PINA/tutorials/tutorial11/tutorial.py

#!/usr/bin/env python
# coding: utf-8

# # Tutorial: PINA and PyTorch Lightning, training tips and visualizations 
# 
# [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathLab/PINA/blob/master/tutorials/tutorial11/tutorial.ipynb)
# 
# In this tutorial, we will delve deeper into the functionality of the `Trainer` class, which serves as the cornerstone for training **PINA** [Solvers](https://mathlab.github.io/PINA/_rst/_code.html#solvers). 
# 
# The `Trainer` class offers a plethora of features aimed at improving model accuracy, reducing training time and memory usage, facilitating logging visualization, and more thanks to the amazing job done by the PyTorch Lightning team!
# 
# Our leading example will revolve around solving the `SimpleODE` problem, as outlined in the [*Introduction to PINA for Physics Informed Neural Networks training*](https://github.com/mathLab/PINA/blob/master/tutorials/tutorial1/tutorial.ipynb). If you haven't already explored it, we highly recommend doing so before diving into this tutorial.
# 
# Let's start by importing useful modules, define the `SimpleODE` problem and the `PINN` solver.

# In[18]:


## routine needed to run the notebook on Google Colab
try:
  import google.colab
  IN_COLAB = True
except:
  IN_COLAB = False
if IN_COLAB:
  get_ipython().system('pip install "pina-mathlab"')

import torch

from pina import Condition, Trainer
from pina.solvers import PINN
from pina.model import FeedForward
from pina.problem import SpatialProblem
from pina.operators import grad
from pina.domain import CartesianDomain
from pina.equation import Equation, FixedValue

class SimpleODE(SpatialProblem):

    output_variables = ['u']
    spatial_domain = CartesianDomain({'x': [0, 1]})

    # defining the ode equation
    def ode_equation(input_, output_):
        u_x = grad(output_, input_, components=['u'], d=['x'])
        u = output_.extract(['u'])
        return u_x - u

    # conditions to hold
    conditions = {
        'x0': Condition(location=CartesianDomain({'x': 0.}), equation=FixedValue(1)),             # We fix initial condition to value 1
        'D': Condition(location=CartesianDomain({'x': [0, 1]}), equation=Equation(ode_equation)), # We wrap the python equation using Equation
    }

    # defining the true solution
    def truth_solution(self, pts):
        return torch.exp(pts.extract(['x']))
    

# sampling for training
problem = SimpleODE()
problem.discretise_domain(1, 'random', locations=['x0'])
problem.discretise_domain(20, 'lh', locations=['D'])

# build the model
model = FeedForward(
    layers=[10, 10],
    func=torch.nn.Tanh,
    output_dimensions=len(problem.output_variables),
    input_dimensions=len(problem.input_variables)
)

# create the PINN object
pinn = PINN(problem, model)


# Till now we just followed the extact step of the previous tutorials. The `Trainer` object
# can be initialized by simiply passing the `PINN` solver

# In[3]:


trainer = Trainer(solver=pinn)


# ## Trainer Accelerator
# 
# When creating the trainer, **by defualt** the `Trainer` will choose the most performing `accelerator` for training which is available in your system, ranked as follow:
# 1. [TPU](https://cloud.google.com/tpu/docs/intro-to-tpu)
# 2. [IPU](https://www.graphcore.ai/products/ipu)
# 3. [HPU](https://habana.ai/)
# 4. [GPU](https://www.intel.com/content/www/us/en/products/docs/processors/what-is-a-gpu.html#:~:text=What%20does%20GPU%20stand%20for,video%20editing%2C%20and%20gaming%20applications) or [MPS](https://developer.apple.com/metal/pytorch/)
# 5. CPU

# For setting manually the `accelerator` run:
# 
# * `accelerator = {'gpu', 'cpu', 'hpu', 'mps', 'cpu', 'ipu'}` sets the accelerator to a specific one

# In[5]:


trainer = Trainer(solver=pinn,
                  accelerator='cpu')


# as you can see, even if in the used system `GPU` is available, it is not used since we set `accelerator='cpu'`.

# ## Trainer Logging
# 
# In **PINA** you can log metrics in different ways. The simplest approach is to use the `MetricTraker` class from `pina.callbacks` as seen in the [*Introduction to PINA for Physics Informed Neural Networks training*](https://github.com/mathLab/PINA/blob/master/tutorials/tutorial1/tutorial.ipynb) tutorial.
# 
# However, expecially when we need to train multiple times to get an average of the loss across multiple runs, `pytorch_lightning.loggers` might be useful. Here we will use `TensorBoardLogger` (more on [logging](https://lightning.ai/docs/pytorch/stable/extensions/logging.html) here), but you can choose the one you prefer (or make your own one).
# 
# We will now import `TensorBoardLogger`, do three runs of training and then visualize the results. Notice we set `enable_model_summary=False` to avoid model summary specifications (e.g. number of parameters), set it to true if needed.
# 

# In[7]:


from pytorch_lightning.loggers import TensorBoardLogger

# three run of training, by default it trains for 1000 epochs
# we reinitialize the model each time otherwise the same parameters will be optimized
for _ in range(3):
    model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )
    pinn = PINN(problem, model)
    trainer = Trainer(solver=pinn,
                      accelerator='cpu',
                      logger=TensorBoardLogger(save_dir='simpleode'),
                      enable_model_summary=False)
    trainer.train()


# We can now visualize the logs by simply running `tensorboard --logdir=simpleode/` on terminal, you should obtain a webpage as the one shown below:

# <p align=\"center\">
# <img src="logging.png" alt=\"Logging API\" width=\"400\"/>
# </p>

# as you can see, by default, **PINA** logs the losses which are shown in the progress bar, as well as the number of epochs. You can always insert more loggings by either defining a **callback** ([more on callbacks](https://lightning.ai/docs/pytorch/stable/extensions/callbacks.html)), or inheriting the solver and modify the programs with different **hooks** ([more on hooks](https://lightning.ai/docs/pytorch/stable/common/lightning_module.html#hooks)).

# ## Trainer Callbacks

# Whenever we need to access certain steps of the training for logging, do static modifications (i.e. not changing the `Solver`) or updating `Problem` hyperparameters (static variables), we can use `Callabacks`. Notice that `Callbacks` allow you to add arbitrary self-contained programs to your training. At specific points during the flow of execution (hooks), the Callback interface allows you to design programs that encapsulate a full set of functionality. It de-couples functionality that does not need to be in **PINA** `Solver`s.
# Lightning has a callback system to execute them when needed. Callbacks should capture NON-ESSENTIAL logic that is NOT required for your lightning module to run.
# 
# The following are best practices when using/designing callbacks.
# 
# * Callbacks should be isolated in their functionality.
# * Your callback should not rely on the behavior of other callbacks in order to work properly.
# * Do not manually call methods from the callback.
# * Directly calling methods (eg. on_validation_end) is strongly discouraged.
# * Whenever possible, your callbacks should not depend on the order in which they are executed.
# 
# We will try now to implement a naive version of `MetricTraker` to show how callbacks work. Notice that this is a very easy application of callbacks, fortunately in **PINA** we already provide more advanced callbacks in `pina.callbacks`.
# 
# <!-- Suppose we want to log the accuracy on some validation poit -->

# In[8]:


from pytorch_lightning.callbacks import Callback
import torch

# define a simple callback
class NaiveMetricTracker(Callback):
    def __init__(self):
        self.saved_metrics = []

    def on_train_epoch_end(self, trainer, __): # function called at the end of each epoch
        self.saved_metrics.append(
            {key: value for key, value in trainer.logged_metrics.items()}
        )


# Let's see the results when applyed to the `SimpleODE` problem. You can define callbacks when initializing the `Trainer` by the `callbacks` argument, which expects a list of callbacks. 

# In[10]:


model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )
pinn = PINN(problem, model)
trainer = Trainer(solver=pinn,
                  accelerator='cpu',
                  enable_model_summary=False,
                  callbacks=[NaiveMetricTracker()])  # adding a callbacks
trainer.train()


# We can easily access the data by calling `trainer.callbacks[0].saved_metrics` (notice the zero representing the first callback in the list given at initialization).

# In[9]:


trainer.callbacks[0].saved_metrics[:3] # only the first three epochs


# PyTorch Lightning also has some built in `Callbacks` which can be used in **PINA**, [here an extensive list](https://lightning.ai/docs/pytorch/stable/extensions/callbacks.html#built-in-callbacks). 
# 
# We can for example try the `EarlyStopping` routine, which automatically stops the training when a specific metric converged (here the `mean_loss`). In order to let the training keep going forever set `max_epochs=-1`.

# In[7]:


# ~2 mins
from pytorch_lightning.callbacks import EarlyStopping

model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )
pinn = PINN(problem, model)
trainer = Trainer(solver=pinn,
                  accelerator='cpu',
                  max_epochs = -1,
                  enable_model_summary=False,
                  callbacks=[EarlyStopping('mean_loss')])  # adding a callbacks
trainer.train()


# As we can see the model automatically stop when the logging metric stopped improving!

# ## Trainer Tips to Boost Accuracy, Save Memory and Speed Up Training
# 
# Untill now we have seen how to choose the right `accelerator`, how to log and visualize the results, and how to interface with the program in order to add specific parts of code at specific points by `callbacks`.
# Now, we well focus on how boost your training by saving memory and speeding it up, while mantaining the same or even better degree of accuracy!
# 
# 
# There are several built in methods developed in PyTorch Lightning which can be applied straight forward in **PINA**, here we report some:
# 
# * [Stochastic Weight Averaging](https://pytorch.org/blog/pytorch-1.6-now-includes-stochastic-weight-averaging/) to boost accuracy
# * [Gradient Clippling](https://deepgram.com/ai-glossary/gradient-clipping) to reduce computational time (and improve accuracy)
# * [Gradient Accumulation](https://lightning.ai/docs/pytorch/stable/common/optimization.html#id3) to save memory consumption  
# * [Mixed Precision Training](https://lightning.ai/docs/pytorch/stable/common/optimization.html#id3) to save memory consumption 
# 
# We will just demonstrate how to use the first two, and see the results compared to a standard training.
# We use the [`Timer`](https://lightning.ai/docs/pytorch/stable/api/lightning.pytorch.callbacks.Timer.html#lightning.pytorch.callbacks.Timer) callback from `pytorch_lightning.callbacks` to take the times. Let's start by training a simple model without any optimization (train for 2000 epochs).

# In[19]:


from pytorch_lightning.callbacks import Timer
from pytorch_lightning import seed_everything

# setting the seed for reproducibility
seed_everything(42, workers=True)

model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )

pinn = PINN(problem, model)
trainer = Trainer(solver=pinn,
                  accelerator='cpu',
                  deterministic=True,  # setting deterministic=True ensure reproducibility when a seed is imposed
                  max_epochs = 2000,
                  enable_model_summary=False,
                  callbacks=[Timer()])  # adding a callbacks
trainer.train()
print(f'Total training time {trainer.callbacks[0].time_elapsed("train"):.5f} s')


# Now we do the same but with StochasticWeightAveraging

# In[36]:


from pytorch_lightning.callbacks import StochasticWeightAveraging

# setting the seed for reproducibility
seed_everything(42, workers=True)

model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )
pinn = PINN(problem, model)
trainer = Trainer(solver=pinn,
                  accelerator='cpu',
                  deterministic=True,
                  max_epochs = 2000,
                  enable_model_summary=False,
                  callbacks=[Timer(),
                             StochasticWeightAveraging(swa_lrs=0.005)])  # adding StochasticWeightAveraging callbacks
trainer.train()
print(f'Total training time {trainer.callbacks[0].time_elapsed("train"):.5f} s')


# As you can see, the training time does not change at all! Notice that around epoch `1600`
# the scheduler is switched from the defalut one `ConstantLR` to the Stochastic Weight Average Learning Rate (`SWALR`).
# This is because by default `StochasticWeightAveraging` will be activated after `int(swa_epoch_start * max_epochs)` with `swa_epoch_start=0.7` by default. Finally, the final `mean_loss` is lower when `StochasticWeightAveraging` is used.
# 
# We will now now do the same but clippling the gradient to be relatively small.

# In[35]:


# setting the seed for reproducibility
seed_everything(42, workers=True)

model = FeedForward(
        layers=[10, 10],
        func=torch.nn.Tanh,
        output_dimensions=len(problem.output_variables),
        input_dimensions=len(problem.input_variables)
    )
pinn = PINN(problem, model)
trainer = Trainer(solver=pinn,
                  accelerator='cpu',
                  max_epochs = 2000,
                  enable_model_summary=False,
                  gradient_clip_val=0.1,          # clipping the gradient
                  callbacks=[Timer(),
                             StochasticWeightAveraging(swa_lrs=0.005)])
trainer.train()
print(f'Total training time {trainer.callbacks[0].time_elapsed("train"):.5f} s')


# As we can see we by applying gradient clipping we were able to even obtain lower error!
# 
# ## What's next?
# 
# Now you know how to use efficiently the `Trainer` class **PINA**! There are multiple directions you can go now:
# 
# 1. Explore training times on different devices (e.g.) `TPU` 
# 
# 2. Try to reduce memory cost by mixed precision training and gradient accumulation (especially useful when training Neural Operators)
# 
# 3. Benchmark `Trainer` speed for different precisions.