Self-adaptive physics-informed quantum machine learning for solving differential equations
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations (DEs). In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, i...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2025-01-01
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| Series: | Machine Learning: Science and Technology |
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| Online Access: | https://doi.org/10.1088/2632-2153/ada3ab |
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| author | Abhishek Setty Rasul Abdusalamov Felix Motzoi |
| author_facet | Abhishek Setty Rasul Abdusalamov Felix Motzoi |
| author_sort | Abhishek Setty |
| collection | DOAJ |
| description | Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations (DEs). In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson’s equation, second-order linear DE, system of DEs, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order DEs. The results indicate a promising approach to the near-term evaluation of DEs on quantum devices. |
| format | Article |
| id | doaj-art-ac8d761f44f349689a716a7d5de0f093 |
| institution | Kabale University |
| issn | 2632-2153 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj-art-ac8d761f44f349689a716a7d5de0f0932025-01-13T07:32:55ZengIOP PublishingMachine Learning: Science and Technology2632-21532025-01-016101500210.1088/2632-2153/ada3abSelf-adaptive physics-informed quantum machine learning for solving differential equationsAbhishek Setty0https://orcid.org/0009-0001-4858-7985Rasul Abdusalamov1https://orcid.org/0000-0003-4988-4794Felix Motzoi2https://orcid.org/0000-0003-4756-5976Department of Continuum Mechanics, RWTH Aachen University , Aachen 52062, Germany; Forschungszentrum Jülich, Institute of Quantum Control (PGI-8) , Jülich D-52425, Germany; Institute for Theoretical Physics, University of Cologne , Cologne D-50937, GermanyDepartment of Continuum Mechanics, RWTH Aachen University , Aachen 52062, GermanyForschungszentrum Jülich, Institute of Quantum Control (PGI-8) , Jülich D-52425, Germany; Institute for Theoretical Physics, University of Cologne , Cologne D-50937, GermanyChebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations (DEs). In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson’s equation, second-order linear DE, system of DEs, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order DEs. The results indicate a promising approach to the near-term evaluation of DEs on quantum devices.https://doi.org/10.1088/2632-2153/ada3abquantum machine learningphysics-informed neural networksvariational quantum algorithmsdifferential equations |
| spellingShingle | Abhishek Setty Rasul Abdusalamov Felix Motzoi Self-adaptive physics-informed quantum machine learning for solving differential equations Machine Learning: Science and Technology quantum machine learning physics-informed neural networks variational quantum algorithms differential equations |
| title | Self-adaptive physics-informed quantum machine learning for solving differential equations |
| title_full | Self-adaptive physics-informed quantum machine learning for solving differential equations |
| title_fullStr | Self-adaptive physics-informed quantum machine learning for solving differential equations |
| title_full_unstemmed | Self-adaptive physics-informed quantum machine learning for solving differential equations |
| title_short | Self-adaptive physics-informed quantum machine learning for solving differential equations |
| title_sort | self adaptive physics informed quantum machine learning for solving differential equations |
| topic | quantum machine learning physics-informed neural networks variational quantum algorithms differential equations |
| url | https://doi.org/10.1088/2632-2153/ada3ab |
| work_keys_str_mv | AT abhisheksetty selfadaptivephysicsinformedquantummachinelearningforsolvingdifferentialequations AT rasulabdusalamov selfadaptivephysicsinformedquantummachinelearningforsolvingdifferentialequations AT felixmotzoi selfadaptivephysicsinformedquantummachinelearningforsolvingdifferentialequations |