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numpy as np\nimport pandas as pd\nimport torch\nimport torch.nn as nn\nimport matplotlib.pyplot as plt\nfrom pathlib import Path\nfrom tqdm.auto import tqdm\nfrom torch.utils.data import Dataset, DataLoader\nimport torch.nn.functional as F\nfrom torch.cuda.amp import autocast, GradScaler\nfrom sklearn.model_selection import train_test_split\nimport random\n# import cv2 # Not used in the provided snippet, can be removed if not needed elsewhere\nimport csv # Not used in the provided snippet, can be removed if not needed elsewhere\nimport time\nimport gc # Garbage Collector for potentially large datasets\n\n# Set random seeds for reproducibility\ndef seed_everything(seed=42):\n    random.seed(seed)\n    np.random.seed(seed)\n    torch.manual_seed(seed)\n    torch.cuda.manual_seed(seed)\n    torch.cuda.manual_seed_all(seed) # if using multi-GPU\n    torch.backends.cudnn.deterministic = True\n    torch.backends.cudnn.benchmark = False # Set to False for determinism\n\nseed_everything()\n\n# Define data paths (adjust if necessary for your environment)\n# Assuming the script runs where '/kaggle/input/...' is accessible\ntry:\n    DATA_PATH = Path('/kaggle/input/waveform-inversion/train_samples')\n    if not DATA_PATH.exists():\n        raise FileNotFoundError # Fallback if Kaggle path doesn't exist\nexcept FileNotFoundError:\n    print(\"Kaggle path not found, using fallback path './data/train_samples'. Please adjust if needed.\")\n    DATA_PATH = Path('./data/train_samples') # Example fallback path\n    # Create dummy data if path doesn't exist for local testing\n    if not DATA_PATH.exists():\n        print(\"Fallback data path not found. Creating dummy data for testing.\")\n        DATA_PATH.mkdir(parents=True, exist_ok=True)\n        # Create a few dummy files\n        for i in range(3):\n            dummy_seis = np.random.rand(10, 5, 1000, 70).astype(np.float32) # N, C, T, X\n            dummy_vel = np.random.rand(10, 1, 70, 70).astype(np.float32) # N, C, Y, X\n            np.save(DATA_PATH / f'sample_{i}_seis.npy', dummy_seis)\n            np.save(DATA_PATH / f'sample_{i}_vel.npy', dummy_vel)\n\n# Find files to load and create Dataset\nall_inputs = sorted([\n    f\n    for f in DATA_PATH.rglob('*.npy')\n    if ('seis' in f.stem) or ('data' in f.stem)\n])\n\nif not all_inputs:\n    raise FileNotFoundError(f\"No input files found in {DATA_PATH}. Check the path and file naming ('seis' or 'data').\")\n\ndef inputs_files_to_output_files(input_files):\n    output_files = []\n    for f in input_files:\n        # Try replacing 'seis' with 'vel' or 'data' with 'model'\n        out_f_vel = Path(str(f).replace('seis', 'vel'))\n        out_f_model = Path(str(f).replace('data', 'model'))\n        \n        # Determine the correct output file based on which input name matched\n        if 'seis' in f.stem:\n            output_files.append(out_f_vel)\n        elif 'data' in f.stem:\n             output_files.append(out_f_model)\n        else:\n            # Fallback or error if naming convention isn't matched\n            # For safety, let's assume 'vel' is the target if unsure\n             print(f\"Warning: Input file {f} doesn't contain 'seis' or 'data'. Assuming corresponding output ends in 'vel'.\")\n             output_files.append(out_f_vel) # Or handle error as appropriate\n\n    return output_files\n\nall_outputs = inputs_files_to_output_files(all_inputs)\n\n# Verify all output files exist\nmissing_outputs = [f for f in all_outputs if not f.exists()]\nif missing_outputs:\n    print(f\"Error: Missing output files corresponding to inputs:\")\n    for f in missing_outputs:\n        print(f\" - {f}\")\n    # Attempt to find corresponding input file for better debugging\n    # This reverse mapping might be complex depending on exact naming rules\n    raise FileNotFoundError(\"Cannot proceed without all corresponding output files.\")\n\nassert len(all_inputs) == len(all_outputs), \"Mismatch between number of input and output files found.\"\n\n# Stratified split (optional, simple split used here)\n# If filenames contain patterns indicating different geological settings, stratify=filenames could be useful\ntrain_inputs, valid_inputs = train_test_split(all_inputs, test_size=0.2, random_state=42)\ntrain_outputs = inputs_files_to_output_files(train_inputs)\nvalid_outputs = inputs_files_to_output_files(valid_inputs)\n\n# Calculate statistics for normalization\ndef calculate_stats(files, n_files_for_stats=20, n_samples_per_file=100):\n    \"\"\"Calculate mean and std for normalization more robustly\"\"\"\n    samples = []\n    # Use a random subset of files for calculation if there are many files\n    files_to_use = random.sample(files, min(len(files), n_files_for_stats)) if len(files) > n_files_for_stats else files\n\n    print(f\"Calculating stats from {len(files_to_use)} files...\")\n    for f in tqdm(files_to_use, desc=\"Calculating stats\"):\n        try:\n            # Use mmap_mode for memory efficiency\n            data = np.load(f, mmap_mode='r')\n            # Ensure we don't try to sample more than available\n            num_available = data.shape[0]\n            indices_to_sample = min(n_samples_per_file, num_available)\n            if indices_to_sample > 0:\n                indices = np.random.choice(num_available, indices_to_sample, replace=False)\n                # Load only the selected samples into memory\n                samples.append(data[indices].astype(np.float32)) # Ensure float32\n            del data # Release mmap handle\n            gc.collect() # Explicitly collect garbage\n        except Exception as e:\n            print(f\"Warning: Could not process file {f} for stats calculation: {e}\")\n            continue # Skip problematic files\n\n    if not samples:\n        print(\"Warning: No samples collected for stats calculation. Using default values (0, 1).\")\n        return 0.0, 1.0\n\n    samples = np.concatenate(samples, axis=0) # Use concatenate for list of arrays\n    mean = np.mean(samples)\n    std = np.std(samples)\n\n    # Avoid division by zero or near-zero std\n    if std < 1e-8:\n        print(f\"Warning: Calculated std is very small ({std}). Setting to 1.0 to avoid issues.\")\n        std = 1.0\n\n    return mean, std\n\n# Calculate stats using a potentially larger subset for better accuracy\ninput_mean, input_std = calculate_stats(train_inputs, n_files_for_stats=50, n_samples_per_file=200)\noutput_mean, output_std = calculate_stats(train_outputs, n_files_for_stats=50, n_samples_per_file=200)\n\nprint(f\"Input stats: mean={input_mean:.4f}, std={input_std:.4f}\")\nprint(f\"Output stats: mean={output_mean:.4f}, std={output_std:.4f}\")\n\n\n# --- Dataset Class ---\nclass SeismicDataset(Dataset):\n    def __init__(self, inputs_files, output_files, n_examples_per_file=500,\n                 input_mean=0.0, input_std=1.0, output_mean=0.0, output_std=1.0,\n                 augment=False, input_shape=(5, 1000, 70), output_shape=(1, 70, 70)):\n        assert len(inputs_files) == len(output_files)\n        self.inputs_files = inputs_files\n        self.output_files = output_files\n        self.n_examples_per_file = n_examples_per_file\n        self.input_mean = input_mean\n        self.input_std = input_std if input_std > 1e-8 else 1.0 # Safety check\n        self.output_mean = output_mean\n        self.output_std = output_std if output_std > 1e-8 else 1.0 # Safety check\n        self.augment = augment\n        self.input_shape = input_shape   # Expected shape C, T, X\n        self.output_shape = output_shape # Expected shape C, Y, X\n\n        # Pre-calculate total length and file index mapping\n        self.file_lengths = []\n        self.file_cumulative_lengths = [0]\n        print(\"Checking dataset file lengths...\")\n        for f in tqdm(self.inputs_files, desc=\"Scanning files\"):\n            try:\n                # Fast shape check without loading full data\n                with open(f, 'rb') as file_handle:\n                    version = np.lib.format.read_magic(file_handle)\n                    shape, _, _ = np.lib.format._read_array_header(file_handle, version)\n                length = shape[0] # Assuming first dimension is number of samples\n                self.file_lengths.append(length)\n                self.file_cumulative_lengths.append(self.file_cumulative_lengths[-1] + length)\n            except Exception as e:\n                print(f\"Warning: Could not read header of {f}: {e}. Assuming 0 length.\")\n                self.file_lengths.append(0)\n                # Adjust cumulative sum accordingly - this file contributes 0 length\n                self.file_cumulative_lengths.append(self.file_cumulative_lengths[-1])\n\n\n        self._total_samples = self.file_cumulative_lengths[-1]\n        print(f\"Total samples found across all files: {self._total_samples}\")\n\n        # Determine effective n_examples_per_file if user requested more than available\n        # This part is tricky because the original code seemed to define __len__ differently\n        # Let's stick to the original logic for now: len is files * n_examples_per_file\n        # but ensure __getitem__ handles cases where sample_idx is out of bounds for a file.\n        self._len = len(self.inputs_files) * self.n_examples_per_file\n\n    def __len__(self):\n        # This length definition means we might try to access indices beyond\n        # the actual number of samples in a file if n_examples_per_file is large.\n        # __getitem__ needs to handle this gracefully (e.g., by wrapping around or sampling randomly).\n        return self._len\n\n    def __getitem__(self, idx):\n        # Calculate which file and which sample *within that file's quota*\n        file_idx = idx // self.n_examples_per_file\n        sample_offset_in_quota = idx % self.n_examples_per_file\n\n        # Get the actual number of samples in the target file\n        actual_samples_in_file = self.file_lengths[file_idx]\n\n        if actual_samples_in_file == 0:\n             # Handle files that couldn't be read or are empty\n             print(f\"Warning: File {self.inputs_files[file_idx]} has 0 samples. Returning zeros.\")\n             X_sample = np.zeros(self.input_shape, dtype=np.float32)\n             y_sample = np.zeros(self.output_shape, dtype=np.float32)\n             X_orig = X_sample.copy()\n             y_orig = y_sample.copy()\n             return torch.from_numpy(X_sample), torch.from_numpy(y_sample), torch.from_numpy(X_orig), torch.from_numpy(y_orig)\n\n\n        # Map the sample_offset_in_quota to an actual index in the file\n        # Use modulo to wrap around if n_examples_per_file > actual_samples_in_file\n        actual_sample_idx = sample_offset_in_quota % actual_samples_in_file\n\n        X = None\n        y = None\n        try:\n            # Load the specific sample using mmap_mode for efficiency\n            X = np.load(self.inputs_files[file_idx], mmap_mode='r')\n            y = np.load(self.output_files[file_idx], mmap_mode='r')\n\n            # Ensure indices are within bounds (should be by modulo logic, but double-check)\n            if actual_sample_idx >= X.shape[0] or actual_sample_idx >= y.shape[0]:\n                 print(f\"Warning: Index calculation error. idx={idx}, file_idx={file_idx}, sample_offset={sample_offset_in_quota}, actual_idx={actual_sample_idx}, shapes X:{X.shape}, y:{y.shape}. Using index 0.\")\n                 actual_sample_idx = 0 # Fallback to index 0\n\n            # Get the specific sample, ensure float32, make copies\n            X_sample = X[actual_sample_idx].astype(np.float32).copy()\n            y_sample = y[actual_sample_idx].astype(np.float32).copy()\n\n            # Store original data for physics computations if needed later (PINNs might use original scale)\n            X_orig = X_sample.copy()\n            y_orig = y_sample.copy()\n\n            # --- Data Validation and Reshaping ---\n            # Ensure input has expected dimensions (C, T, X)\n            if X_sample.shape != self.input_shape:\n                 # Attempt common fixes like adding channel dim if missing\n                 if len(X_sample.shape) == 2 and self.input_shape[0] == 1: # (T, X) -> (1, T, X)\n                     X_sample = np.expand_dims(X_sample, axis=0)\n                 elif len(X_sample.shape) == 3 and X_sample.shape[0] == self.input_shape[1] and X_sample.shape[1] == self.input_shape[2] and self.input_shape[0] == 1 : # (T,X,C?) -> (C,T,X) very unlikely\n                     print(f\"Warning: Unexpected input shape {X_sample.shape} for file {self.inputs_files[file_idx]}, sample {actual_sample_idx}. Attempting transpose. Expected {self.input_shape}\")\n                     # This case is ambiguous, need more info on data format\n                     # X_sample = np.transpose(X_sample, (2, 0, 1)) # Example transpose C last -> C first\n                 else:\n                     # If shape mismatch persists, raise error or return zeros\n                     print(f\"Error: Input shape mismatch! Got {X_sample.shape}, expected {self.input_shape} for file {self.inputs_files[file_idx]}, sample {actual_sample_idx}. Returning zeros.\")\n                     X_sample = np.zeros(self.input_shape, dtype=np.float32)\n                     X_orig = X_sample.copy()\n                     # Don't necessarily zero y_sample, maybe it's okay\n            \n            # Ensure output has expected dimensions (C, Y, X)\n            if y_sample.shape != self.output_shape:\n                if len(y_sample.shape) == 2 and self.output_shape[0] == 1: # (Y, X) -> (1, Y, X)\n                    y_sample = np.expand_dims(y_sample, axis=0)\n                else:\n                    print(f\"Error: Output shape mismatch! Got {y_sample.shape}, expected {self.output_shape} for file {self.output_files[file_idx]}, sample {actual_sample_idx}. Returning zeros.\")\n                    y_sample = np.zeros(self.output_shape, dtype=np.float32)\n                    y_orig = y_sample.copy()\n                    \n            # --- Normalization ---\n            X_sample = (X_sample - self.input_mean) / self.input_std\n            y_sample = (y_sample - self.output_mean) / self.output_std\n\n            # --- Data Augmentation ---\n            if self.augment:\n                # Horizontal flip (axis=2 assuming shape C,Y,X or C,T,X)\n                if random.random() < 0.5:\n                    X_sample = np.flip(X_sample, axis=2).copy() # Use copy() after flip\n                    y_sample = np.flip(y_sample, axis=2).copy()\n\n                # Add small random noise\n                if random.random() < 0.3:\n                    noise_level = random.uniform(0.01, 0.05) * self.input_std # Scale noise relative to std\n                    X_sample += np.random.normal(0, noise_level, X_sample.shape).astype(np.float32)\n\n            # Return tensors\n            return torch.from_numpy(X_sample), torch.from_numpy(y_sample), torch.from_numpy(X_orig), torch.from_numpy(y_orig)\n\n        except Exception as e:\n             print(f\"Error loading or processing sample {idx} (file {file_idx}, sample {actual_sample_idx}): {e}\")\n             # Return zeros or handle error appropriately\n             X_sample = np.zeros(self.input_shape, dtype=np.float32)\n             y_sample = np.zeros(self.output_shape, dtype=np.float32)\n             X_orig = X_sample.copy()\n             y_orig = y_sample.copy()\n             return torch.from_numpy(X_sample), torch.from_numpy(y_sample), torch.from_numpy(X_orig), torch.from_numpy(y_orig)\n        finally:\n            # Explicitly delete large objects and collect garbage\n            del X, y\n            # gc.collect() # Collecting garbage frequently can slow down dataloading\n\n\n# --- Determine Input/Output Shapes from Data ---\n# Load one sample to determine shapes dynamically\nprint(\"Determining data shapes...\")\ntry:\n    temp_ds = SeismicDataset(train_inputs, train_outputs, n_examples_per_file=1)\n    temp_loader = DataLoader(temp_ds, batch_size=1)\n    x_sample, y_sample, _, _ = next(iter(temp_loader))\n    INPUT_SHAPE = tuple(x_sample.shape[1:]) # Shape after batch dim: (C, T, X)\n    OUTPUT_SHAPE = tuple(y_sample.shape[1:]) # Shape after batch dim: (C, Y, X)\n    print(f\"Detected Input Shape (C, T, X): {INPUT_SHAPE}\")\n    print(f\"Detected Output Shape (C, Y, X): {OUTPUT_SHAPE}\")\n    del temp_ds, temp_loader, x_sample, y_sample # Clean up\n    gc.collect()\nexcept Exception as e:\n    print(f\"Could not automatically determine shapes: {e}. Using defaults.\")\n    # Fallback to expected shapes if loading fails\n    INPUT_SHAPE = (5, 1000, 70)  # C, T, X\n    OUTPUT_SHAPE = (1, 70, 70)   # C, Y, X\n\n# --- Instantiate Datasets and DataLoaders ---\nprint(\"Creating datasets...\")\n# Use detected shapes\ndstrain = SeismicDataset(train_inputs, train_outputs, input_mean=input_mean, input_std=input_std,\n                         output_mean=output_mean, output_std=output_std, augment=True,\n                         input_shape=INPUT_SHAPE, output_shape=OUTPUT_SHAPE, n_examples_per_file=500) # Adjust n_examples if needed\ndsvalid = SeismicDataset(valid_inputs, valid_outputs, input_mean=input_mean, input_std=input_std,\n                         output_mean=output_mean, output_std=output_std, augment=False,\n                         input_shape=INPUT_SHAPE, output_shape=OUTPUT_SHAPE, n_examples_per_file=500)\n\n# Adjust batch size based on GPU memory\nBATCH_SIZE = 16 # Reduced from 32 as PINNs can be memory intensive\nNUM_WORKERS = 2 # Reduced from 4 to avoid potential issues with mmap and multiprocessing\n\nprint(\"Creating dataloaders...\")\ndltrain = DataLoader(dstrain, batch_size=BATCH_SIZE, shuffle=True, pin_memory=True, drop_last=True, num_workers=NUM_WORKERS, persistent_workers=NUM_WORKERS > 0)\ndlvalid = DataLoader(dsvalid, batch_size=BATCH_SIZE, shuffle=False, pin_memory=True, drop_last=False, num_workers=NUM_WORKERS, persistent_workers=NUM_WORKERS > 0)\n\n\n# --- Differential Operators (Potentially for advanced PINN loss) ---\nclass DifferentialOperators:\n    @staticmethod\n    def gradient(f, dim, dx=1.0, order=1):\n        \"\"\"Compute gradient of f along a specified dimension using torch.gradient\"\"\"\n        grads = f\n        for _ in range(order):\n            grads = torch.gradient(grads, dim=dim, spacing=dx)[0] # torch.gradient returns tuple\n        return grads\n\n    @staticmethod\n    def laplacian(f, dx=1.0, dy=1.0):\n        \"\"\"Compute Laplacian of f (2D) using torch.gradient\"\"\"\n        # Assuming f has shape [..., Y, X]\n        grad_y = torch.gradient(f, dim=-2, spacing=dy)[0]\n        grad_x = torch.gradient(f, dim=-1, spacing=dx)[0]\n        \n        f_yy = torch.gradient(grad_y, dim=-2, spacing=dy)[0]\n        f_xx = torch.gradient(grad_x, dim=-1, spacing=dx)[0]\n        \n        return f_xx + f_yy\n\n    @staticmethod\n    def wave_equation(u, v, dt=0.004, dx=10.0, dy=10.0):\n        \"\"\"\n        Wave equation residual: ∂²u/∂t² - v² * (∂²u/∂x² + ∂²u/∂y²) = 0\n        Assumes u shape: [batch, time, y, x]\n        Assumes v shape: [batch, 1, y, x] or [batch, y, x] (broadcastable)\n        \"\"\"\n        # Compute second time derivative (∂²u/∂t²) - using central differences\n        # Need padding or slicing to handle boundaries\n        u_tt = (u[:, 2:, :, :] - 2 * u[:, 1:-1, :, :] + u[:, :-2, :, :]) / (dt**2) # Shape: [batch, time-2, y, x]\n\n        # Compute Laplacian for each time step in the valid range\n        # Need to compute Laplacian on u corresponding to the time steps of u_tt\n        u_for_laplacian = u[:, 1:-1, :, :] # Shape: [batch, time-2, y, x]\n        laplacian_u = torch.zeros_like(u_for_laplacian)\n        \n        # Calculate Laplacian spatially for each time step\n        # This loop is slow; ideally vectorize if possible or use Conv2d kernel\n        # for b in range(u_for_laplacian.shape[0]): # Can likely remove batch loop\n        #     for t in range(u_for_laplacian.shape[1]): # Time loop might be unavoidable if memory constrained\n        #         laplacian_u[b, t, :, :] = DifferentialOperators.laplacian(u_for_laplacian[b, t, :, :], dx, dy)\n        \n        # Vectorized Laplacian calculation across time and batch:\n        grad_y = torch.gradient(u_for_laplacian, dim=-2, spacing=dy)[0]\n        grad_x = torch.gradient(u_for_laplacian, dim=-1, spacing=dx)[0]\n        f_yy = torch.gradient(grad_y, dim=-2, spacing=dy)[0]\n        f_xx = torch.gradient(grad_x, dim=-1, spacing=dx)[0]\n        laplacian_u = f_xx + f_yy # Shape: [batch, time-2, y, x]\n\n        # Ensure v is broadcastable: Add time dimension if needed\n        if v.dim() == 3: # [batch, y, x]\n            v = v.unsqueeze(1) # -> [batch, 1, y, x]\n        if v.dim() == 4 and v.shape[1] == 1: # [batch, 1, y, x]\n             v_squared = v**2 # Broadcasts over time dim of laplacian_u implicitly\n        else:\n             # Handle cases where v might have time dimension? Unlikely for velocity model.\n             raise ValueError(f\"Unexpected velocity model shape: {v.shape}\")\n\n\n        # Compute residual of wave equation\n        # v² * Laplacian might need broadcasting if v is [batch, 1, y, x]\n        residual = u_tt - v_squared * laplacian_u # Shape: [batch, time-2, y, x]\n\n        return residual # Residual ideally should be zero\n\n# --- Model Components ---\n\n# Basic ConvBlock with Residual Connection\nclass ConvBlock(nn.Module):\n    def __init__(self, in_channels, out_channels, kernel_size=3, padding=1):\n        super().__init__()\n        self.conv1 = nn.Conv2d(in_channels, out_channels, kernel_size=kernel_size, padding=padding, bias=False) # Bias false if using BN\n        self.bn1 = nn.BatchNorm2d(out_channels)\n        self.relu = nn.ReLU(inplace=True)\n        self.conv2 = nn.Conv2d(out_channels, out_channels, kernel_size=kernel_size, padding=padding, bias=False)\n        self.bn2 = nn.BatchNorm2d(out_channels)\n        \n        # Residual connection\n        if in_channels == out_channels:\n            self.residual = nn.Identity()\n        else:\n            # Projection shortcut\n            self.residual = nn.Sequential(\n                nn.Conv2d(in_channels, out_channels, kernel_size=1, bias=False),\n                nn.BatchNorm2d(out_channels)\n            )\n            \n    def forward(self, x):\n        identity = self.residual(x)\n        \n        out = self.conv1(x)\n        out = self.bn1(out)\n        out = self.relu(out)\n        \n        out = self.conv2(out)\n        out = self.bn2(out)\n        \n        out += identity # Add residual connection\n        out = self.relu(out) # Apply activation after addition\n        \n        return out\n\n# Simple Attention Block (Channel Attention like SE-Block)\nclass AttentionBlock(nn.Module):\n    def __init__(self, in_channels, reduction=8):\n        super().__init__()\n        self.pool = nn.AdaptiveAvgPool2d(1) # Global Average Pooling\n        self.fc = nn.Sequential(\n            nn.Linear(in_channels, in_channels // reduction, bias=False),\n            nn.ReLU(inplace=True),\n            nn.Linear(in_channels // reduction, in_channels, bias=False),\n            nn.Sigmoid()\n        )\n        \n    def forward(self, x):\n        b, c, _, _ = x.size()\n        y = self.pool(x).view(b, c) # Squeeze\n        y = self.fc(y).view(b, c, 1, 1) # Excite\n        return x * y.expand_as(x) # Scale original feature map\n\n# Physics-based encoder block (could be simpler or more complex)\nclass PhysicsEncoder(nn.Module):\n    def __init__(self, input_channels, hidden_size=32):\n        super().__init__()\n        # Using ConvBlock for consistency\n        self.block1 = ConvBlock(input_channels, hidden_size, kernel_size=5, padding=2)\n        self.block2 = ConvBlock(hidden_size, hidden_size, kernel_size=5, padding=2)\n        \n    def forward(self, x):\n        x = self.block1(x)\n        x = self.block2(x)\n        return x\n\n# --- Hybrid UNet PINN Model ---\nclass HybridUNetPINN(nn.Module):\n    def __init__(self, input_channels=INPUT_SHAPE[0], output_channels=OUTPUT_SHAPE[0], \n                 target_size=(OUTPUT_SHAPE[1], OUTPUT_SHAPE[2]), # Y, X\n                 physics_weight=0.1):\n        super().__init__()\n        \n        self.target_size = target_size # e.g., (70, 70)\n        self.input_channels = input_channels\n        self.output_channels = output_channels\n\n        # --- Data-driven encoder path ---\n        # Channels: input_channels -> 32 -> 64 -> 128 -> 256\n        self.enc1 = ConvBlock(input_channels, 32)\n        self.pool1 = nn.MaxPool2d(kernel_size=2, stride=2) # Reduces spatial dimensions by 2\n        self.enc2 = ConvBlock(32, 64)\n        self.pool2 = nn.MaxPool2d(kernel_size=2, stride=2)\n        self.enc3 = ConvBlock(64, 128)\n        self.pool3 = nn.MaxPool2d(kernel_size=2, stride=2)\n        self.enc4 = ConvBlock(128, 256)\n        self.pool4 = nn.MaxPool2d(kernel_size=2, stride=2)\n        \n        # --- Physics encoder path ---\n        # Output size should match enc1 output for concatenation later\n        self.physics_encoder = PhysicsEncoder(input_channels, hidden_size=32) \n        \n        # --- Bottleneck / Middle with attention ---\n        # Input to middle is output of enc4 after pooling\n        self.middle = ConvBlock(256, 512)\n        self.attention = AttentionBlock(512) # Apply attention in the bottleneck\n        \n        # --- Decoder path with skip connections ---\n        # Upsampling can use ConvTranspose2d or Interpolate + Conv\n        self.up4 = nn.ConvTranspose2d(512, 256, kernel_size=2, stride=2) # Input: 512, Output: 256\n        self.dec4 = ConvBlock(256 + 256, 256) # Concatenate up4 output and enc4 output\n        \n        self.up3 = nn.ConvTranspose2d(256, 128, kernel_size=2, stride=2)\n        self.dec3 = ConvBlock(128 + 128, 128) # Concatenate up3 output and enc3 output\n        \n        self.up2 = nn.ConvTranspose2d(128, 64, kernel_size=2, stride=2)\n        self.dec2 = ConvBlock(64 + 64, 64)   # Concatenate up2 output and enc2 output\n        \n        self.up1 = nn.ConvTranspose2d(64, 32, kernel_size=2, stride=2)\n        # Concatenate up1 output, enc1 output, AND physics_features output\n        self.dec1 = ConvBlock(32 + 32 + 32, 32) # (up1 + enc1 + physics) -> 32\n        \n        # --- Final layer to get desired output channels ---\n        self.final_conv = nn.Conv2d(32, output_channels, kernel_size=1)\n        \n        # --- Optional Physics-based refinement layer ---\n        # Takes the initial output + physics features to refine the velocity model\n        # Input channels: output_channels from final_conv + hidden_size from physics_encoder\n        self.physics_refine = nn.Sequential(\n            ConvBlock(output_channels + 32, 32), # Process combined features\n            nn.Conv2d(32, output_channels, kernel_size=1) # Output refined velocity adjustment\n        )\n        \n        # Physics weight for loss balancing (can be adjusted during training)\n        self.physics_weight = physics_weight\n        \n        # Store normalization parameters for physics loss calculation\n        self.output_mean = 0.0\n        self.output_std = 1.0\n        \n    def set_normalization_params(self, output_mean, output_std):\n        self.output_mean = output_mean\n        self.output_std = output_std if output_std > 1e-8 else 1.0\n        \n    def forward(self, x, physics_enabled=True):\n        # x shape: [B, C_in, T, X_in] -> e.g., [B, 5, 1000, 70]\n\n        # --- Encoder ---\n        enc1 = self.enc1(x)     # Output spatial size depends on input T, X_in and conv padding\n        enc2 = self.enc2(self.pool1(enc1))\n        enc3 = self.enc3(self.pool2(enc2))\n        enc4 = self.enc4(self.pool3(enc3))\n        \n        # --- Physics Branch ---\n        # Run in parallel with the encoder\n        if physics_enabled:\n            # This encoder should output features matching enc1's spatial size\n            physics_features = self.physics_encoder(x) \n        else:\n            # Create placeholder zeros if physics is disabled\n            # Need to know the spatial size of enc1 here. Let's assume it's the same as x for now (if padding='same')\n            # If convs change size, need to calculate expected size.\n            # Assuming ConvBlock with kernel=3, padding=1 keeps size the same.\n            physics_features_shape = (x.size(0), 32, x.size(2), x.size(3))\n            physics_features = torch.zeros(physics_features_shape, device=x.device, dtype=x.dtype)\n            \n        # --- Bottleneck ---\n        middle_in = self.pool4(enc4)\n        middle_out = self.middle(middle_in)\n        middle_out = self.attention(middle_out)\n        \n        # --- Decoder ---\n        # Upsample and concatenate with skip connections\n        dec4_in = self.up4(middle_out)\n        # Ensure spatial dimensions match enc4 before concatenation\n        # Use F.interpolate if needed, but ConvTranspose2d(stride=2) should double the size\n        if dec4_in.shape[2:] != enc4.shape[2:]:\n            dec4_in = F.interpolate(dec4_in, size=enc4.shape[2:], mode='bilinear', align_corners=False)\n        dec4 = self.dec4(torch.cat([dec4_in, enc4], dim=1))\n        \n        dec3_in = self.up3(dec4)\n        if dec3_in.shape[2:] != enc3.shape[2:]:\n            dec3_in = F.interpolate(dec3_in, size=enc3.shape[2:], mode='bilinear', align_corners=False)\n        dec3 = self.dec3(torch.cat([dec3_in, enc3], dim=1))\n        \n        dec2_in = self.up2(dec3)\n        if dec2_in.shape[2:] != enc2.shape[2:]:\n             dec2_in = F.interpolate(dec2_in, size=enc2.shape[2:], mode='bilinear', align_corners=False)\n        dec2 = self.dec2(torch.cat([dec2_in, enc2], dim=1))\n        \n        dec1_in = self.up1(dec2)\n        if dec1_in.shape[2:] != enc1.shape[2:]:\n             dec1_in = F.interpolate(dec1_in, size=enc1.shape[2:], mode='bilinear', align_corners=False)\n        \n        # Concatenate decoder output, encoder skip connection, and physics features\n        # Ensure physics_features spatial dims match enc1\n        if physics_features.shape[2:] != enc1.shape[2:]:\n            physics_features_resized = F.interpolate(physics_features, size=enc1.shape[2:], mode='bilinear', align_corners=False)\n        else:\n            physics_features_resized = physics_features\n            \n        dec1 = self.dec1(torch.cat([dec1_in, enc1, physics_features_resized], dim=1))\n\n        # --- Final Processing & Cropping/Resizing ---\n        # The output of dec1 might have spatial dimensions related to the *input* T, X_in\n        # We need the output to be the target size (Y, X), e.g., (70, 70)\n        \n        # Strategy 1: Crop the center (if output is larger than target)\n        # Strategy 2: Use a final conv + interpolation (more flexible)\n        \n        # Let's use Strategy 2 for more generality\n        # Apply final conv to get initial prediction\n        initial_pred_features = self.final_conv(dec1) # Shape: [B, C_out, H, W]\n        \n        # Interpolate features to the target size\n        initial_pred = F.interpolate(initial_pred_features, size=self.target_size, mode='bilinear', align_corners=False)\n        \n        # --- Physics-based Refinement (Optional) ---\n        if physics_enabled:\n            # Also resize physics_features_resized to target size to concatenate\n            physics_features_target_size = F.interpolate(physics_features_resized, size=self.target_size, mode='bilinear', align_corners=False)\n            \n            # Concatenate initial prediction and physics features\n            refine_input = torch.cat([initial_pred, physics_features_target_size], dim=1)\n            \n            # Get the refinement adjustment\n            refinement = self.physics_refine(refine_input)\n            \n            # Add the refinement to the initial prediction (residual style)\n            final_pred = initial_pred + refinement\n        else:\n            final_pred = initial_pred\n            \n        return final_pred # Shape: [B, C_out, target_Y, target_X]\n\n    def compute_physics_loss(self, seismic_data_norm, velocity_pred_norm, dx=10.0, dy=10.0, dt=0.004):\n        \"\"\"\n        Compute physics-informed loss based on proxies or simplified wave equation terms.\n        Inputs are normalized, need to denormalize velocity for physical constraints.\n        \"\"\"\n        # --- De-normalize Predicted Velocity ---\n        # Ensure model has normalization parameters set\n        if not hasattr(self, 'output_mean') or not hasattr(self, 'output_std'):\n             print(\"Warning: output_mean/output_std not set on model. Using raw prediction for physics loss.\")\n             velocity_pred_physical = velocity_pred_norm\n        else:\n             velocity_pred_physical = velocity_pred_norm * self.output_std + self.output_mean\n\n        # --- Physics Constraint 1: Velocity Smoothness ---\n        # Penalize large gradients in the velocity model\n        # velocity_pred_physical shape: [B, C_out, Y, X] - assume C_out=1\n        if velocity_pred_physical.shape[1] > 1:\n            print(\"Warning: Physics loss assumes single channel velocity output. Using first channel.\")\n            vel_to_diff = velocity_pred_physical[:, 0:1, :, :]\n        else:\n            vel_to_diff = velocity_pred_physical\n\n        vel_grad_y = DifferentialOperators.gradient(vel_to_diff, dim=-2, dx=dy)\n        vel_grad_x = DifferentialOperators.gradient(vel_to_diff, dim=-1, dx=dx)\n        # L2 norm of gradients\n        smoothness_loss = torch.mean(vel_grad_x**2 + vel_grad_y**2)\n\n        # --- Physics Constraint 2: Realistic Velocity Bounds ---\n        # Penalize velocities outside a plausible physical range (e.g., 1.5 km/s to 6.0 km/s)\n        # Use ReLU for one-sided penalty\n        lower_bound = 1.5 # km/s\n        upper_bound = 6.0 # km/s\n        # Ensure output_mean/std are in compatible units (e.g., km/s)\n        realistic_bounds_loss = torch.mean(\n            F.relu(lower_bound - velocity_pred_physical) + \\\n            F.relu(velocity_pred_physical - upper_bound)\n        )\n        \n        # --- Physics Constraint 3: Wave Equation Residual (Simplified/Proxy) ---\n        # Option A: Use the *actual* wave equation (Computationally expensive, requires input wavefield 'u')\n        # This requires the input seismic data to be the actual wavefield 'u'.\n        # If seismic_data_norm represents 'u', we need to denormalize it too.\n        # wave_eq_loss = torch.mean(DifferentialOperators.wave_equation(u_physical, velocity_pred_physical, dt, dx, dy)**2)\n\n        # Option B: Use a proxy - e.g., penalize mismatch between wavefield gradients and velocity\n        # This is highly problem-specific and requires careful formulation.\n\n        # Let's stick to Smoothness and Bounds for this implementation, as they are common and robust.\n        # The full wave equation requires careful handling of inputs/outputs.\n        \n        # --- Combine Physics Losses ---\n        # Weights can be tuned\n        w_smooth = 1.0\n        w_bounds = 0.5 # Can adjust weight relative to smoothness\n        \n        total_physics_loss = w_smooth * smoothness_loss + w_bounds * realistic_bounds_loss\n        \n        # Apply the overall physics_weight scaling factor\n        return total_physics_loss * self.physics_weight\n\n\n# --- Combined Loss Function ---\nclass HybridLoss(nn.Module):\n    def __init__(self, alpha=0.8, ssim_weight=0.1):\n        super().__init__()\n        self.alpha = alpha # Weight for L1 vs MSE/Structural term\n        self.ssim_weight = ssim_weight # Weight for the SSIM-like term\n        self.l1 = nn.L1Loss()\n        self.mse = nn.MSELoss() # Keep MSE as an option or part of structural term\n\n    def ssim_like_loss(self, pred, target, C1=1e-4, C2=9e-4):\n        \"\"\" Simplified SSIM-like loss component focusing on structure \"\"\"\n        mu_p = torch.mean(pred, dim=[2, 3], keepdim=True)\n        mu_t = torch.mean(target, dim=[2, 3], keepdim=True)\n        \n        sigma_p_sq = torch.mean((pred - mu_p)**2, dim=[2, 3], keepdim=True)\n        sigma_t_sq = torch.mean((target - mu_t)**2, dim=[2, 3], keepdim=True)\n        sigma_pt = torch.mean((pred - mu_p) * (target - mu_t), dim=[2, 3], keepdim=True)\n        \n        # Calculate SSIM components (simplified)\n        # Luminance term (using means) - less important if data is normalized\n        # Contrast term (using variances)\n        # Structure term (using covariance)\n        \n        # Use the structural term: (2 * sigma_pt + C2) / (sigma_p_sq + sigma_t_sq + C2)\n        structural_term = (2.0 * sigma_pt + C2) / (sigma_p_sq + sigma_t_sq + C2)\n        \n        # Loss is typically 1 - SSIM\n        # We average over batch and channels\n        return torch.mean(1.0 - structural_term)\n\n    def forward(self, pred, target, physics_loss=None):\n        # --- Data-driven component ---\n        l1_loss = self.l1(pred, target)\n        \n        # Optional: Add SSIM-like structural loss\n        # structural_loss = self.ssim_like_loss(pred, target)\n        \n        # Combine L1 and MSE (or structural loss)\n        # data_loss = self.alpha * l1_loss + (1 - self.alpha) * structural_loss\n        # Simpler: Weighted sum of L1 and MSE\n        mse_loss = self.mse(pred, target)\n        data_loss = self.alpha * l1_loss + (1 - self.alpha) * mse_loss\n        \n        # --- Combine with Physics-based loss ---\n        if physics_loss is not None:\n            total_loss = data_loss + physics_loss # Physics loss is already weighted in compute_physics_loss\n        else:\n            total_loss = data_loss\n            \n        return total_loss, data_loss # Return both for logging\n\n# --- Initialization ---\ndevice = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\nprint(f\"Using device: {device}\")\n\nmodel = HybridUNetPINN(\n    input_channels=INPUT_SHAPE[0], \n    output_channels=OUTPUT_SHAPE[0],\n    target_size=(OUTPUT_SHAPE[1], OUTPUT_SHAPE[2]),\n    physics_weight=0.1 # Initial physics weight\n).to(device)\n\n# Set normalization parameters on the model instance (important for physics loss)\nmodel.set_normalization_params(output_mean, output_std)\n\n# --- Optimizer ---\n# Use AdamW with weight decay\n# Separate parameter groups for potentially different learning rates (optional but good practice)\nphysics_param_ids = set(id(p) for p in model.physics_encoder.parameters()) | \\\n                    set(id(p) for p in model.physics_refine.parameters())\n\nbase_params = [p for p in model.parameters() if id(p) not in physics_param_ids]\nphysics_params = [p for p in model.parameters() if id(p) in physics_param_ids]\n\noptimizer = torch.optim.AdamW([\n    {'params': base_params, 'lr': 3e-4, 'weight_decay': 1e-5}, # Slightly higher LR for main path\n    {'params': physics_params, 'lr': 1e-4, 'weight_decay': 1e-5} # Lower LR for physics path potentially\n], lr=3e-4) # Default LR if not specified in groups\n\n# --- Loss Function ---\ncriterion = HybridLoss(alpha=0.8) # 80% L1, 20% MSE for data loss\n\n# --- Learning Rate Scheduler ---\n# Cosine annealing is a good choice\nscheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=50, eta_min=1e-6)\n\n# --- Mixed Precision Training Scaler ---\nscaler = GradScaler(enabled=torch.cuda.is_available()) # Only enable if using CUDA\n\n# --- Early Stopping ---\nclass EarlyStopping:\n    def __init__(self, patience=10, min_delta=0.0001, verbose=True): # Increased patience\n        self.patience = patience\n        self.min_delta = min_delta\n        self.counter = 0\n        self.best_loss = float('inf')\n        self.early_stop = False\n        self.verbose = verbose\n        \n    def __call__(self, val_loss):\n        if val_loss < self.best_loss - self.min_delta:\n            if self.verbose:\n                print(f\"Validation loss decreased ({self.best_loss:.6f} --> {val_loss:.6f}). Resetting counter.\")\n            self.best_loss = val_loss\n            self.counter = 0\n        else:\n            self.counter += 1\n            if self.verbose:\n                print(f\"Validation loss did not improve from {self.best_loss:.6f}. Counter: {self.counter}/{self.patience}\")\n            if self.counter >= self.patience:\n                if self.verbose:\n                    print(\"Early stopping triggered.\")\n                self.early_stop = True\n\nearly_stopping = EarlyStopping(patience=10) # More patience\n\n# --- Checkpoint Saving ---\ndef save_checkpoint(model, optimizer, scheduler, epoch, loss, filename=\"checkpoint.pt\"):\n    print(f\"Saving checkpoint to {filename}...\")\n    checkpoint = {\n        'epoch': epoch,\n        'model_state_dict': model.state_dict(),\n        'optimizer_state_dict': optimizer.state_dict(),\n        'loss': loss,\n    }\n    if scheduler is not None:\n        checkpoint['scheduler_state_dict'] = scheduler.state_dict()\n    torch.save(checkpoint, filename)\n\n# --- Training Function ---\ndef train_epoch(model, dataloader, optimizer, criterion, device, scaler, current_physics_weight):\n    model.train()\n    total_loss_accum = 0.0\n    data_loss_accum = 0.0\n    physics_loss_accum = 0.0\n    \n    # Update model's internal physics weight\n    model.physics_weight = current_physics_weight \n    \n    progress_bar = tqdm(dataloader, desc='Train', leave=False)\n    for data in progress_bar:\n        # Inputs: normalized seismic data [B, C_in, T, X]\n        # Targets: normalized velocity model [B, C_out, Y, X]\n        # Inputs_orig, Targets_orig: original scale data (not used directly in this training loop version)\n        inputs, targets, _, _ = data \n        inputs = inputs.to(device)\n        targets = targets.to(device)\n        \n        optimizer.zero_grad()\n        \n        # Use autocast for mixed precision\n        with autocast(enabled=scaler.is_enabled()):\n            # Forward pass\n            outputs = model(inputs, physics_enabled=True) # Ensure physics path is active\n            \n            # Compute physics loss (using normalized inputs/outputs as needed by the function)\n            # compute_physics_loss handles denormalization internally if required\n            physics_loss = model.compute_physics_loss(inputs, outputs)\n            \n            # Compute total loss (data loss + physics loss)\n            total_loss, data_loss = criterion(outputs, targets, physics_loss)\n            \n        # Scale loss and backward pass\n        scaler.scale(total_loss).backward()\n        \n        # Gradient clipping (optional but recommended)\n        scaler.unscale_(optimizer) # Unscale gradients before clipping\n        torch.nn.utils.clip_grad_norm_(model.parameters(), max_norm=1.0)\n        \n        # Optimizer step\n        scaler.step(optimizer)\n        \n        # Update scaler for next iteration\n        scaler.update()\n        \n        # Accumulate losses for epoch average\n        total_loss_accum += total_loss.item()\n        data_loss_accum += data_loss.item() # data_loss from criterion\n        physics_loss_accum += physics_loss.item() # physics_loss from model.compute_physics_loss\n\n        # Update progress bar\n        progress_bar.set_postfix({\n            'loss': total_loss.item(), \n            'data_l': data_loss.item(), \n            'phys_l': physics_loss.item()\n        })\n\n    \n    n_batches = len(dataloader)\n    avg_total_loss = total_loss_accum / n_batches\n    avg_data_loss = data_loss_accum / n_batches\n    avg_physics_loss = physics_loss_accum / n_batches\n    \n    return {\n        'total_loss': avg_total_loss,\n        'data_loss': avg_data_loss,\n        'physics_loss': avg_physics_loss\n    }\n\n# --- Validation Function ---\ndef validate(model, dataloader, criterion, device, current_physics_weight):\n    model.eval()\n    total_loss_accum = 0.0\n    data_loss_accum = 0.0\n    physics_loss_accum = 0.0\n    \n    # Ensure model's physics weight is set for validation consistency (though it doesn't affect gradients)\n    model.physics_weight = current_physics_weight\n    \n    with torch.no_grad(): # No gradients needed for validation\n        progress_bar = tqdm(dataloader, desc='Valid', leave=False)\n        for data in progress_bar:\n            inputs, targets, _, _ = data\n            inputs = inputs.to(device)\n            targets = targets.to(device)\n            \n            # Forward pass - can disable physics computation here if only evaluating data loss for validation speed\n            # outputs = model(inputs, physics_enabled=False) \n            # physics_loss = torch.tensor(0.0) # Set to zero if disabled\n            \n            # OR evaluate with physics enabled for comparable loss metric\n            outputs = model(inputs, physics_enabled=True)\n            physics_loss = model.compute_physics_loss(inputs, outputs)\n\n            # Compute loss\n            total_loss, data_loss = criterion(outputs, targets, physics_loss)\n            \n            # Accumulate losses\n            total_loss_accum += total_loss.item()\n            data_loss_accum += data_loss.item()\n            physics_loss_accum += physics_loss.item()\n\n            progress_bar.set_postfix({\n                'val_loss': total_loss.item()            \n            })\n\n    n_batches = len(dataloader)\n    avg_total_loss = total_loss_accum / n_batches\n    avg_data_loss = data_loss_accum / n_batches\n    avg_physics_loss = physics_loss_accum / n_batches\n    \n    return {\n        'total_loss': avg_total_loss,\n        'data_loss': avg_data_loss,\n        'physics_loss': avg_physics_loss\n    }\n\n\n# --- Training Loop ---\nn_epochs = 50 # Or adjust as needed\nhistory = []\nbest_valid_loss = float('inf')\n\n# Dynamic weighting schedule for physics loss (optional)\n# Starts low, increases, then potentially stabilizes\n# Example: Linear increase then constant\nwarmup_epochs = 10\nmax_physics_weight = 0.2 # Max weight to reach\nphysics_weight_schedule = np.concatenate([\n    np.linspace(0.01, max_physics_weight, warmup_epochs), # Linear increase\n    np.full(n_epochs - warmup_epochs, max_physics_weight) # Stay at max\n])\n# Ensure schedule length matches n_epochs\nif len(physics_weight_schedule) < n_epochs:\n     physics_weight_schedule = np.pad(physics_weight_schedule, (0, n_epochs - len(physics_weight_schedule)), mode='edge')\nelif len(physics_weight_schedule) > n_epochs:\n     physics_weight_schedule = physics_weight_schedule[:n_epochs]\n\n\nprint(\"Starting training...\")\nfor epoch in range(1, n_epochs + 1):\n    start_time = time.time()\n    \n    # Get current physics weight from schedule\n    current_physics_weight = physics_weight_schedule[epoch-1]\n    \n    # Train\n    train_metrics = train_epoch(model, dltrain, optimizer, criterion, device, scaler, current_physics_weight)\n    \n    # Validate\n    valid_metrics = validate(model, dlvalid, criterion, device, current_physics_weight)\n    \n    # Step the scheduler (after validation)\n    if scheduler:\n        scheduler.step()\n    \n    epoch_time = time.time() - start_time\n    \n    # Log history\n    current_lr = optimizer.param_groups[0]['lr'] # Get current LR\n    history.append({\n        'epoch': epoch,\n        'train_loss': train_metrics['total_loss'],\n        'valid_loss': valid_metrics['total_loss'],\n        'train_data_loss': train_metrics['data_loss'],\n        'valid_data_loss': valid_metrics['data_loss'],\n        'train_physics_loss': train_metrics['physics_loss'],\n        'valid_physics_loss': valid_metrics['physics_loss'],\n        'physics_weight': current_physics_weight,\n        'lr': current_lr,\n        'time': epoch_time\n    })\n    \n    # Print epoch summary\n    print(f'Epoch {epoch}/{n_epochs} | T Loss: {train_metrics[\"total_loss\"]:.5f} | V Loss: {valid_metrics[\"total_loss\"]:.5f} | '\n          f'T Data L: {train_metrics[\"data_loss\"]:.5f} | V Data L: {valid_metrics[\"data_loss\"]:.5f} | '\n          f'T Phys L: {train_metrics[\"physics_loss\"]:.5f} | V Phys L: {valid_metrics[\"physics_loss\"]:.5f} | '\n          f'Phys W: {current_physics_weight:.3f} | LR: {current_lr:.6f} | Time: {epoch_time:.2f}s')\n    \n    # Save best model based on validation loss\n    if valid_metrics['total_loss'] < best_valid_loss:\n        print(f\"Validation loss improved ({best_valid_loss:.6f} --> {valid_metrics['total_loss']:.6f}). Saving best model...\")\n        best_valid_loss = valid_metrics['total_loss']\n        save_checkpoint(model, optimizer, scheduler, epoch, best_valid_loss, 'best_hybrid_pinn_model.pt')\n    \n    # --- Visualization (every few epochs) ---\n    if epoch % 5 == 0 or epoch == 1 or epoch == n_epochs:\n        print(\"Generating visualization...\")\n        model.eval() # Ensure model is in eval mode for visualization\n        with torch.no_grad():\n            # Get a batch from validation loader\n            try:\n                 vis_inputs, vis_targets, _, _ = next(iter(dlvalid))\n                 vis_inputs = vis_inputs.to(device)\n                 vis_targets = vis_targets.to(device) # Targets remain normalized here\n                 \n                 # Get predictions with and without physics (for comparison)\n                 outputs_with_physics = model(vis_inputs, physics_enabled=True)\n                 outputs_without_physics = model(vis_inputs, physics_enabled=False) # Requires model changes or separate pass\n                 \n                 # Select first item in batch for visualization\n                 idx_vis = 0\n                 \n                 # Denormalize for visualization (using stored stats)\n                 target_vis = vis_targets[idx_vis, 0].cpu().numpy() * output_std + output_mean\n                 pred_phys_vis = outputs_with_physics[idx_vis, 0].cpu().numpy() * output_std + output_mean\n                 pred_no_phys_vis = outputs_without_physics[idx_vis, 0].cpu().numpy() * output_std + output_mean\n                 \n                 fig, axes = plt.subplots(2, 2, figsize=(12, 10)) # Adjusted size\n                 fig.suptitle(f'Epoch {epoch} | Validation Loss: {valid_metrics[\"total_loss\"]:.5f}')\n                 \n                 # Plot Ground Truth\n                 ax = axes[0, 0]\n                 im = ax.imshow(target_vis, aspect='auto', cmap='viridis')\n                 ax.set_title('Ground Truth Velocity')\n                 plt.colorbar(im, ax=ax, label='Velocity (km/s?)') # Add unit guess\n                 \n                 # Plot Prediction with Physics\n                 ax = axes[0, 1]\n                 im = ax.imshow(pred_phys_vis, aspect='auto', cmap='viridis')\n                 ax.set_title('Prediction (with Physics)')\n                 plt.colorbar(im, ax=ax, label='Velocity (km/s?)')\n                 \n                 # Plot Prediction without Physics\n                 ax = axes[1, 0]\n                 im = ax.imshow(pred_no_phys_vis, aspect='auto', cmap='viridis')\n                 ax.set_title('Prediction (Data-Only)')\n                 plt.colorbar(im, ax=ax, label='Velocity (km/s?)')\n                 \n                 # Plot Difference (Ground Truth - Prediction with Physics)\n                 ax = axes[1, 1]\n                 diff = target_vis - pred_phys_vis\n                 vmax = np.abs(diff).max() # Symmetric color scale around zero\n                 im = ax.imshow(diff, aspect='auto', cmap='seismic', vmin=-vmax, vmax=vmax)\n                 ax.set_title('Difference (GT - Physics Pred)')\n                 plt.colorbar(im, ax=ax, label='Velocity Difference')\n                 \n                 plt.tight_layout(rect=[0, 0.03, 1, 0.95]) # Adjust layout to prevent title overlap\n                 plt.savefig(f'epoch_{epoch}_visualization.png') # Save the figure\n                 plt.show()\n\n            except Exception as e:\n                 print(f\"Error during visualization: {e}\")\n                 # Continue training even if visualization fails\n\n\n    # --- Early stopping check ---\n    early_stopping(valid_metrics['total_loss'])\n    if early_stopping.early_stop:\n        break # Exit training loop\n\nprint(\"Training finished.\")\n\n# --- Plot Training History ---\nprint(\"Plotting training history...\")\nhistory_df = pd.DataFrame(history)\n\nfig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10), sharex=True) # Share x-axis (epochs)\n\n# Plot Losses on ax1\nax1.plot(history_df['epoch'], history_df['train_loss'], label='Train Total Loss', color='tab:blue')\nax1.plot(history_df['epoch'], history_df['valid_loss'], label='Valid Total Loss', color='tab:orange')\nax1.plot(history_df['epoch'], history_df['train_data_loss'], label='Train Data Loss', linestyle='--', color='tab:blue', alpha=0.7)\nax1.plot(history_df['epoch'], history_df['valid_data_loss'], label='Valid Data Loss', linestyle='--', color='tab:orange', alpha=0.7)\nax1.plot(history_df['epoch'], history_df['train_physics_loss'], label='Train Physics Loss', linestyle=':', color='tab:green', alpha=0.7)\nax1.plot(history_df['epoch'], history_df['valid_physics_loss'], label='Valid Physics Loss', linestyle=':', color='tab:red', alpha=0.7)\nax1.set_ylabel('Loss')\nax1.set_title('Training and Validation Losses')\nax1.legend(loc='upper right')\nax1.grid(True, linestyle='--', alpha=0.6)\n# Consider log scale if losses vary widely: ax1.set_yscale('log')\n\n# Plot Learning Rate and Physics Weight on ax2\nax2_lr = ax2\nax2_pw = ax2.twinx() # Create secondary y-axis for physics weight\n\n# Plot LR\nline_lr, = ax2_lr.plot(history_df['epoch'], history_df['lr'], label='Learning Rate (LR)', color='tab:purple')\nax2_lr.set_xlabel('Epoch')\nax2_lr.set_ylabel('Learning Rate', color=line_lr.get_color())\nax2_lr.tick_params(axis='y', labelcolor=line_lr.get_color())\n# Optional: Use log scale for LR if it changes drastically\n# ax2_lr.set_yscale('log')\n\n# Plot Physics Weight\nline_pw, = ax2_pw.plot(history_df['epoch'], history_df['physics_weight'], label='Physics Weight', color='tab:cyan')\nax2_pw.set_ylabel('Physics Weight', color=line_pw.get_color())\nax2_pw.tick_params(axis='y', labelcolor=line_pw.get_color())\nax2_pw.set_ylim(bottom=0) # Physics weight shouldn't be negative\n\nax2.set_title('Learning Rate and Physics Weight Schedule')\n# Combine legends from both y-axes\nlines = [line_lr, line_pw]\nlabels = [l.get_label() for l in lines]\nax2_lr.legend(lines, labels, loc='center right')\nax2.grid(True, linestyle='--', alpha=0.6)\n\n\nfig.tight_layout()\nplt.savefig('training_history.png') # Save the history plot\nplt.show()\n\nprint(\"Script finished.\")","metadata":{"_uuid":"c51d0354-4cf4-4b8e-b1ea-933a6263062b","_cell_guid":"cf45902b-1260-4e2f-81e2-71c461a091c9","trusted":true,"collapsed":false,"jupyter":{"outputs_hidden":false},"execution":{"iopub.status.busy":"2025-04-11T20:14:17.182700Z","iopub.execute_input":"2025-04-11T20:14:17.183376Z"}},"outputs":[],"execution_count":null}]}