A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

Perovskite solar cells offer high efficiency & low cost, but complex structures limit modeling. A new Python simulator ...

Perovskite solar cells (PSCs) have emerged as promising alternative for next generation photovoltaics due to their superior ...

Perovskite solar cells (PSCs) have emerged as promising alternative for next generation photovoltaics due to their superior power conversion efficiencies (record currently at 34.9% for ...

Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful method for solving differential equations by leveraging machine learning techniques. However, while neural ...

Abstract: In this paper, a novel approach leveraging artificial neural networks is introduced to approximate solutions for partial differential equations. The one ...

A modular framework implementing Physics-Informed Neural Networks (PINNs) with Gradient Normalization for solving differential equations including Navier-Stokes equations for crystal growth modeling.

Learn how to use Python as a vector calculator for electric fields. This video shows how to represent charges and position vectors, compute field direction and magnitude, and solve problems faster ...

In this video, we compute and visualize the electric field from two charges using Python, showing how to calculate field vectors and plot the results clearly. Perfect for learning electrostatics, ...

A Mathematician with early access to XAI Grok 4.20, found a new Bellman function for one of the problems he had been working ...

A differential equation is an equality constraining a mathematical function in relation to its derivatives over one or multiple variables. Such equations may constitute the mathematical model for a ...