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Contents

• DeepBSDE Description
• HJB equation
• Environment Requirements
• Quick Start
• Script Description
  • Script and Sample Code
  • Script Parameters
  • Training Process
  • Evaluation Process
• Description of Random Situation

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

The Hamilton-Jacobi-Bellman (HJB) equation is the continuous-time analog to the discrete deterministic dynamic programming algorithm, 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 key 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 on GPU

Default:

python train.py

Full command is as follows:

python train.py \
    --save_ckpt false \
    --save_ckpt_path ./checkpoints \
    --load_ckpt_path ./checkpoints/deepbsde_HJBLQ_end.ckpt \
    --log_path ./logs \
    --print_interval 100 \
    --total_time 1.0 \
    --dim 100 \
    --num_time_interval 20 \
    --y_init_range 0 1 \
    --num_hiddens 110 110 \
    --lr_values 0.01 0.01 \
    --lr_boundaries 1000 \
    --num_iterations 1001 \
    --batch_size 64 \
    --valid_size 256 \
    --sink_size 100 \
    --file_format MINDIR \
    --amp_level O0 \
    --device_id 0 \
    --mode 0

Script Description

Script and Sample Code

.
├── 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
├── config.yaml                # config file for deepbsde
├── export.py                  # export models API entry
├── README_CN.md
├── README.md
└── train.py                   # python training script
└── eval.py                    # python evaluation script

Script Parameters

Parameters for both training and evaluation can be set in config.yaml

• config for HBJ

Training Process

python train.py

The python command above will print the training process to the console:

step: 0, loss: 1225.2937, interval: 8.1262, total: 8.1262
eval loss: 4979.3413, Y0: 0.2015
step: 100, loss: 320.9811, interval: 11.70984, total: 19.2246
eval loss: 1399.8747, Y0: 1.1023
step: 200, loss: 160.01154, interval: 6.7937, total: 26.0184
eval loss: 807.4655, Y0: 1.4009
...

After training, you'll get the last checkpoint file in the save_ckpt_path directory, ./checkpoints by default .

Evaluation Process

Before running the command below, please check load_ckpt_path used for evaluation in config.yaml. An example would be ./checkpoints/deepbsde_HJBLQ_end.ckpt

python eval.py

The above python command will print the evaluation result to the console:

eval loss: 5.146923065185527, Y0: 4.59813117980957
Total time running eval 5.8552136129312079 seconds

Description of Random Situation

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