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Data-driven corrections of the 1D heat equation

This repository contains the code used for my master's thesis Introducing CoSTA: A Deep Neural Network Enabled Approach to Improving Physics-Based Numerical Simulations.

Please cite the master's thesis or the related article Deep neural network enabled corrective source term approach to hybrid analysis and modeling if you publish academic works utilizing code from this repository.

File overview:

  • config.py: Main configuration file.
  • datasets.py: Used for creating training, validation and test sets.
  • determine_fine_resolution.py: Used for determining the spatial and temporal resolution required for the numerical solution to change less than some pre-determined amount as the spatial grid is refined by a factor 3 or as the temporal grid is refined by a factor 2.
  • inspect_dataset.py: Used for verifying that the data generated by datasets.py is correct.
  • inspect_systems.py: Used for visualizing the temporal development of different physical systems.
  • main.py: Main entry point for training and evaluating data-driven correction models. Supported command line options:
    • --dataset: Create new dataset.
    • --train: Train new model.
    • --test: Evaluate the performance of a trained model.
  • models.py: Defines different neural network models.
  • physics.py: The numerical solver of the 1D heat equation which is used by datasets.py to generate data.
  • test.py: Used for evaluating the performance of a trained model.
  • train.py: Used for training a model.
  • util.py: Contains various helper functions.

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Development of data-driven correction methods for the 1D heat equation.

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