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Training an FNO with incremental meta-learning
===============================================
A demo of the Incremental FNO meta-learning algorithm on our small Darcy-Flow dataset.
This tutorial demonstrates incremental meta-learning for neural operators, which allows
the model to gradually increase its complexity during training. This approach can lead to:
- Better convergence properties
- More stable training dynamics
- Improved generalization
- Reduced computational requirements during early training
The incremental approach starts with a small number of Fourier modes and gradually
increases the model capacity as training progresses.
"""
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Import dependencies
# -------------------
# We import the necessary modules for incremental FNO training
import torch
import matplotlib.pyplot as plt
import sys
from neuralop.models import FNO
from neuralop.data.datasets import load_darcy_flow_small
from neuralop.utils import count_model_params
from neuralop.training import AdamW
from neuralop.training.incremental import IncrementalFNOTrainer
from neuralop.data.transforms.data_processors import IncrementalDataProcessor
from neuralop import LpLoss, H1Loss
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Loading the Darcy-Flow dataset
# ------------------------------
# We load the Darcy-Flow dataset with multiple resolutions for incremental training.
train_loader, test_loaders, output_encoder = load_darcy_flow_small(
n_train=100,
batch_size=16,
test_resolutions=[16, 32],
n_tests=[100, 50],
test_batch_sizes=[32, 32],
)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Configuring incremental training
# --------------------------------
# We set up the incremental FNO model with a small starting number of modes.
# The model will gradually increase its capacity during training.
# We choose to update the modes using the incremental gradient explained algorithm
incremental = True
if incremental:
starting_modes = (2, 2) # Start with very few modes
else:
starting_modes = (8, 8) # Standard number of modes
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Creating the incremental FNO model
# ----------------------------------
# We create an FNO model with a maximum number of modes that can be reached
# during incremental training. The model starts with fewer modes and grows.
model = FNO(
max_n_modes=(8, 8), # Maximum modes the model can reach
n_modes=starting_modes, # Starting number of modes
hidden_channels=32,
in_channels=1,
out_channels=1,
)
model = model.to(device)
n_params = count_model_params(model)
# %%
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#
# <div style="margin-top: 3em;"></div>
#
# Setting up the optimizer and scheduler
# -------------------------------------
# We use AdamW optimizer with weight decay for regularization
optimizer = AdamW(model.parameters(), lr=8e-3, weight_decay=1e-4)
scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=30)
# %%
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#
# <div style="margin-top: 3em;"></div>
#
# Configuring incremental data processing
# ---------------------------------------
# If one wants to use Incremental Resolution, one should use the IncrementalDataProcessor.
# When passed to the trainer, the trainer will automatically update the resolution.
#
# Key parameters for incremental resolution:
#
# - incremental_resolution: bool, default is False. If True, increase the resolution of the input incrementally
# - incremental_res_gap: parameter for resolution updates
# - subsampling_rates: a list of resolutions to use
# - dataset_indices: a list of indices of the dataset to slice to regularize the input resolution
# - dataset_resolution: the resolution of the input
# - epoch_gap: the number of epochs to wait before increasing the resolution
# - verbose: if True, print the resolution and the number of modes
data_transform = IncrementalDataProcessor(
in_normalizer=None,
out_normalizer=None,
device=device,
subsampling_rates=[2, 1], # Resolution scaling factors
dataset_resolution=16, # Base resolution
dataset_indices=[2, 3], # Dataset indices for regularization
epoch_gap=10, # Epochs between resolution updates
verbose=True, # Print progress information
)
data_transform = data_transform.to(device)
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Setting up loss functions
# -------------------------
# We use H1 loss for training and L2 loss for evaluation
l2loss = LpLoss(d=2, p=2)
h1loss = H1Loss(d=2)
train_loss = h1loss
eval_losses = {"h1": h1loss, "l2": l2loss}
# %%
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#
# <div style="margin-top: 3em;"></div>
#
# Displaying training configuration
# ---------------------------------
# We display the model parameters, optimizer, scheduler, and loss functions
# to verify our incremental training setup
print("\n### N PARAMS ###\n", n_params)
print("\n### OPTIMIZER ###\n", optimizer)
print("\n### SCHEDULER ###\n", scheduler)
print("\n### LOSSES ###")
print("\n### INCREMENTAL RESOLUTION + GRADIENT EXPLAINED ###")
print(f"\n * Train: {train_loss}")
print(f"\n * Test: {eval_losses}")
sys.stdout.flush()
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Configuring the IncrementalFNOTrainer
# --------------------------------------
# We set up the IncrementalFNOTrainer with various incremental learning options.
# Other options include setting incremental_loss_gap = True.
# If one wants to use incremental resolution, set it to True.
# In this example we only update the modes and not the resolution.
# When using incremental resolution, keep in mind that the number of modes
# initially set should be strictly less than the resolution.
#
# Key parameters for incremental training:
#
# - incremental_grad: bool, default is False. If True, use the base incremental algorithm based on gradient variance
# - incremental_grad_eps: threshold for gradient variance
# - incremental_buffer: number of buffer modes to calculate gradient variance
# - incremental_max_iter: initial number of iterations
# - incremental_grad_max_iter: maximum iterations to accumulate gradients
# - incremental_loss_gap: bool, default is False. If True, use the incremental algorithm based on loss gap
# - incremental_loss_eps: threshold for loss gap
# Create the IncrementalFNOTrainer with our configuration
trainer = IncrementalFNOTrainer(
model=model,
n_epochs=20,
data_processor=data_transform,
device=device,
verbose=True,
incremental_loss_gap=False, # Use gradient-based incremental learning
incremental_grad=True, # Enable gradient-based mode updates
incremental_grad_eps=0.9999, # Gradient variance threshold
incremental_loss_eps=0.001, # Loss gap threshold
incremental_buffer=5, # Buffer modes for gradient calculation
incremental_max_iter=1, # Initial iterations
incremental_grad_max_iter=2, # Maximum gradient accumulation iterations
)
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Training the incremental FNO model
# ----------------------------------
# We train the model using incremental meta-learning. The trainer will:
# 1. Start with a small number of Fourier modes
# 2. Gradually increase the model capacity based on gradient variance
# 3. Monitor the incremental learning progress
# 4. Evaluate on test data throughout training
trainer.train(
train_loader,
test_loaders,
optimizer,
scheduler,
regularizer=False,
training_loss=train_loss,
eval_losses=eval_losses,
)
# %%
# .. raw:: html
#
# <div style="margin-top: 3em;"></div>
#
# Visualizing incremental FNO predictions
# ----------------------------------------
# We visualize the model's predictions after incremental training.
# Note that we trained on a very small resolution for a very small number of epochs.
# In practice, we would train at larger resolution on many more samples.
#
# However, for practicality, we created a minimal example that:
# i) fits in just a few MB of memory
# ii) can be trained quickly on CPU
#
# In practice we would train a Neural Operator on one or multiple GPUs
test_samples = test_loaders[32].dataset
fig = plt.figure(figsize=(7, 7))
for index in range(3):
data = test_samples[index]
# Input x
x = data["x"].to(device)
# Ground-truth
y = data["y"].to(device)
# Model prediction: incremental FNO output
out = model(x.unsqueeze(0))
# Plot input x
ax = fig.add_subplot(3, 3, index * 3 + 1)
x = x.cpu().squeeze().detach().numpy()
y = y.cpu().squeeze().detach().numpy()
ax.imshow(x, cmap="gray")
if index == 0:
ax.set_title("Input x")
plt.xticks([], [])
plt.yticks([], [])
# Plot ground-truth y
ax = fig.add_subplot(3, 3, index * 3 + 2)
ax.imshow(y.squeeze())
if index == 0:
ax.set_title("Ground-truth y")
plt.xticks([], [])
plt.yticks([], [])
# Plot model prediction
ax = fig.add_subplot(3, 3, index * 3 + 3)
ax.imshow(out.cpu().squeeze().detach().numpy())
if index == 0:
ax.set_title("Incremental FNO prediction")
plt.xticks([], [])
plt.yticks([], [])
fig.suptitle("Incremental FNO predictions on Darcy-Flow data", y=0.98)
plt.tight_layout()
fig.show()
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