""" 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 # #
# # 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 # #
# # 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 # #
# # 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 # #
# # 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) # %% # .. raw:: html # #
# # 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) # %% # .. raw:: html # #
# # 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 # #
# # 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} # %% # .. raw:: html # #
# # 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 # #
# # 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 # #
# # 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 # #
# # 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()