Nonlinear partial differential equations (PDEs) characterise a wide range of complex phenomena in science and engineering, from fluid dynamics to signal processing in biomedical systems. In recent ...

We consider a specific type of nonlinear partial differential equation (PDE) that appears in mathematical finance as the result of solving some optimization problems. We review some examples of such ...

Partial differential equations (PDEs) lie at the heart of many different fields of Mathematics and Physics: Complex Analysis, Minimal Surfaces, Kähler and Einstein Geometry, Geometric Flows, ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

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 ...