Inverse Boundary Value and Optimal Control Problems on Graphs: A Neural and Numerical Synthesis
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Abstract (arXiv)
A general setup for deterministic system identification problems on graphs with Dirichlet and Neumann boundary conditions is introduced. When control nodes are available along the boundary, we apply a discretize-then-optimize method to estimate an optimal control. A key piece in the present architecture is our boundary injected message passing neural network. This will produce more accurate predictions that are considerably more stable in proximity of the boundary. Also, a regularization technique based on graphical distance is introduced that helps with stabilizing the predictions at nodes far from the boundary.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 10 of its 23 references that are in the map. First posted on arXiv 6 Jun 2022.
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References · 10
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
- 2017Inductive Representation Learning on Large Graphscited by 6,320
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,576
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
- 2021GRAND: Graph Neural Diffusioncited by 258
- 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
- 2019Pontryagin Differentiable Programming: An End-to-End Learning and Control Frameworkcited by 52
- 2020Neural Ordinary Differential Equation Control of Dynamics on Graphscited by 24
- 2020Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systemscited by 22
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