23 citations · 31 across the 9 of their papers we have counts for
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cs.LG2024★ 1 cited
Graph Neural PDE Solvers with Conservation and Similarity-Equivariance
Masanobu Horie, Naoto Mitsume
Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state co…
cs.LG2022★ 23 cited
Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions
Masanobu Horie, Naoto Mitsume
Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs)…
cs.LG2020★ 3 cited
Isometric Transformation Invariant and Equivariant Graph Convolutional Networks
Masanobu Horie, Naoki Morita, Toshiaki Hishinuma +2
Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solvin…