GPINN: Physics-informed Neural Network with Graph Embedding

by   Yuyang Miao, et al.
Imperial College London

This work proposes a Physics-informed Neural Network framework with Graph Embedding (GPINN) to perform PINN in graph, i.e. topological space instead of traditional Euclidean space, for improved problem-solving efficiency. The method integrates topological data into the neural network's computations, which significantly boosts the performance of the Physics-Informed Neural Network (PINN). The graph embedding technique infuses extra dimensions into the input space to encapsulate the spatial characteristics of a graph while preserving the properties of the original space. The selection of these extra dimensions is guided by the Fiedler vector, offering an optimised pathologic notation of the graph. Two case studies are conducted, which demonstrate significant improvement in the performance of GPINN in comparison to traditional PINN, particularly in its superior ability to capture physical features of the solution.


page 3

page 6

page 7


An energy-based error bound of physics-informed neural network solutions in elasticity

An energy-based a posteriori error bound is proposed for the physics-inf...

Learning the solution operator of a nonlinear parabolic equation using physics informed deep operator network

This study focuses on addressing the challenges of solving analytically ...

Graph Space Embedding

We propose the Graph Space Embedding (GSE), a technique that maps the in...

Differentiable Physics-informed Graph Networks

While physics conveys knowledge of nature built from an interplay betwee...

TROPHY: A Topologically Robust Physics-Informed Tracking Framework for Tropical Cyclones

Tropical cyclones (TCs) are among the most destructive weather systems. ...

Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

The eco-toll estimation problem quantifies the expected environmental co...

Please sign up or login with your details

Forgot password? Click here to reset