Mapping cell development with mathematics-informed machine learning

The development of humans and other animals unfolds gradually over time, with cells taking on specific roles and functions ...
IEEE

A Complex-Valued Neural Operator for Solving 2-D Wave Equations Based on Graph Neural Networks

Abstract: In this work, we propose a complex-valued neural operator (CV-NeuralOp) based on graph neural networks (GNNs) to solve 2-D wave equations. Inspired by Green’s function method for solving ...
SciELO

Differential transformation method for solving one-space-dimensional telegraph equation

In this research, the Differential Transformation Method (DTM) has been utilized to solve the hyperbolic Telegraph equation. This method can be used to obtain the exact solutions of this equation. In ...
Live Science

'Dramatic revision of a basic chapter in algebra': Mathematicians devise new way to solve devilishly difficult equations

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...
Fabbaloo

DIMON: The AI Model That Drastically Speeds Up Solving Partial Differential Equations

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 ...
GitHub

Solving Ordinary Differential Equations Numerical Method Implementation in Python

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...
marktechpost

Newton Informed Neural Operator: A Novel Machine Learning Approach for Computing Multiple Solutions of Nonlinear Partials Differential Equations

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...
marktechpost

This Paper Unravels the Mysteries of Operator Learning: A Comprehensive Mathematical Guide to Mastering Dynamical Systems and PDEs (Partial Differential Equation) through ...

The remarkable potentials of Artificial Intelligence (AI) and Deep Learning have paved the way for a variety of fields ranging from computer vision and language modeling to healthcare, biology, and ...