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Contents

• Heat Transfer PINNs Description
• Dataset
• Environment Requirements
• Quick Start
• Script Description
  • Script and Sample Code
  • Script Parameters
  • Training Process
  • Evaluation Process

Heat Transfer PINNs Description

By designing a custom loss function for standard fully-connected deep neural networks, enforcing the known laws of physics governing the different setups, work of Raissi et al. showed that it was possible to either solve or discover with surprisingly good accuracy Partial Differential Equations from noisy and scarce data. The very kind that is widespread in real-life applications.

This repository reproduces the heat transfer scenario with Physics Informed Neural Networks (PINN).

paper:Raissi M, Perdikaris P, Karniadakis G E. Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations[J]. arXiv preprint arXiv:1711.10561, 2017.

Dataset

The training dataset and pretrained checkpoint files will be downloaded automatically at the first launch.

The dataset is provided in file ./data/1d_transient_100.mat, including the following variables:

• Dataset size
  • tau: (100, 1) in [0, 1]
  • eta: (256, 1) in [-1, 1]
  • theta: (100, 256)
• Data format: .mat files
  • Note: Data will be processed in process.py
• The dataset is in the ./data directory, the directory structure is as follows:

├── data
│   └── 1d_transient_100.mat

If you need to download the dataset and checkpoint files manually, please visit this link.

Environment Requirements

• Hardware(Ascend/GPU)
  • Prepare hardware environment with Ascend or GPU processor.
• Framework
  • MindSpore
• For more information, please check the resources below:
  • MindSpore Tutorials
  • MindSpore Python API

Quick Start

After installing MindSpore via the official website and the required dataset above, you can start training and valuation as follows:

• running on Ascend or on GPU

Default:

python train.py

Full command:

python train.py \
    --layers 2 20 20 20 20 20 20 20 20 1 \
    --save_ckpt true \
    --save_fig true \
    --load_ckpt false \
    --save_ckpt_path ./checkpoints \
    --load_data_path ./data \
    --load_ckpt_path ./checkpoints/model_200adam_float32.ckpt \
    --figures_path ./figures \
    --log_path ./logs \
    --print_interval 10 \
    --ckpt_interval 10 \
    --lr 0.03 \
    --n_t 200 \
    --n_f 10000 \
    --b1 0.9 \
    --epochs 200 \
    --lbfgs false \
    --nt_epochs 200 \
    --download_data pinn_heattransfer \
    --force_download false \
    --amp_level O0 \
    --device_id 0 \
    --mode 0

Script Description

Script and Sample Code

File structures are as follows:

├── pinn_heattransfer
│   ├── checkpoints                       # checkpoints files
│   ├── data                              # data files
│   │   └── 1d_transient_100.mat          # 1d transient 100 matlab dataset
│   ├── figures                           # plot figures
│   ├── logs                              # log files
│   ├── src                               # source codes
│   │   ├── network.py                    # neural network definition
│   │   ├── plot.py                       # plotting functions
│   │   └── process.py                    # data and network preparations
│   ├── config.yaml                       # hyper-parameters configuration
│   ├── README.md                         # English model descriptions
│   ├── README_CN.md                      # Chinese model description
│   ├── train.py                          # python training script
│   └── eval.py                           # python evaluation script

Script Parameters

Training Process

• running on GPU/Ascend

  python train.py

  The loss values during training will be printed in the console, which can also be inspected after training in log file.

  # grep "loss:" log
  step: 0, loss: 1.1074585, interval: 23.024836778640747s, total: 23.024836778640747s
  step: 10, loss: 0.24028176, interval: 29.892443895339966s, total: 52.91728067398071s
  step: 20, loss: 0.2183091, interval: 29.853577613830566s, total: 82.77085828781128s
  step: 30, loss: 0.14730139, interval: 29.850199937820435s, total: 112.62105822563171s
  step: 40, loss: 0.068295084, interval: 29.85150957107544s, total: 142.47256779670715s
  step: 50, loss: 0.045247488, interval: 29.851693391799927s, total: 172.32426118850708s
  step: 60, loss: 0.093925714, interval: 29.878837823867798s, total: 202.20309901237488s
  step: 70, loss: 0.04949145, interval: 29.850360870361328s, total: 232.0534598827362s
  ...

• After training, you can still review the training process through the log file saved in log_path, ./logs directory by default.

• The model checkpoint will be saved in save_ckpt_path, ./checkpoint directory by default.

Evaluation Process

Before running the command below, please check the checkpoint loading path load_ckpt_path specified in config.yaml for evaluation.

• running on GPU/Ascend

  python eval.py

  You can view the process and results through the log_path, ./logs by default. The result pictures are saved in figures_path, ./figures by default.