The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses
This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. H-PINN addresses challenges in convergence and accuracy when initial parameter gue...
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| Language: | English |
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Elsevier
2025-06-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X25000023 |
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| author | Yohan Chandrasukmana Helena Margaretha Kie Van Ivanky Saputra |
| author_facet | Yohan Chandrasukmana Helena Margaretha Kie Van Ivanky Saputra |
| author_sort | Yohan Chandrasukmana |
| collection | DOAJ |
| description | This paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. H-PINN addresses challenges in convergence and accuracy when initial parameter guesses are far from their actual values. The training process is divided into two phases: data fitting and parameter optimization. This phased approach is based on Hadamard’s conditions for well-posed problems, which emphasize that the uniqueness of a solution relies on the specified initial and boundary conditions. The model is trained using the Adam optimizer, along with a combined learning rate scheduler. To ensure reliability and consistency, we repeated each numerical experiment five times across three different initial guesses. Results showed significant improvements in parameter accuracy compared to the standard PINN, highlighting H-PINN’s effectiveness in scenarios with substantial deviations in initial guesses. |
| format | Article |
| id | doaj-art-c58a3a785151460d9bc8dbd7cc871a34 |
| institution | Kabale University |
| issn | 2666-657X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Examples and Counterexamples |
| spelling | doaj-art-c58a3a785151460d9bc8dbd7cc871a342025-01-31T05:12:31ZengElsevierExamples and Counterexamples2666-657X2025-06-017100175The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guessesYohan Chandrasukmana0Helena Margaretha1Kie Van Ivanky Saputra2Department of Mathematics, Universitas Pelita Harapan, M.H. Thamrin Boulevard 1100, Tangerang, 15811, IndonesiaCorresponding author.; Department of Mathematics, Universitas Pelita Harapan, M.H. Thamrin Boulevard 1100, Tangerang, 15811, IndonesiaDepartment of Mathematics, Universitas Pelita Harapan, M.H. Thamrin Boulevard 1100, Tangerang, 15811, IndonesiaThis paper presents the Hadamard-Physics-Informed Neural Network (H-PINN) for solving inverse problems in partial differential equations (PDEs), specifically the heat equation and the Korteweg–de Vries (KdV) equation. H-PINN addresses challenges in convergence and accuracy when initial parameter guesses are far from their actual values. The training process is divided into two phases: data fitting and parameter optimization. This phased approach is based on Hadamard’s conditions for well-posed problems, which emphasize that the uniqueness of a solution relies on the specified initial and boundary conditions. The model is trained using the Adam optimizer, along with a combined learning rate scheduler. To ensure reliability and consistency, we repeated each numerical experiment five times across three different initial guesses. Results showed significant improvements in parameter accuracy compared to the standard PINN, highlighting H-PINN’s effectiveness in scenarios with substantial deviations in initial guesses.http://www.sciencedirect.com/science/article/pii/S2666657X25000023PINNH-PINNCombined learning rate schedulerInverse problems of PDEHadamard’s conditions |
| spellingShingle | Yohan Chandrasukmana Helena Margaretha Kie Van Ivanky Saputra The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses Examples and Counterexamples PINN H-PINN Combined learning rate scheduler Inverse problems of PDE Hadamard’s conditions |
| title | The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses |
| title_full | The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses |
| title_fullStr | The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses |
| title_full_unstemmed | The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses |
| title_short | The Hadamard-PINN for PDE inverse problems: Convergence with distant initial guesses |
| title_sort | hadamard pinn for pde inverse problems convergence with distant initial guesses |
| topic | PINN H-PINN Combined learning rate scheduler Inverse problems of PDE Hadamard’s conditions |
| url | http://www.sciencedirect.com/science/article/pii/S2666657X25000023 |
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