CollisionOperatorLearning

DeepONet-based learning of the Boltzmann-type collision operator

Workflow

Training set

Generation of particle distribution

We use KiT-RT to produce a bunch of particle distribution functions. Follow the constructions in KiT-RT main repository to build the binary file. Execute the compiled binary by handing over a valid config file, e.g.,

KiT-RT config/data_generation_1d.cfg

Also, more simply, using the configuration file/data_generation_gaussian.py, you can create toy data by:

Sampling a Gaussian with random mean and random variance within a compact domain. Sampling two Gaussians with random mean and random variance and adding them together. Sampling a Gaussian with random mean and random variance, perturbing it by a polynomial amount, and adding them together. An example of the execution code would be, e.g.,

python3 toy_data_generation_gaussian.py train_300_test_300 --seed 0 --integration_order 100 --num_train 100 --num_test 100

Computation of collision integral

The code for learning the operator from the input function f to Q(f, f) using DeepONet is 'train.py'. The code for executing the training using DeepONet is as follows:

1) vanila DeepONet wo/ bias

python3 train.py 1d_3_8_3_8_wo_bias --seed 0 --gpu 0 --dimension 1 --data_file toy --integration_order 100 --model deeponet --branch_hidden 100 8 8 8 --trunk_hidden 1 8 8 8 --use_bias no --epochs 100000 --lambda 0

2) vanila DeepONet w/ bias

3) (soft constraint) DeepONet with additional orthogonal loss

python3 train.py 1d_3_8_3_8_soft_lamb01 --seed 0 --gpu 1 --dimension 1 --data_file toy --integration_order 100 --model deeponet --branch_hidden 100 8 8 8 --trunk_hidden 1 8 8 8 --use_bias vanila --epochs 100000 --lambda 0.1

4) (Hard constraint) DeepONet with gram schmidt for basis

python3 train.py 1d_3_8_3_8_hard_gram --seed 0 --gpu 2 --dimension 1 --data_file toy --integration_order 100 --model deeponet --branch_hidden 100 8 8 8 --trunk_hidden 1 8 8 8 --use_bias no --use_gram --epochs 100000 --lambda 0

5) (Hard constraint) DeepONet with special bias (depends on input function)

python3 train.py 1d_3_8_3_8_hard_special --seed 0 --gpu 3 --dimension 1 --data_file toy --integration_order 100 --model deeponet --branch_hidden 100 8 8 8 --trunk_hidden 1 8 8 8 --use_bias depend --epochs 100000 --lambda 0

DeepOnet model

DeepONet model is located in the 'model' folder. 'deeponet.py' is a modified version of the DeepONet model that adds the one additional output of the trunk net instead of the last bias term to suit our collision operator purpose.

Solution algorithm

Linear Boltzmann equation

• KiT-RT
• neuralEntropyClosures
• Kinetic.jl

Nonlinear Boltzmann equation

• Kinetic.jl