Were Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?

• URL: http://arxiv.org/abs/2506.04742v2
• Date: Mon, 22 Sep 2025 13:30:04 GMT
• Title: Were Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?
• Authors: Oliver G. S. Lundqvist, Fabricio Oliveira,
• Abstract summary: We show that a simple neural operator architecture, such as DeepONet, can solve multiple optimal control problems with a single physics-informed training phase and a subsequent optimization phase.<n>Our results show acceptable accuracy for practical applications and potential computational savings for more complex and higher-dimensional problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepONet, coupled with an unconstrained optimization routine, can solve multiple optimal control problems with a single physics-informed training phase and a subsequent optimization phase. We achieve this by adding a penalty term based on the differential equation residual to the cost function and computing gradients with respect to the control using automatic differentiation through the trained neural operator within an iterative optimization routine. Our results show acceptable accuracy for practical applications and potential computational savings for more complex and higher-dimensional problems.

Related papers

• Optimizing Optimizers for Fast Gradient-Based Learning [53.81268610971847]
  We lay the theoretical foundation for automating design in gradient-based learning.<n>By treating gradient loss signals as a function that translates to parameter motions, the problem reduces to a family of convex optimization problems.
  arXiv  Detail & Related papers  (2025-12-06T09:50:41Z)
• Self-Supervised Penalty-Based Learning for Robust Constrained Optimization [4.297070083645049]
  We propose a new methodology for parameterized constrained robust optimization, based on learning with a self-supervised penalty-based loss function.<n>Our approach is able to effectively learn neural network approximations whose inference time is significantly smaller than the time of traditional solvers.
  arXiv  Detail & Related papers  (2025-03-07T06:42:17Z)
• Training Neural ODEs Using Fully Discretized Simultaneous Optimization [2.290491821371513]
  Training Neural Ordinary Differential Equations (Neural ODEs) requires solving differential equations at each epoch, leading to high computational costs.<n>In particular, we employ a collocation-based, fully discretized formulation and use IPOPT-a solver for large-scale nonlinear optimization.<n>Our results show significant potential for (collocation-based) simultaneous Neural ODE training pipelines.
  arXiv  Detail & Related papers  (2025-02-21T18:10:26Z)
• Complexity-Aware Training of Deep Neural Networks for Optimal Structure Discovery [0.0]
  We propose a novel algorithm for combined unit and layer pruning of deep neural networks that functions during training and without requiring a pre-trained network to apply.<n>Our algorithm optimally trades-off learning accuracy and pruning levels while balancing layer vs. unit pruning and computational vs. parameter complexity.<n>We show that the proposed algorithm converges to solutions of the optimization problem corresponding to networks.
  arXiv  Detail & Related papers  (2024-11-14T02:00:22Z)
• Unlearning as multi-task optimization: A normalized gradient difference approach with an adaptive learning rate [105.86576388991713]
  We introduce a normalized gradient difference (NGDiff) algorithm, enabling us to have better control over the trade-off between the objectives.<n>We provide a theoretical analysis and empirically demonstrate the superior performance of NGDiff among state-of-the-art unlearning methods on the TOFU and MUSE datasets.
  arXiv  Detail & Related papers  (2024-10-29T14:41:44Z)
• Solving Functional Optimization with Deep Networks and Variational Principles [0.2633434651741688]
  We show how to leverage the calculus of variations to design deep neural networks to solve functional optimization problems.<n>Our approach is crucial when the solution is a function defined over an unknown interval or supporttextemdash such as in minimum-time control problems.<n>We show that CalVNet can be trained in an unsupervised manner, without relying on ground-truth data.
  arXiv  Detail & Related papers  (2024-10-08T18:21:35Z)
• NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition [67.46012350241969]
  This paper proposes a general acceleration methodology called NeuralStagger. It decomposing the original learning tasks into several coarser-resolution subtasks. We demonstrate the successful application of NeuralStagger on 2D and 3D fluid dynamics simulations.
  arXiv  Detail & Related papers  (2023-02-20T19:36:52Z)
• Learning to Optimize Permutation Flow Shop Scheduling via Graph-based Imitation Learning [70.65666982566655]
  Permutation flow shop scheduling (PFSS) is widely used in manufacturing systems. We propose to train the model via expert-driven imitation learning, which accelerates convergence more stably and accurately. Our model's network parameters are reduced to only 37% of theirs, and the solution gap of our model towards the expert solutions decreases from 6.8% to 1.3% on average.
  arXiv  Detail & Related papers  (2022-10-31T09:46:26Z)
• Unsupervised Optimal Power Flow Using Graph Neural Networks [172.33624307594158]
  We use a graph neural network to learn a nonlinear parametrization between the power demanded and the corresponding allocation. We show through simulations that the use of GNNs in this unsupervised learning context leads to solutions comparable to standard solvers.
  arXiv  Detail & Related papers  (2022-10-17T17:30:09Z)
• Near-optimal control of dynamical systems with neural ordinary differential equations [0.0]
  Recent advances in deep learning and neural network-based optimization have contributed to the development of methods that can help solve control problems involving high-dimensional dynamical systems. We first analyze how truncated and non-truncated backpropagation through time affect runtime performance and the ability of neural networks to learn optimal control functions.
  arXiv  Detail & Related papers  (2022-06-22T14:11:11Z)
• Joint inference and input optimization in equilibrium networks [68.63726855991052]
  deep equilibrium model is a class of models that foregoes traditional network depth and instead computes the output of a network by finding the fixed point of a single nonlinear layer. We show that there is a natural synergy between these two settings. We demonstrate this strategy on various tasks such as training generative models while optimizing over latent codes, training models for inverse problems like denoising and inpainting, adversarial training and gradient based meta-learning.
  arXiv  Detail & Related papers  (2021-11-25T19:59:33Z)
• Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning [89.31889875864599]
  We propose an efficient model-based reinforcement learning algorithm for learning in multi-agent systems. Our main theoretical contributions are the first general regret bounds for model-based reinforcement learning for MFC. We provide a practical parametrization of the core optimization problem.
  arXiv  Detail & Related papers  (2021-07-08T18:01:02Z)
• Combinatorial Optimization with Physics-Inspired Graph Neural Networks [0.0]
  We show how graph neural networks can be used to solve optimization problems. We find that the neural network performs on par or outperforms existing solvers.
  arXiv  Detail & Related papers  (2021-07-02T16:54:35Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)
• ODEN: A Framework to Solve Ordinary Differential Equations using Artificial Neural Networks [0.0]
  We prove a specific loss function, which does not require knowledge of the exact solution, to evaluate neural networks' performance. Neural networks are shown to be proficient at approximating continuous solutions within their training domains. A user-friendly and adaptable open-source code (ODE$mathcalN$) is provided on GitHub.
  arXiv  Detail & Related papers  (2020-05-28T15:34:10Z)
• Optimizing Wireless Systems Using Unsupervised and Reinforced-Unsupervised Deep Learning [96.01176486957226]
  Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems. In this article, we introduce unsupervised and reinforced-unsupervised learning frameworks for solving both variable and functional optimization problems.
  arXiv  Detail & Related papers  (2020-01-03T11:01:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.