Nature

An improved data-free surrogate model for solving partial differential equations using deep neural networks

Partial differential equations (PDEs) are ubiquitous in natural science and engineering problems. Traditional discrete methods for solving PDEs are usually time-consuming and labor-intensive due to ...
Nature

Physics-informed attention-based neural network for hyperbolic partial differential equations: application to the Buckley–Leverett problem

Physics-informed neural networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs) and are in principle capable of ...