Spatial Shortcuts in Graph Neural Controlled Differential Equations
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Abstract (arXiv)
We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.
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References · 14
- 2015Deep Residual Learning for Image Recognitioncited by 52,096
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
- 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2017Neural Message Passing for Quantum Chemistrycited by 3,487
- 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
- 2020Temporal Graph Networks for Deep Learning on Dynamic Graphscited by 530
- 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
- 2022On Neural Differential Equationscited by 268
- 2019Causality for Machine Learningcited by 243
- 2019Graph Neural Ordinary Differential Equationscited by 154
- 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
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