Complex Hessian equations extend the classical framework of the complex Monge–Ampère equation by involving the m-th elementary symmetric function of the eigenvalues of the complex Hessian. This ...

Recent decades have witnessed a bloom in research at the interface of complex geometry and nonlinear partial differential equations. This interdisciplinary field explores the deep and intricate ...

The team has improved the capabilities of physics-informed neural networks (PINNs), a type of artificial intelligence that incorporates physical laws into the learning process. Researchers from the ...

A research team at Duke University has developed a new AI framework that can uncover simple, understandable rules that govern some of the most complex dynamics found in nature and technology. The AI ...

In theory, almost any aspect of the physical world can be modeled and analyzed mathematically. In practice though, performing the mathematical manipulations required to perform an analysis can rapidly ...

A team of engineers has proven that their analog computing device, called a memristor, can complete complex, scientific computing tasks while bypassing the limitations of digital computing. A team of ...