This is my implementation of the Deep Conjugate Direction Method by Kaneda et al, 2023. It uses a neural network to act as a preconditioner in the Conjugate Gradient Descent Method.
Provided in src/ are the training, evaluation and data creation codes whilemodels/ contains a ready to use model.
Training data is generated from matrices found in fluid flow problems that help solve for pressure of the fluid.
Running src/create_dataset.py creates a training dataset, adding -t as a command line argument marks the data for testing to be used by src/eval.py.
A new model can be trained up with train.py.
The method holds up quite well for matrices of size 512x512 — it outperforms classical CGD up to a tested tolerance of 1e-8
as long as the test matrix is not singnificantly different from training one. In the context of fluid flow, different matrices arise from
different internal boundaries; when the test domain is about ~20-30% the resulting matrices differ enough from the training matrix
that the model lags behind classical methods.
In the plot the solid lines correspond to the results the classical and neural preconditioners on randomized domains, whereas individual points are for specific domains.