First, we install the PyTorch and matplotlib libraries using pip, ensuring you have the necessary tools for building neural networks and visualizing the results in your Google Colab environment. Copy ...

This repository provides some basic examples of using deep neural networks and feed-forward and LSTM-like neural networks to solve ordinary differential equations (ODEs), partial differential ...

A library for solving differential equations using neural networks based on PyTorch, used by multiple research groups around the world, including at Harvard IACS.

The paper aims to utilize an integral transform, specifically the Khalouta transform, an abstraction of various integral transforms, to address fractional differential equations using both ...

Pro golfers keep their swing path — a buzzword-y way of saying, the direction of their swing — it a pretty neutral place. Within a few degrees either side of where they're aiming. Amateur golfers?

Abstract: This paper introduces two novel methods for solving multi-order fractional differential equations using Bernstein polynomials. The first method, referred to as the fractional operational ...

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 ...