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This is the materials about learning a personalized ODE integrator for some specific family.

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Personalized Algorithm Generation: A Case Study in Meta-Learning ODE Integrators

Requirements

This project uses python 3.8. Set up the project using the following step:

Install

$pip install -r requirements.txt

Test on Different Targets

Look at examples.

  • Go to the folder
    $cd examples
  • Run the training process (eg. linear traget)
    $python main_linear.py
  • Change the parameters (such as learning rate, integrator stage, targeted order and so on) in configuration file
    • For "linear target", a huge weight is multiplied on Taylor-based regularizer as a scale because this value is too small.
    • For "square_nonlinear target", we multiply an increasing weight on MSE loss and a decreasing one on Taylor-based regularizer in order to focus on different loss in the training.

See the evaluation

  • Ordercheck Run ipynb file ordercheck.
  • Plot the MSE on Van der Pol Oscillator and the Brussealtor. Run ipynb file plot error bar.
  • See the figures according to above evaluation in results.

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  • Jupyter Notebook 94.6%
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