This is the source code repository for the Data-Centric Engineering paper "Incomplete to complete multiphysics forecasting - a hybrid approach for learning unknown phenomena" by Nilam Tathawadekar, Nguyen Anh Khoa Doan, Camilo F. Silva, Nils Thuerey: Full Paper
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete partial differential equations (PDE) solver that provides known, but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network – PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network - PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization, and allows for larger simulation time steps.
- TensorFlow 1.15
- PhiFlow 1.5.0
We recommend installing via pip, e.g., with pip install tensorflow-gpu==1.15 phiflow==1.5.0
A makefile is included in a folder of each scenario. Running the scripts will generate training and test datasets, train a model and apply it to the test datasets. The repository includes all the scenarios discussed in the paper - Planar-v0, uniform-Bunsen, nonUniform-Bunsen32 and nonUniform-Bunsen100. Here, we provide an example with the nonUniform-Bunsen32 case, all other scenarios include similar files.
You can generate the training and testing datasets by running:
make nonUniform-Bunsen32-react-set # Generate training datasets
make nonUniform-Bunsen32-react-testset # Generate test datasets
This will create 300 time steps of training data for 12 different non-uniform inlet velocity excitations. Similarly, 12 test datasets are generated with different inlet velocity excitations. Here is a visualization of 2 training examples:
The hybrid NN-PDE model can be trained for m=2 using the following command.
make NU-Bunsen32-hyb-unet-sol2 # Train a model
The hybrid NN-PDE model can be trained for m=32 using the following command.
make NU-Bunsen32-hyb-unet-sol32 # Train a model
The model is initialized using the weights of the model with m=2 for stable training. This is done by using --resume option in the training file. NU-Bunsen32-hyb-unet-sol32/tf folder is created and the dataStats.pickle and model_epoch100.h5 files obtained by running m=2 model are copied into it. solver_class_train_new.py includes the PhiFlow implementation of the non-reactive flow solver.
The trained neural network model can be used to predict the flame evolution at test conditions using the following command:
make NU-Bunsen32-hyb-unet-sol32/run_test # Run test
Given the initial conditions for temperature and mass fraction fields, it predicts the flame evolution over 300 time steps. It creates .npz files for temperature, mass fraction fields and velocity in NU-Bunsen32-hyb-unet-sol32/run_test folder for all testsets. Here is an example of the comparison between the output obtained using the trained hybrid NN-PDE solver with the ground truth data:
The codes related to the baseline method of purely data-driven (PDD) approach discussed in our paper are also included for each scenario in the respective directory. The PDD model can be trained and tested using -pdd- commands in respective makefiles.
If you find the approach useful, please cite our paper via:
@article{tathawadekar2022incomplete,
title={Incomplete to complete multiphysics forecasting-a hybrid approach for learning unknown phenomena},
author={Tathawadekar, Nilam Nandkishor and Doan, Nguyen Anh Khoa and Silva, Camilo Fernando and Thuerey, Nils},
year={2022}
}
This work was supported by the ERC Consolidator Grant SpaTe (CoG-2019-863850).
Here is a visualization of different flame dynamics predicted using the hybrid NN-PDE approach.
