From 6deae68f120b38060479fc47855668c4225afc55 Mon Sep 17 00:00:00 2001 From: thivin Date: Mon, 29 Jul 2024 13:35:34 +0530 Subject: [PATCH] Joss Paper Corrections - 1 - Added the minimal API documentation to the main documentation page - Made corrections as per the [review](https://github.com/openjournals/joss-reviews/issues/6764) --- docs/index.rst | 33 ++++++++++++++++++++- joss/jats/paper.jats | 69 ++++++++++--------------------------------- joss/paper.md | 56 ++--------------------------------- joss/paper.pdf | Bin 345730 -> 317564 bytes 4 files changed, 49 insertions(+), 109 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index 60a22f3..37fad19 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -41,6 +41,7 @@ FastVPINNs is a robust tensor-based framework for solving partial differential e The framework is based on the work by `FastVPINNs Paper `_. hp-Variational PINNs were originally proposed in the `hp-VPINNs Paper `_. + Statement of Need ~~~~~~~~~~~~~~~~~ The FastVPINNs Python package addresses two main challenges in existing hp-VPINNs implementations. Current hp-VPINNs implementations suffer from computational inefficiency, with training times scaling linearly as the number of elements within the domain increases. Additionally, the existing implementation cannot handle complex computational domains that consist of skewed quadrilateral elements. @@ -49,7 +50,6 @@ FastVPINNs relies on two novel contributions to address these limitations. First The enhancements provided by FastVPINNs, including faster training times and the ability to handle complex geometries, enable broader application of the hp-VPINNs framework to real-world problems in various scientific fields. - hp-Variational Physics-informed neural network ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -60,6 +60,37 @@ For more details on the theory and implementation of hp-VPINNs, please refer to .. image:: images/vpinns.png :alt: VPINNs Image +Usage +~~~~~ + +The package provides a simple API to train and solve PDE using VPINNs. The following code snippet demonstrates how to train a hp-VPINN model for the 2D Poisson equation for a structured grid using less than 6 API calls to the FastVPINNs library. + +.. code-block:: python + + #load the geometry + domain = Geometry_2D("quadrilateral", "internal", 100, 100, "./") + cells, boundary_points = domain.generate_quad_mesh_internal(x_limits=[0, 1],y_limits=[0, 1],n_cells_x=4, n_cells_y=4, num_boundary_points=400) + + # load the FEspace + fespace = Fespace2D(domain.mesh,cells,boundary_points,domain.mesh_type,fe_order=5,fe_type="jacobi",quad_order=5,quad_type="legendre", fe_transformation_type="bilinear",bound_function_dict=bound_function_dict,bound_condition_dict=bound_condition_dict, + forcing_function=rhs,output_path=i_output_path,generate_mesh_plot=True) + + # Instantiate Data handler + datahandler = DataHandler2D(fespace, domain, dtype=tf.float32) + + # Instantiate the model with the loss function for the model + model = DenseModel(layer_dims=[2, 30, 30, 30, 1],learning_rate_dict=0.01,params_dict=params_dict, + loss_function=pde_loss_poisson, ## Loss function of poisson2D + input_tensors_list=[in_tensor, dir_in, dir_out], + orig_factor_matrices=[datahandler.shape_val_mat_list,datahandler.grad_x_mat_list, datahandler.grad_y_mat_list], + force_function_list=datahandler.forcing_function_list, tensor_dtype=tf.float32, + use_attention=i_use_attention, ## Archived (not in use) + activation=i_activation, + hessian=False) + + # Train the model + for epoch in range(1000): + model.train_step() .. toctree:: :maxdepth: 3 diff --git a/joss/jats/paper.jats b/joss/jats/paper.jats index 0fc1da3..402daa4 100644 --- a/joss/jats/paper.jats +++ b/joss/jats/paper.jats @@ -323,8 +323,8 @@ a Creative Commons Attribution 4.0 International License (CC BY We have also shown that with proper hyperparameter selection, FastVPINNs can outperform PINNs both in terms of accuracy and training time, especially for problems with high frequency solutions.

-

Our FastVPINNs framework is built using - TensorFlow-v2.0(Abadi +

Our FastVPINNs framework is built using TensorFlow-v2.0 + (Abadi et al., 2015), and provides an elegant API for users to solve both forward and inverse problems for PDEs like the Poisson, Helmholtz and Convection-Diffusion equations. With the current level of API @@ -426,58 +426,13 @@ a Creative Commons Attribution 4.0 International License (CC BY Minimal Working Example

With the higher level of abstraction provided by the FastVPINNs - framework, users can solve a PDE with just six API calls. Shown below - is a minimal working example to solve the Poisson equation using the - FastVPINNs framework.

- #load the geometry -domain = Geometry_2D("quadrilateral", "internal", - 100, 100, "./") -cells, boundary_points = - domain.generate_quad_mesh_internal(\ - x_limits=[0, 1], y_limits=[0, 1],\ - n_cells_x=4, n_cells_y=4,\ - num_boundary_points=400) - -# Note: Users need to provide the necessary -# boundary values and the forcing function - -# load the FEspace -fespace = Fespace2D(domain.mesh,cells,boundary_points,\ - domain.mesh_type,fe_order=5,\ - fe_type="jacobi",quad_order=5,\ - quad_type="legendre", \ - fe_transformation_type="bilinear"\ - bound_function_dict=bound_function_dict,\ - bound_condition_dict=bound_condition_dict,\ - forcing_function=rhs,\ - output_path=i_output_path,\ - generate_mesh_plot=True) - -# Instantiate Data handler -dh = datahandler2D(fespace, domain, dtype=tf.float32) - -# Instantiate the model with the loss function for the model -model = DenseModel(layer_dims=[2, 30, 30, 30, 1],\ - learning_rate_dict=0.01,params_dict=params_dict, - ## Loss function of poisson2D - loss_function=pde_loss_poisson, - input_tensors_list=\ - [in_tensor, - dir_in, - dir_out], - orig_factor_matrices=\ - [dh.shape_val_mat_list, - dh.grad_x_mat_list, - dh.grad_y_mat_list], - force_function_list=dh.forcing_function_list,\ - tensor_dtype=tf.float32, - use_attention=i_use_attention, - activation=i_activation, - hessian=False) - -# Train the model -for epoch in range(1000): - model.train_step() + framework, users can solve a PDE with just six API calls. A Minimal + working example to solve the Poisson equation using the FastVPINNs + framework ca be found + here. + The example files with detailed documentation can be found in the + Tutorials + section of the documentation.

Testing @@ -529,6 +484,7 @@ for epoch in range(1000): Elsevier 2019 378 + 10.1016/j.jcp.2018.10.045 686 707 @@ -554,6 +510,7 @@ for epoch in range(1000): FastVPINNs: Tensor-driven acceleration of VPINNs for complex geometries 2024 https://arxiv.org/abs/2404.12063 + 10.48550/arXiv.2404.12063 @@ -568,6 +525,7 @@ for epoch in range(1000): Elsevier 2021 374 + 10.1016/j.cma.2020.113547 113547 @@ -582,6 +540,7 @@ for epoch in range(1000): Variational physics-informed neural networks for solving partial differential equations arXiv preprint arXiv:1912.00873 2019 + 10.48550/arXiv.1912.00873 @@ -631,6 +590,7 @@ for epoch in range(1000): TensorFlow: Large-scale machine learning on heterogeneous systems 2015 https://www.tensorflow.org/ + 10.48550/arXiv.1603.04467 @@ -642,6 +602,7 @@ for epoch in range(1000): Finite elements: Theory and algorithms Cambridge University Press 2017 + 10.1017/9781108235013 diff --git a/joss/paper.md b/joss/paper.md index b2d0ae4..3882a12 100644 --- a/joss/paper.md +++ b/joss/paper.md @@ -84,7 +84,7 @@ Where $K_k$ is the $k^{th}$ element in the domain, $v_k$ is the test function in The existing implementation of hp-VPINNs framework [@hp_vpinns_github] suffers from two major challenges. One being the inabilty of the framework to handle complex geometries and the other being the increased training time associated with the increase in number of elements within the domain. In the work [@anandh2024fastvpinns], we presented FastVPINNs, which addresses both of these challenges. FastVPINNs handles complex geometries by using bilinear transformation, and it uses a tensor-based loss computation to reduce the dependency of training time on number of elements. The current implementation of FastVPINNs can acheive an speed-up of upto a 100 times when compared with the existing implementation of hp-VPINNs. We have also shown that with proper hyperparameter selection, FastVPINNs can outperform PINNs both in terms of accuracy and training time, especially for problems with high frequency solutions. -Our FastVPINNs framework is built using TensorFlow-v2.0[@tensorflow2015-whitepaper], and provides an elegant API for users to solve both forward and inverse problems for PDEs like the Poisson, Helmholtz and Convection-Diffusion equations. With the current level of API abstraction, users should be able to solve PDEs with less than six API calls as shown in the minimal working example section. The framework is well-documented with examples, which can enable users to get started with the framework with ease. +Our FastVPINNs framework is built using TensorFlow-v2.0 [@tensorflow2015-whitepaper], and provides an elegant API for users to solve both forward and inverse problems for PDEs like the Poisson, Helmholtz and Convection-Diffusion equations. With the current level of API abstraction, users should be able to solve PDEs with less than six API calls as shown in the minimal working example section. The framework is well-documented with examples, which can enable users to get started with the framework with ease. The ability of the framework to allow users to train a hp-VPINNs to solve a PDE both faster and with minimal code, can result in widespread application of this method on several real-world problems, which often require complex geometries with a large number of elements within the domain. @@ -120,59 +120,7 @@ This module contains custom subclasses of the `tensorflow.keras.Model` class, wh # Minimal Working Example {#sec:minimal-working-example} -With the higher level of abstraction provided by the FastVPINNs framework, users can solve a PDE with just six API calls. Shown below is a minimal working example to solve the Poisson equation using the FastVPINNs framework. - -```python -#load the geometry -domain = Geometry_2D("quadrilateral", "internal", - 100, 100, "./") -cells, boundary_points = - domain.generate_quad_mesh_internal(\ - x_limits=[0, 1], y_limits=[0, 1],\ - n_cells_x=4, n_cells_y=4,\ - num_boundary_points=400) - -# Note: Users need to provide the necessary -# boundary values and the forcing function - -# load the FEspace -fespace = Fespace2D(domain.mesh,cells,boundary_points,\ - domain.mesh_type,fe_order=5,\ - fe_type="jacobi",quad_order=5,\ - quad_type="legendre", \ - fe_transformation_type="bilinear"\ - bound_function_dict=bound_function_dict,\ - bound_condition_dict=bound_condition_dict,\ - forcing_function=rhs,\ - output_path=i_output_path,\ - generate_mesh_plot=True) - -# Instantiate Data handler -dh = datahandler2D(fespace, domain, dtype=tf.float32) - -# Instantiate the model with the loss function for the model -model = DenseModel(layer_dims=[2, 30, 30, 30, 1],\ - learning_rate_dict=0.01,params_dict=params_dict, - ## Loss function of poisson2D - loss_function=pde_loss_poisson, - input_tensors_list=\ - [in_tensor, - dir_in, - dir_out], - orig_factor_matrices=\ - [dh.shape_val_mat_list, - dh.grad_x_mat_list, - dh.grad_y_mat_list], - force_function_list=dh.forcing_function_list,\ - tensor_dtype=tf.float32, - use_attention=i_use_attention, - activation=i_activation, - hessian=False) - -# Train the model -for epoch in range(1000): - model.train_step() -``` +With the higher level of abstraction provided by the FastVPINNs framework, users can solve a PDE with just six API calls. A Minimal working example to solve the Poisson equation using the FastVPINNs framework ca be found [here](https://cmgcds.github.io/fastvpinns/#usage). 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