Neural networks are increasingly used to construct numerical solution methods for partial
differential equations. In this expository review, we introduce and contrast three important …

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics,
thermal/electronic transport, electromagnetism, and optics. Topology optimization is an …

In this work we investigate the possibility of using physics-informed neural networks (PINNs)
to approximate the Euler equations that model high-speed aerodynamic flows. In particular …

Recently, the advent of deep learning has spurred interest in the development of physics-
informed neural networks (PINN) for efficiently solving partial differential equations (PDEs) …

In this paper, we employ the emerging paradigm of physics-informed neural networks
(PINNs) for the solution of representative inverse scattering problems in photonic …

Abstract Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system
discovery that has been shown to successfully recover governing dynamical systems from …

The various studies of partial differential equations (PDEs) are hot topics of mathematical
research. Among them, solving PDEs is a very important and difficult task. Since many …

The Fokker--Planck (FP) equation governing the evolution of the probability density function
(PDF) is applicable to many disciplines, but it requires specification of the coefficients for …

Over the last few decades, existing Partial Differential Equation (PDE) solvers have
demonstrated a tremendous success in solving complex, non-linear PDEs. Although …

We introduce multi-head neural networks (MH-NNs) to physics-informed machine learning,
which is a type of neural networks (NNs) with all nonlinear hidden layers as the body and …