Contents

• Contents
• DeepBSDE Description
• Environment Requirements
• Quick Start
• Script Description
  • Script and Sample Code
  • Script Parameters
  • Training Process
  • Evaluation Process
• Model Description
  • Evaluation Performance
  • Inference Performance
• Description of Random Situation
• ModelZoo Homepage

DeepBSDE Description

DeepBSDE is a power of deep neural networks by developing a strategy for solving a large class of high-dimensional nonlinear PDEs using deep learning. The class of PDEs that we deal with is (nonlinear) parabolic PDEs.

paper: Han J , Arnulf J , Weinan E . Solving high-dimensional partial differential equations using deep learning[J]. Proceedings of the National Academy of Sciences, 2018:201718942-.

HJB equation

Hamilton–Jacobi–Bellman Equation which is the term curse of dimensionality was first used explicitly by Richard Bellman in the context of dynamic programming, which has now become the cornerstone in many areas such as economics, behavioral science, computer science, and even biology, where intelligent decision making is the main issue.

Environment Requirements

• Hardware(GPU)
  • Prepare hardware environment with 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, you can start training and evaluation as follows:

  # Running training example
  export CUDA_VISIBLE_DEVICES=0
  python train.py --config_path=./config/HJBLQ_config.yaml
  OR
  bash ./scripts/run_train.sh [CONFIG_YAML] [DEVICE_ID](option, default is 0)

  # Running evaluation example
  python eval.py --config_path=./config/HJBLQ_config.yaml
  OR
  bash ./scripts/run_eval.sh [CONFIG_YAML] [DEVICE_ID](option, default is 0)

Script Description

Script and Sample Code

.
├── config
│     └── HJBLQ_config.yaml    # default config for HJB equation.
├── src
│     ├── config.py            # config parse script.
│     ├── equation.py          # equation definition and dataset helper.
│     ├── eval_utils.py        # evaluation callback and evaluation utils.
│     └── net.py               # DeepBSDE network structure.
├── eval.py                    # evaluation API entry.
├── export.py                  # export models API entry.
├── README_CN.md
├── README.md
├── requirements.txt           # requirements of third party package.
└── train.py                   # train API entry.

Script Parameters

Parameters for both training and evaluation can be set in CONFIG_YAML

• config for HBJ

    # eqn config
    eqn_name: "HJBLQ"        # Equation function name.
    total_time: 1.0          # The total time of equation function.
    dim: 100                 # Hidden layer dims.
    num_time_interval: 20    # Number of interval times.
  
    # net config
    y_init_range: [0, 1]     # The y_init random initialization range.
    num_hiddens: [110, 110]  # A list of hidden layer's filter number.
    lr_values: [0.01, 0.01]  # lr_values of piecewise_constant_lr.
    lr_boundaries: [1000]    # lr_boundaries of piecewise_constant_lr.
    num_iterations: 2000     # Iterations numbers.
    batch_size: 64           # batch_size when training.
    valid_size: 256          # batch_size when evaluation.
    logging_frequency: 100   # logging and evaluation callback frequency.
  
    # other config
    device_target: "GPU"     # Device where the code will be implemented. Optional values is GPU.
    log_dir: "./logs"        # The path of log saving.
    file_format: "MINDIR"    # Export model type.

For more configuration details, please refer the yaml file ./config/HJBLQ_config.yaml.

Training Process

• Running on GPU

  python train.py --config_path=./config/HJBLQ_config.yaml > train.log 2>&1 &

• The python command above will run in the background, you can view the results through the file train.log。

  The loss value can be achieved as follows:

  epoch: 1 step: 100, loss is 245.3738
  epoch time: 26883.370 ms, per step time: 268.834 ms
  total step: 100, eval loss: 1179.300, Y0: 1.400, elapsed time: 34
  epcoh: 2 step: 100, loss is 149.6593
  epoch time: 3184.401 ms, per step time: 32.877 ms
  total step: 200, eval loss: 659.457, Y0: 1.693, elapsed time: 37
  ...
  

  After training, you'll get the last checkpoint file under the folder log_dir in config.

Evaluation Process

• Evaluation on GPU

  Before running the command below, please check the checkpoint path used for evaluation. Such as ./log/deepbsde_HJBLQ_end.ckpt

  python eval.py --config_path=./config/HJBLQ_config.yaml > eval.log  2>&1 &

  The above python command will run in the background. You can view the results through the file "eval.log". The error of evaluation is as follows:

  eval loss: 5.146923065185527, Y0: 4.59813117980957
  

Model Description

Evaluation Performance

Parameters	GPU
Model Version	DeepBSDE
Resource	NV SMX2 V100-32G
uploaded Date	7/5/2021 (month/day/year)
MindSpore Version	1.2.0
Training Parameters	step=2000, see ./config/HJBLQ_config.yaml for details
Optimizer	Adam
Loss	2.11
Speed	32ms/step
Total time	3 min
Parameters	650K
Checkpoint for Fine tuning	7.8M (.ckpt file)

Inference Performance

Parameters	GPU
Model Version	DeepBSDE
Resource	NV SMX2 V100-32G
uploaded Date	7/5/2021 (month/day/year)
MindSpore Version	1.2.0
outputs	eval loss & Y0
Y0	Y0: 4.59

Description of Random Situation

We use random in equation.py，which can be set seed to fixed randomness.

ModelZoo Homepage

Please check the official homepage.