3 accepted papers
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the $i$-th neuron in a nonlinear operator layer is defined by $\mathcal O_i(u) = \sig…
Solving nonlinear partial differential equations (PDEs) with multiple solutions is essential in various fields, including physics, biology, and engineering. However, traditional numerical methods, such as finite element and finite difference methods, often face challenges when dealing with nonlinear…
Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We model such process by an interacting particle system with attractive and repulsive forces and the Allen-Cahn force arising i…