Physics-informed neural operators for optimal control: A comparative study of DeepONet, fourier, and laplace neural operators

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School of Science | Master's thesis
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Date

2025-07-31

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Systems and Operations Research

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Degree programme

Master's Programme in Mathematics and Operations Research

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en

Pages

95

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Abstract

Neural operators have emerged as powerful surrogates for learning solution maps of differential equations. Yet, their application to optimal control remains underexplored. This thesis presents a unified control framework based on Physics-Informed Neural Operators (PINO) for solving parametric optimal control problems governed by ordinary differential equations. We investigate three prominent architectures - DeepONet, Fourier Neural Operator (FNO), and Laplace Neural Operator (LNO) - and train them using an unsupervised approach. The framework is benchmarked on a suite of analytically solvable control problems, including linear-quadratic regulation, oscillatory forcing, polynomial tracking, and singular arc problems. Our results reveal trade-offs across architectures: FNO achieves the fastest convergence, DeepONet excels in initial condition enforcement and prediction accuracy, while LNO provides competitive solutions on transient-rich problems. All experiments are reproducible, and the training pipeline is architecture-agnostic. This work provides the first comparative study of neural operator architectures in a PINO-based optimal control setting and offers insights into their suitability for physics-constrained learning tasks.

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Supervisor

Oliveira, Fabricio

Thesis advisor

Lundqvist, Oliver

Keywords

neural operators, optimal control, physics-informed learning, DeepONet, fourier neural operator, laplace neural operator

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https://urn.fi/URN:NBN:fi:aalto-202508196354

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[dipl] Perustieteiden korkeakoulu / SCI