This article addresses sampled-data control of 2-D Kuramoto–Sivashinsky equation over a rectangular domain $\Omega$ . We suggest to divide the into notation="LaTeX">$N$ subdomains, where sensors provide spati...

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of PDE into loss function network-based surrogate model unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained opti...

Many systems of partial differential equations are posed on all of R" and have Euclidean symmetry. These include the Navier-Stokes equations, the Boussinesq equations, the Kuramoto-Sivashinsky equation and reaction-diffusion systems (with constant diffusion coefficients). In many applications, where these and related Euclidean equivariant equations are used, time independent, spatially periodic...