Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …

Despite great progress in simulating multiphysics problems using the numerical
discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate …

Recent work in scientific machine learning has developed so-called physics-informed neural
network (PINN) models. The typical approach is to incorporate physical domain knowledge …

In this article, we propose physics-informed neural operators (PINO) that combine training
data and physics constraints to learn the solution operator of a given family of parametric …

The classical development of neural networks has primarily focused on learning mappings
between finite dimensional Euclidean spaces or finite sets. We propose a generalization of …

Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …

Neural networks (NNs) are currently changing the computational paradigm on how to
combine data with mathematical laws in physics and engineering in a profound way …

Here we propose a generalized space-time domain decomposition approach for the physics-
informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on …

Physics-informed neural networks (PINNs) have lately received great attention thanks to
their flexibility in tackling a wide range of forward and inverse problems involving partial …

Implicitly defined, continuous, differentiable signal representations parameterized by neural
networks have emerged as a powerful paradigm, offering many possible benefits over …