Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330385 
Year of Publication: 
2025
Citation: 
[Journal:] Operations Research Forum [ISSN:] 2662-2556 [Volume:] 6 [Issue:] 4 [Article No.:] 153 [Publisher:] Springer International Publishing [Place:] Cham [Year:] 2025
Publisher: 
Springer International Publishing, Cham
Abstract: 
The good choice of hyperparameters is crucial for the successful application of deep learning (DL) networks in order to find accurate solutions or the best parameter in solving partial differential equations (PDEs), that are sensitive to errors in coefficient estimation. For this purpose, hyperparameter optimization of multi-output physics-informed neural networks (HOMO-PINNs) is based on the optimal search of PINN hyperparameters for solving PDEs with uncertain coefficients in the uncertainty quantification (UQ) field. By testing this novel methodology on different PDEs, the relationship between activation functions, the number of output neurons, and the degree of coefficient uncertainty can be observed. The experimental results show that adding output neurons to the neural network (NN), even if a theoretically incorrect activation function is chosen, keeps the predicted solution accurate.
Subjects: 
Physics-informed neural network
Numerical methods
PDE
Uncertainty quantification
PINN
Hyperparameter optimization
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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