Almost all of our knowledge of the deep Earth is obtained using such data. We have applied geometric methods to study the inverse problems related to the wave, heat, and conductivity equations, as ...

A new method, physics-informed invertible neural networks (PI-INN), addresses Bayesian inverse problems by modeling parameter fields and solution functions. PI-INN achieves accurate posterior ...

The Riemann hypothesis is the most important open question in number theory—if not all of mathematics. It has occupied experts for more than 160 years. And the problem appeared both in ...