A new hybrid quantum-classical operator splitting method solves nonlinear parabolic PDEs up to 100 dimensions with provably ...

In this chapter we study one of the fundamental problems of numerical analysis, namely the numerical solutions of nonlinear equations. Most equations arising in practice are nonlinear and are rarely ...

Physics-informed neural networks (PINNs) often struggle to solve stiff partial differential equations (PDEs) with moving boundaries, such as convection-dominated droplet drying with shrinking domains ...

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 ...