This repository stores PINN(s) implementations in TensorFlow 2 to solve von Karman vortex streets (inverse problem, 01_von_Karman), Burgers equation (forward problem, 02_Burgers), 2D wave equation (forward problem, 03_wave), 1D diffusion equation (forward problem, 04_diffusion). Automatic differentiation, a generalization of back-propagation, is used to exploit the representation power of the conventional neural network architecture and to satisfy the govering equations, initial, and boundary conditions. This allows PINN(s) to learn the dynamics from scarce datasets / solve initial and boundary value problems, that are challenging for standard neural network architectures. While the original work builds PINNs using TensorFlow 1, the codes in this repository implement them with TensorFlow 2 for GPU-based acceleration + further acceleration provided by L-LAAF.

Further descriptions (usage, options, etc.) can be found in the corresponding directories.

1D Burgers (FDM vs. PINN)	1D diffusion (FDM vs. PINN)	2D wave (PINN)

pip install -r requirements.txt to have the identical environment as the author. Or install the following:

These codes are part of our paper ( jp / en ). Please cite us as:

@article{ShotaDEGUCHI2021,
  title={UNKNOWN PARAMETER ESTIMATION USING PHYSICS-INFORMED NEURAL NETWORKS WITH NOISED OBSERVATION DATA},
  author={Shota DEGUCHI and Yosuke SHIBATA and Mitsuteru ASAI},
  journal={Journal of Japan Society of Civil Engineers, Ser. A2 (Applied Mechanics (AM))},
  volume={77},
  number={2},
  pages={I_35-I_45},
  year={2021},
  doi={10.2208/jscejam.77.2_I_35}
}

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