDEs) are mathematical equations that involve unknown multivariate functions and their partial derivatives. They are the cornerstone of modelling a vast array of ...

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 ...

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) ...

Partial differential equations (PDE) describe the behavior of fluids, structures, heat transfer, wave propagation, and other physical phenomena of scientific and engineering interest. This course ...

Notice: This repository is no longer under active maintenance. It is highly recommended to utilize implementations of Physics-Informed Neural Networks (PINNs) available in PyTorch, JAX, and TensorFlow ...

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various ...

An advanced course in the analytical and numerical study of ordinary and partial differential equations, building on techniques developed in Differential Equations I. Ordinary differential equations: ...

Abstract: In this paper, the controllability property for Caputo fractional delay Partial Random Differential Equations (PRDE) in Banach space are investigated. By utilizing the principles from ...