Nature

Generative discovery of partial differential equations by learning from math handbooks

Data-driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data-driven techniques face the ...
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 ...