Abstract: Dynamic equations provide mathematical frameworks to capture the evolving behavior of systems, which is essential in various fields. While the zeroing neural network (ZNN) is one of the most ...

The original version of this story appeared in Quanta Magazine. At the turn of the 20th century, the renowned mathematician David Hilbert had a grand ambition to bring a more rigorous, mathematical ...

Abstract: Simulation of radar sounder (RS) data is important for understanding the radar response of subsurface features to facilitate the interpretation of the real data. Conventional electromagnetic ...

For the conventional staggered-grid finite-difference scheme (C-SFD), although the spatial finite-difference (FD) operator can reach 2M th-order accuracy, the FD discrete wave equation is the only ...

Arterial baroreflex assessment using vasoactive substances enables investigators to collect data pairs over a wide range of blood pressures and reflex reactions. These data pairs relate intervals ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

In many physical systems, the governing equations are known with high confidence, but direct numerical solution is prohibitively expensive. Often this situation is alleviated by writing effective ...

Werner Heisenberg won the 1932 Nobel Prize for helping to found the field of quantum mechanics and developing foundational ideas like the Copenhagen interpretation and the uncertainty principle. The ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense. The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous ...