Abstract
Flood forecasting is usually performed by means of physically based models or conceptual models. Data-driven methods such as Artificial Neural Networks (ANN) are a promising solution as they can extract complex non-linear dependencies between inputs and outputs with robustness, generalization, and computational efficiency. However, the ANNs still rank below the classical method of numerical solvers for Saint Venant Equations in terms of accuracy. To bridge the accuracy gap, this work focuses on devising a Physics Informed Neural Network (PINN) model for spatial-temporal scale flood forecasting based on the Saint Venant Equations. The ANN architecture is extended to PINN with the implementation of the custom Partial Differential Equation (PDE) loss. This procedure allows to quickly steer the learning algorithm toward a true solution. A synthetic dataset was developed by performing numerical simulations of the Saint Venant Equations for training and evaluation of the PINN model. The results demonstrate that the PINN model performs better than the ANN Models and is suitable for water depth forecasting.
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Appendices
Appendix
Appendix 1: Hyperparameter Settings
Attribute | Value |
|---|---|
Activation function | ReLU |
Number of layers | 3 [19] |
Number of neurons | Gird search; (n1, n2, n3) |
Number of epochs | Early stopping |
Learning rate | 0.0001 |
Early stopping patience | 1 |
Batch size | 128 |
Optimizer | Adam |
Loss function | MSE |
Appendix 2: Grid Search Result for Best Number of Neurons in Each Layer for Every Model
Model | Grid (n1, n2, n3) |
|---|---|
ANN 1 | 5, 5, 5 |
ANN 2 | 25, 25, 5 |
PINN | 5, 5, 5 |
PINN 3s | 15, 5, 5 |
PINN 5s | 25, 15, 25 |
Appendix 3: Generated Datasets for Training, Validation and Testing for Different PINN Models with Flood Scenarios in the Legend
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Mahesh, R.B., Leandro, J., Lin, Q. (2022). Physics Informed Neural Network for Spatial-Temporal Flood Forecasting. In: Kolathayar, S., Mondal, A., Chian, S.C. (eds) Climate Change and Water Security. Lecture Notes in Civil Engineering, vol 178. Springer, Singapore. https://doi.org/10.1007/978-981-16-5501-2_7
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