In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network
(PINN) for solving partial differential equations on static and evolving surfaces. For the static …

Stress orientation information is invaluable to evaluate active tectonic forces within the
Earth's crust. The global dataset provided by the World Stress Map offers a rich resource of …

Learning operators mapping between infinite-dimensional Banach spaces via neural
networks has attracted a considerable amount of attention in recent years. In this paper, we …

Non-overlapping domain decomposition methods are natural for solving interface problems
arising from various disciplines, however, the numerical simulation requires technical …

The warming and thawing of permafrost are the primary factors that impact the stability of
embankments in cold regions. However, due to uncertainties in thermal boundaries and soil …

Green's function characterizes a partial differential equation (PDE) and maps its solution in
the entire domain as integrals. Finding the analytical form of Green's function is a non-trivial …

We present a subspace method based on neural networks (SNN) for solving the partial
differential equation with high accuracy. The basic idea of our method is to use some …

The robust and efficient numerical solution of coupled hydro-poromechanical problems is of
paramount importance in many application fields, in particular in geomechanics and …

Despite the growing popularity of physics-informed neural networks (PINNs), their
applicability in the long-time integration of partial differential equations (PDEs) remains …

In this study, we propose a novel phase field smoothing-physics informed neural network
(PFS-PINN) approach to efficiently solve partial differential equations (PDEs) with …