This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...

Exact solutions of the Schrödinger equation have long provided fundamental insights into quantum mechanics by furnishing explicit analytical expressions for wave functions and energy spectra. These ...

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 ...