repository·main·Indexed 18 days ago
https://github.com/lu-group/deeponet-fnoA research repository providing implementations and datasets for comparing DeepONet and Fourier Neural Operators (FNO) across scientific computing benchmarks. It includes code and data for problems such as the Advection equation, Burgers' equation, Darcy problems (rectangular and triangular domains), linear instability waves, Navier-Stokes, and Euler equations. The repository features FNO1d and FNO2d architectures, spectral convolution implementations, and utilities for data normalization and loading from MAT or H5 files.
The dataset for the Darcy problem in a triangular domain with a notch is hosted externally. You can access the data files via the following SharePoint link:
https://yaleedu-my.sharepoint.com/:f:/g/personal/lu_lu_yale_edu/Ei-oRTd9XvBEjwdAqOl1kUYBr2cGoeiJigfL1yuvS1mzaw?e=vUoqEbThe repository provides datasets for three variations of the Advection equation. These datasets are hosted externally on SharePoint and can be accessed via the following links:
The dataset for the Darcy problem in a rectangular domain (piecewise constant) is sourced from the original Fourier Neural Operator repository. You can download the data via the provided SharePoint link.
Note: This data is specifically for the piecewise constant version of the Darcy problem in a rectangular domain.
Data Link: https://yaleedu-my.sharepoint.com/:f:/g/personal/lu_lu_yale_edu/Ei-oRTd9XvBEjwdAqOl1kUYBr2cGoeiJigfL1yuvS1mzaw?e=vUoqEbThe Burgers' equation dataset used in this repository is sourced from the original Fourier Neural Operator implementation. You can download the data via the provided SharePoint link.
Data Link: https://yaleedu-my.sharepoint.com/:f:/g/personal/lu_lu_yale_edu/Ei-oRTd9XvBEjwdAqOl1kUYBr2cGoeiJigfL1yuvS1mzaw?e=vUoqEbThe repository is organized into datasets and corresponding code implementations for several scientific problems. You can find specific implementations in the src/ directory and their associated data in the data/ directory.
data/burgers and src/burgersdata/darcy_rectangular_pwc and src/darcy_rectangular_pwcdata/darcy_triangular_notch and src/darcy_triangular_notchsrc/advection_II_IIIdata/instability_wave and src/instability_waveOther problems available (check directories for specific code/data):
When setting up an FNO2d model, consider the following hyperparameter constraints observed in the implementation:
modes1 & modes2: These define the number of Fourier modes used in the spectral convolution. They should be chosen based on the grid resolution (e.g., modes1 $\le$ $n_t$, modes2 $\le$ $n_x/2 + 1$).width: The hidden channel dimension. Increasing width increases model capacity but significantly increases memory usage. For example, a width of 64 is used in the reference implementation, but higher values may cause Out-of-Memory (OOM) errors on consumer GPUs.FNO2d uses self.fc0 = nn.Linear(3, self.width), meaning it expects an input with 3 channels (typically representing the coefficient function, spatial coordinates, and time).The DeepONet architecture in this implementation is defined by the following parameters:
p): The dimension of the Branch and Trunk net outputs (default: 100).layer_B): Defines the structure of the Branch network. Example: [num, 128, 128, p] where num is the input dimension.layer_T): Defines the structure of the Trunk network. Example: [2, 128, 128, 128, p] where 2 represents the input coordinates (x, y).h): The number of points used for resolution (default: num).bs): Number of samples per training step (default: 100).nx): The number of spatial points for the Trunk net (default: 2295).20000).This script implements a POD-based (Proper Orthogonal Decomposition) DeepONet training pipeline for the Darcy triangular notch problem. It uses a hybrid architecture where a CNN processes input functions (branch net) and combines them with a pre-computed POD basis to reconstruct the solution field.
DataSet to generate minibatches and compute the POD basis.FNN (Feedforward Neural Network) and a CNN (Convolutional Neural Network) that maps input functions to coefficients.u_basis using tf.einsum to predict the full solution field.AdamOptimizer to minimize the mean squared error between the predicted and ground truth solution fields.SaveData to persist results.The script uses several hardcoded hyperparameters that define the network architecture and data dimensions:
p: Output dimension of Branch/Trunk.modes: Number of POD modes.s, s_in: Dimensions for the FNN layers.layer_B: Dimensions for the Branch net output layers.h, w: Resolution for the CNN input.bs: Batch size.nx: Size of the input for the Trunk net.tensorflow.compat.v1)dataset, fnn, conv, savedataimport os
# Set GPU device
os.environ['CUDA_VISIBLE_DEVICES']='1'
# The script is executed as a standalone training entrypoint
if __name__ == "__main__":
main()