Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his ...

Abstract: Based on deep neural network, elliptic partial differential equations in complex regions are solved. Accurate and effective strategies and numerical methods for elliptic partial differential ...

The 2025 Minnesota Miss Basketball winner, Jordan Ode, announced Friday that she's entering the transfer portal after her freshman season at Michigan State University. Will she be a Golden Gopher next ...

Physics-aware machine learning integrates domain-specific physical knowledge into machine learning models, leading to the development of physics-informed neural networks (PINNs). PINNs embed physical ...

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...

As an engineer, I've been following the discussion around AI and Physics-Informed Neural Networks (PINNs) with a mix of curiosity and healthy skepticism. To move beyond the hype, I decided to build ...

Artificial Intelligence (AI) has transformed how machines interact with and interpret the world, powering technologies from language models to autonomous systems. While AI is often associated with ...

This paper proposes a novel machine learning paradigm called the generative adversarial tri-model (GAT) to incorporate analytical knowledge into neural networks through a unique positive-sum game ...

This program solves the ordinary 2nd order differential equation of the (damped) mass-spring oscillator in explicit form. This equation has the form: m d²/dt² u + k d/dt u + c u = F(t). Where t is the ...

Whether it's physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to ...

Abstract: Many natural and engineering phenomena can be attributed to the ordinary differential equation problems, and Euler methods are the most commonly used for solving ordinary differential ...