Implementation of PINN, based on Tensorflow GradientTape.

Based on Shota Deguchi code https://github.com/ShotaDeguchi/DN_PINN.

Introduces TeX-like input of differential equations and arbitrary names of functions (see settings.yaml example).

Requirements

Python requirements are listed in file requirements.txt.

For GPU usage install CUDA Toolkit.

Usage

Please make the following directories

• saved_weights
• best_weights
• results

in each working directory, as required by train.py, utils.py.

To train a model, run

python train.py

To define a model fill settings.yaml file the following way:

set parameters of the training

ARGS:
  epochs: 5000     # max number of epochs
  batch_size: -1   # batch size for one epoch
  patience: 1000   # number of epochs without lowering loss before early stop

set model parameters

MODEL:
  f_in : 2          # number of input variables/nodes in output layers
  f_out: 3          # number of output variables/nodes in output layer
  f_hid: 20           # width of hidden layers
  depth: 3            # number of hidden layers
  in_lb: "[0.,-1.]"   # lower bounds of input variables
  in_ub: "[1.,1.]"    # upper bounds of input variables
  act: tanh         # activation function
  seed: 0             # random seed

set number of points generated for plotting grid

NS:
  nx: [100, 100]

IN_VAR_NAMES:
 [t, x]      # names of input functions/variables to be used in loss definition

OUT_VAR_NAMES:
 [s, i, r]   # names of output functions/variables to be used in loss definition

CUSTOM_CONSTS:  # custom defined variables to be used in loss definition
  epsilon: 0.1
  gamma: 0.3
  beta: 0.5

CUSTOM_FUNCS:   # custom defined variables to be used in loss definition, should depend on input variables and may depend on other custom vars and consts
  f: 1.+ x*0
  exact: x

set collocation, border etc. conditions to be used in loss

CONDS:
  pde:                                                             # arbitrary name for condition
     eq_string:  (d/dt) s - epsilon* (d/dx)^2 s ,                  # left side, dependant on PINN output and its derivatives
                 (d/dt) i + gamma* i - epsilon* (d/dx)^2 i , 
                 (d/dt) r - gamma* i - epsilon* (d/dx)^2 r
     right_side: x*[0., 0., 0.]                                    # right side, non-dependant of PINN outputs
     point_area:  [[tmin, tmax], [xmin, xmax]]                     # limits for input variables, used to generate collocation points
     N: int(1e4)                                                   # number of collocation points generated
     ```

## Device (CPU / GPU)
`train.py` assumes the use of a GPU. To train a model on the CPU, simply change the flag parameter in `config_gpu(flag)` from `flag=0` to `flag=-1`. A short description can be found in `config_gpu.py`.