Abstract Physics-Informed Neural Networks (PINNs) and extended PINNs (XPINNs) have
emerged as a promising approach in computational science and engineering for solving …

We propose to enhance the training of physics-informed neural networks. To this aim, we
introduce nonlinear additive and multiplicative preconditioning strategies for the widely used …

Hybrid algorithms, which combine black-box machine learning methods with experience
from traditional numerical methods and domain expertise from diverse application areas, are …

We present a unified hard-constraint framework for solving geometrically complex PDEs with
neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary …

In this paper we present a Fourier feature based deep domain decomposition method (F-
D3M) for partial differential equations (PDEs). Currently, deep neural network based …

Parametric optimal control problems governed by partial differential equations (PDEs) are
widely found in scientific and engineering applications. Traditional grid-based numerical …

Physics-informed neural networks (PINNs) have shown promise in solving various partial
differential equations (PDEs). However, training pathologies have negatively affected the …

Deep learning methods have been developed to solve interface problems, benefiting from
meshless features and the ability to approximate complex interfaces. However, existing …

PDE-constrained shape optimization has been playing an important role in a large variety of
engineering applications. Traditional mesh-dependent shape optimization methods often …

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