2000 character limit reached
Inverse Boundary Value and Optimal Control Problems on Graphs: A Neural and Numerical Synthesis
Published 6 Jun 2022 in cs.LG, cs.NA, and math.NA | (2206.02911v2)
Abstract: 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.
- CasADi – A software framework for nonlinear optimization and optimal control. Mathematical Programming Computation, 11(1):1–36, 2019.
- Neural ordinary differential equation control of dynamics on graphs. Physical Review Research, 4(1):013221, 2022.
- F. M. Bass. A new product growth for model consumer durables. Management science, 15(5):215–227, 1969.
- J. T. Betts. Practical methods for optimal control and estimation using nonlinear programming. SIAM, 2010.
- A simulation of a covid-19 epidemic based on a deterministic seir model. Frontiers in public health, 8:230, 2020.
- D. Centola. The spread of behavior in an online social network experiment. science, 329(5996):1194–1197, 2010.
- Grand: Graph neural diffusion. In International Conference on Machine Learning, pages 1407–1418. PMLR, 2021.
- A comparison study of deep galerkin method and deep ritz method for elliptic problems with different boundary conditions. arXiv preprint arXiv:2005.04554, 2020.
- Neural ordinary differential equations. Advances in neural information processing systems, 31, 2018.
- G. Cybenko. Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems, 2(4):303–314, 1989.
- M. Diehl and S. Gros. Numerical optimal control. Optimization in Engineering Center (OPTEC), 2011.
- Differentiable predictive control: Deep learning alternative to explicit model predictive control for unknown nonlinear systems. Journal of Process Control, 116:80–92, 2022.
- How to train your neural ode: the world of jacobian and kinetic regularization. In International Conference on Machine Learning, pages 3154–3164. PMLR, 2020.
- Inductive representation learning on large graphs. Advances in neural information processing systems, 30, 2017.
- K. Hornik. Approximation capabilities of multilayer feedforward networks. Neural networks, 4(2):251–257, 1991.
- Tackling the curse of dimensionality with physics-informed neural networks. arXiv preprint arXiv:2307.12306, 2023.
- Pontryagin differentiable programming: An end-to-end learning and control framework. Advances in Neural Information Processing Systems, 33:7979–7992, 2020.
- T. N. Kipf and M. Welling. Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907, 2016.
- Enforcing exact boundary and initial conditions in the deep mixed residual method. arXiv preprint arXiv:2008.01491, 2020.
- New product diffusion models in marketing: A review and directions for research. Journal of marketing, 54(1):1–26, 1990.
- J. Nocedal and S. J. Wright. Numerical optimization. Springer, 1999.
- Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561, 2017.
- Latent ordinary differential equations for irregularly-sampled time series. Advances in neural information processing systems, 32, 2019.
- Graph neural networks: A review of methods and applications. AI open, 1:57–81, 2020.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.