mlsanityData to 7 Oct 2026

KANtrol: A Physics-Informed Kolmogorov-Arnold Network Framework for Solving Multi-Dimensional and Fractional Optimal Control Problems

arXiv 2409.06649 ↗First posted 10 Sep 2024math.OC cs.LG cs.NAcited by 3

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Abstract (arXiv)

In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the integral parts within the problem, particularly for integro-differential state equations. We also demonstrate how automatic differentiation is utilized to compute exact derivatives for integer-order dynamics, while for fractional derivatives of non-integer order, we employ matrix-vector product discretization within the KAN framework. We tackle multi-dimensional problems, including the optimal control of a 2D heat partial differential equation. The results of our simulations, which cover both forward and parameter identification problems, show that the KANtrol framework outperforms classical MLPs in terms of accuracy and efficiency.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 28 of its 80 references that are in the map. First posted on arXiv 10 Sep 2024.

Builds on

28 of 80 references.

References · 28

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  3. 2015Automatic differentiation in machine learning: a surveycited by 846
  4. 2019Variational Physics-Informed Neural Networks For Solving Partial Differential Equationscited by 144
  5. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 82
  6. 2024Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networkscited by 64
  7. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  8. 2021Physics-Informed Neural Networks for AC Optimal Power Flowcited by 52
  9. 2021Optimal control of PDEs using physics-informed neural networkscited by 51
  10. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
  11. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  12. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
16 more
  1. 2021Implicit energy regularization of neural ordinary-differential-equation controlcited by 29
  2. 2016Real-time optimal control via Deep Neural Networks: study on landing problemscited by 27
  3. 2020Solving inverse-PDE problems with physics-aware neural networkscited by 27
  4. 2024Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KANcited by 25
  5. 2022Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equationscited by 20
  6. 2022Physics-informed neural networks for PDE-constrained optimization and controlcited by 19
  7. 2024Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamicscited by 14
  8. 2023AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problemscited by 12
  9. 2023deepFDEnet: A Novel Neural Network Architecture for Solving Fractional Differential Equationscited by 7
  10. 2023A Comparison of Mesh-Free Differentiable Programming and Data-Driven Strategies for Optimal Control under PDE Constraintscited by 6
  11. 2024Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problemscited by 6
  12. 2022Physics-informed ConvNet: Learning Physical Field from a Shallow Neural Networkcited by 5
  13. 2016Fractional Calculus In Image Processing: A Reviewcited by 3
  14. 2023Solving Elliptic Optimal Control Problems via Neural Networks and Optimality Systemcited by 3
  15. 2024Accelerating Fractional PINNs using Operational Matrices of Derivativecited by 3
  16. 2024PINNIES: An Efficient Physics-Informed Neural Network Framework to Integral Operator Problemscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 0; 2026: 1.

3 papers.

  1. 2024On the Convergence of (Stochastic) Gradient Descent for Kolmogorov--Arnold Networkscited by 0
  2. 2024CIKAN: Constraint Informed Kolmogorov-Arnold Networks for Autonomous Spacecraft Rendezvous using Time Shift Governorcited by 0
  3. 2026High-Fidelity Modeling of Stochastic Chemical Dynamics on Complex Manifolds: A Multi-Scale SIREN-PINN Framework for the Curvature-Perturbed Ginzburg-Landau Equationcited by 0