Physics-informed attention-based neural network for solving non-linear partial differential equations

Understand

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs).

• PINNs are based on simple architectures, and learn the behavior of complex physical systems by optimizing the network parameters to minimize the residual of the underlying PDE.
• Current network architectures share some of the limitations of classical numerical discretization schemes when applied to non-linear differential equations in continuum mechanics.
• A paradigmatic example is the solution of hyperbolic conservation laws that develop highly localized nonlinear shock waves.