Optimal control of PDEs using physics-informed neural networks

Mowlavi, Saviz; Nabi, Saleh

doi:10.1016/j.jcp.2022.111731

Cited by 32 publications

(16 citation statements)

References 42 publications

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“…We use an MIMOONets to solve the PDEs system (23). The solution operator G 1 and G 2 of f and u d can be represented as follows…”

Section: Linear Elliptic Optimal Control Problemmentioning

confidence: 99%

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Deep Multi-Input and Multi-Output Operator Networks Method for Optimal Control of Pdes

Yong

Luo

Sun

2023

Preprint

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“…We use an MIMOONets to solve the PDEs system (23). The solution operator G 1 and G 2 of f and u d can be represented as follows…”

Section: Linear Elliptic Optimal Control Problemmentioning

confidence: 99%

“…Many researchers are interested in using neural networks to replace traditional numerical methods. A methodology and a set of guidelines for solving optimal control problems with PINNs are proposed in [22,23]. Barry-Straume et al use a two-stage framework to solve PDE-constrained optimization problems [24].…”

Section: Introductionmentioning

confidence: 99%

Deep Multi-Input and Multi-Output Operator Networks Method for Optimal Control of Pdes

Yong

Luo

Sun

2023

Preprint

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“…Recently, several successes have been made in solving PDE-constrained optimal control problems with deep-learning-based approaches. For example, a physics-informed neural network (PINN) method is designed to solve optimal control problems by adding the cost functional to the standard PINN loss [34,29]. Meanwhile, deep-learning-based surrogate models [56,30] and operator learning methods [55,20] are proposed to achieve fast inference for the optimal control solution without intensive computations.…”

mentioning

confidence: 99%

“…On the one hand, neural networks enable the classic DAL framework to solve parametric problems simultaneously with the aid of random sampling rather than the discretization of the coupled spatial domain and parametric domain. On the other hand, unlike the PINN-based penalty methods [42,29,34,11], the introduction of DAL avoids directly solving the complex KKT system with various penalty terms. Numerical results will show that, AONN can obtain high precision solutions to a series of parametric optimal control problems.…”

mentioning

confidence: 99%

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AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems

Peng¹,

Xiao²,

Tang³

et al. 2023

Preprint

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Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated solutions of PDEs with different parameter settings, which is computationally prohibitive especially for problems with high-dimensional parameter spaces. Although recently proposed neural network methods make it possible to obtain the optimal solutions simultaneously for different parameters, challenges still remain when dealing with problems with complex constraints. In this paper, we propose AONN, an adjoint-oriented neural network method, to overcome the limitations of existing approaches in solving parametric optimal control problems. In AONN, the neural networks are served as parametric surrogate models for the control, adjoint and state functions to get the optimal solutions all at once. In order to reduce the training difficulty and handle complex constraints, we introduce an iterative training framework inspired by the classical direct-adjoint looping (DAL) method so that penalty terms arising from the Karush-Kuhn-Tucker (KKT) system can be avoided. Once the training is done, parameter-specific optimal solutions can be quickly computed through the forward propagation of the neural networks, which may be further used for analyzing the parametric properties of the optimal solutions. The validity and efficiency of AONN is demonstrated through a series of numerical experiments with problems involving various types of parameters.

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Physics‐Informed Neural Networks to Model and Control Robots: A Theoretical and Experimental Investigation

Liu,

Borja,

Della Santina

2024

Advanced Intelligent Systems

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This work concerns the application of physics‐informed neural networks to the modeling and control of complex robotic systems. Achieving this goal requires extending physics‐informed neural networks to handle nonconservative effects. These learned models are proposed to combine with model‐based controllers originally developed with first‐principle models in mind. By combining standard and new techniques, precise control performance can be achieved while proving theoretical stability bounds. These validations include real‐world experiments of motion prediction with a soft robot and trajectory tracking with a Franka Emika Panda manipulator.

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Optimal control of PDEs using physics-informed neural networks

Cited by 32 publications

References 42 publications

Deep Multi-Input and Multi-Output Operator Networks Method for Optimal Control of Pdes

Deep Multi-Input and Multi-Output Operator Networks Method for Optimal Control of Pdes

AONN: An adjoint-oriented neural network method for all-at-once solutions of parametric optimal control problems

Physics‐Informed Neural Networks to Model and Control Robots: A Theoretical and Experimental Investigation

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