Upload folder using huggingface_hub

.devcontainer/devcontainer.json

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+// For format details, see https://aka.ms/devcontainer.json. For config options, see the
+// README at: https://github.com/devcontainers/templates/tree/main/src/python
+{
+	"name": "Python 3 - Dedalus",
+	// Or use a Dockerfile or Docker Compose file. More info: https://containers.dev/guide/dockerfile
+	"image": "mcr.microsoft.com/devcontainers/python:1-3.12-bullseye",
+	
+	// Features to add to the dev container. More info: https://containers.dev/features.
+	"features": {
+		"ghcr.io/rocker-org/devcontainer-features/miniforge:2": {},
+		"ghcr.io/devcontainers/features/node:1": {}
+	},
+
+	// Use 'forwardPorts' to make a list of ports inside the container available locally.
+	// "forwardPorts": [],
+
+	// Use 'postCreateCommand' to run commands after the container is created.
+	"postCreateCommand": "bash .devcontainer/setup.sh",
+	"containerEnv": {
+		"CONDA_DEFAULT_ENV": "dedalus3"
+	},
+ 
+	// Configure tool-specific properties.
+	"customizations": {
+		"vscode": {
+            "extensions":[
+                "ms-python.python",
+                "ms-python.vscode-pylance"
+            ],
+			"settings": {
+				"python.pythonPath": "/opt/conda/envs/dedalus3/bin/python"
+			}
+		}
+	}
+
+	// Uncomment to connect as root instead. More info: https://aka.ms/dev-containers-non-root.
+	// "remoteUser": "root"
+}

.devcontainer/setup.sh

@@ -0,0 +1,33 @@
+#!/bin/bash
+set -e
+
+# Download the Dedalus install script to a temporary location
+DEDALUS_INSTALL_SCRIPT="$(mktemp)"
+curl -fsSL https://raw.githubusercontent.com/DedalusProject/dedalus_conda/master/conda_install_dedalus3.sh -o "$DEDALUS_INSTALL_SCRIPT"
+
+# Ensure conda is initialized (adjust path if needed for your container)
+if [ -f /opt/conda/etc/profile.d/conda.sh ]; then
+    source /opt/conda/etc/profile.d/conda.sh
+elif [ -f "$HOME/miniconda3/etc/profile.d/conda.sh" ]; then
+    source "$HOME/miniconda3/etc/profile.d/conda.sh"
+fi
+
+# Install Dedalus only if the environment does not exist
+if ! conda info --envs | grep -q dedalus3; then
+    conda activate base
+    bash "$DEDALUS_INSTALL_SCRIPT"
+fi
+
+
+conda activate dedalus3
+
+conda env config vars set OMP_NUM_THREADS=1
+conda env config vars set NUMEXPR_MAX_THREADS=1
+
+# Install additional Python packages from requirements.txt
+if [ -f requirements.txt ]; then
+    pip install -r requirements.txt
+fi
+
+# Clean up the temporary install script
+rm -f "$DEDALUS_INSTALL_SCRIPT"

.gitignore

@@ -0,0 +1,250 @@
+# Created by https://www.toptal.com/developers/gitignore/api/linux,macos,windows,python
+# Edit at https://www.toptal.com/developers/gitignore?templates=linux,macos,windows,python
+
+### Linux ###
+*~
+
+# temporary files which can be created if a process still has a handle open of a deleted file
+.fuse_hidden*
+
+# KDE directory preferences
+.directory
+
+# Linux trash folder which might appear on any partition or disk
+.Trash-*
+
+# .nfs files are created when an open file is removed but is still being accessed
+.nfs*
+
+### macOS ###
+# General
+.DS_Store
+.AppleDouble
+.LSOverride
+
+# Icon must end with two \r
+Icon
+
+
+# Thumbnails
+._*
+
+# Files that might appear in the root of a volume
+.DocumentRevisions-V100
+.fseventsd
+.Spotlight-V100
+.TemporaryItems
+.Trashes
+.VolumeIcon.icns
+.com.apple.timemachine.donotpresent
+
+# Directories potentially created on remote AFP share
+.AppleDB
+.AppleDesktop
+Network Trash Folder
+Temporary Items
+.apdisk
+
+### macOS Patch ###
+# iCloud generated files
+*.icloud
+
+### Python ###
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
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+# Distribution / packaging
+.Python
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+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+.pybuilder/
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# poetry
+#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
+#   This is especially recommended for binary packages to ensure reproducibility, and is more
+#   commonly ignored for libraries.
+#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
+#poetry.lock
+
+# pdm
+#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
+#pdm.lock
+#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
+#   in version control.
+#   https://pdm.fming.dev/#use-with-ide
+.pdm.toml
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+
+# PyCharm
+#  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
+#  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
+#  and can be added to the global gitignore or merged into this file.  For a more nuclear
+#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
+#.idea/
+
+### Python Patch ###
+# Poetry local configuration file - https://python-poetry.org/docs/configuration/#local-configuration
+poetry.toml
+
+# ruff
+.ruff_cache/
+
+# LSP config files
+pyrightconfig.json
+
+### Windows ###
+# Windows thumbnail cache files
+Thumbs.db
+Thumbs.db:encryptable
+ehthumbs.db
+ehthumbs_vista.db
+
+# Dump file
+*.stackdump
+
+# Folder config file
+[Dd]esktop.ini
+
+# Recycle Bin used on file shares
+$RECYCLE.BIN/
+
+# Windows Installer files
+*.cab
+*.msi
+*.msix
+*.msm
+*.msp
+
+# Windows shortcuts
+*.lnk
+
+# End of https://www.toptal.com/developers/gitignore/api/linux,macos,windows,python

LICENSE

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+MIT License
+
+Copyright (c) 2025 Adam Thorpe
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# 2D Poisson Equation Dataset
+
+Numerical solutions to the 2D Poisson equation with mixed boundary conditions using Dedalus spectral methods.
+
+![Sample Plot](sample_plot.png)
+
+## Equation
+
+The 2D Poisson equation boundary value problem:
+
+**PDE**: ∇²u = f(x,y)     in Ω = [0, Lx] × [0, Ly]
+
+**Boundary Conditions**:
+- u(x,0) = g(x)     (Dirichlet on bottom)
+- ∂u/∂y(x,Ly) = h(x)   (Neumann on top)
+
+## Variables
+
+The dataset returns a dictionary with the following fields:
+
+### Coordinates
+- `spatial_coordinates`: (2, Nx, Ny) - Combined X,Y coordinate meshgrids
+
+### Solution Fields  
+- `solution_field`: (Nx, Ny) - Solution u(x,y)
+- `forcing_function`: (Nx, Ny) - Random forcing function f(x,y)
+
+### Boundary Conditions
+- `boundary_condition_bottom`: (Nx,) - Bottom Dirichlet BC g(x)
+- `boundary_condition_top_gradient`: (Nx,) - Top Neumann BC h(x)
+
+## Dataset Parameters
+
+- **Domain**: [0, 2π] × [0, π] (2D rectangular domain)
+- **Grid points**: 256 × 128 (Nx × Ny)
+- **Discretization**: Fourier(x) × Chebyshev(y) spectral methods
+- **Solver**: Dedalus LBVP (Linear Boundary Value Problem)
+
+### Randomization
+- **Forcing function**: Generated using Gaussian processes with random length scales
+- **Boundary conditions**: Fixed sinusoidal bottom BC, zero top gradient BC
+- **Amplitude**: Random amplitude scaling for forcing functions (0.5 to 3.0)
+
+## Physical Context
+
+This dataset simulates steady-state physical systems governed by the 2D Poisson equation. 
+The equation models phenomena where the spatial distribution depends on source/sink terms, including:
+
+**Applications**:
+- Electrostatic potential in the presence of charge distributions
+- Steady-state heat conduction with internal heat sources  
+- Fluid stream functions for incompressible flow
+- Gravitational potential from mass distributions
+
+## Usage
+
+```python
+from dataset import PoissonDataset
+
+# Create dataset
+dataset = PoissonDataset()
+
+# Generate a sample
+sample = next(iter(dataset))
+
+# Access solution data
+spatial_coords = sample["spatial_coordinates"]  # X, Y meshgrids
+solution = sample["solution_field"]            # u(x,y)
+forcing = sample["forcing_function"]           # f(x,y)
+```
+
+## Visualization
+
+Run the plotting script to visualize samples:
+
+```bash
+python plot_sample.py      # 2D visualization of forcing, solution, and BCs
+```
+
+## Data Generation
+
+Generate the full dataset:
+
+```bash
+python generate_data.py
+```
+
+This creates train/test splits saved as chunked parquet files in the `data/` directory.

data/test-00000-of-00002.parquet

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dataset.py

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+"""
+2D Poisson equation dataset with mixed boundary conditions.
+
+Solves the boundary value problem:
+    ∇²u = f(x,y)     in Ω = [0, Lx] × [0, Ly]
+    u(x,0) = g(x)    on bottom boundary  
+    ∂u/∂y(x,Ly) = h(x) on top boundary
+
+Uses Dedalus spectral methods with Fourier(x) × Chebyshev(y) discretization.
+The forcing function f(x,y) is randomly generated using Gaussian processes
+to create diverse training samples.
+
+Physical applications: electrostatic potential, steady-state heat conduction,
+fluid stream functions.
+"""
+
+import numpy as np
+from torch.utils.data import IterableDataset
+
+import dedalus.public as d3
+from functools import partial
+from sklearn.metrics.pairwise import rbf_kernel
+import logging
+
+logger = logging.getLogger(__name__)
+
+
+def sample_gp_prior(kernel, X, n_samples=1):
+    """
+    Sample from Gaussian Process prior for generating smooth random fields.
+    """
+    if X.ndim == 1:
+        X = X.reshape(-1, 1)
+
+    K = kernel(X, X)
+
+    prior = np.random.multivariate_normal(
+        mean=np.zeros(X.shape[0]),
+        cov=K,
+        size=n_samples,
+    )
+
+    return prior
+
+
+def sample_gp_posterior(kernel, X, y, xt, n_samples=1):
+    """Sample from Gaussian Process posterior for boundary conditions."""
+    if X.ndim == 1:
+        X = X.reshape(-1, 1)
+    if y.ndim == 1:
+        y = y.reshape(-1, 1)
+    if xt.ndim == 1:
+        xt = xt.reshape(-1, 1)
+
+    K = kernel(X, X)
+    Kt = kernel(X, xt)
+    Ktt = kernel(xt, xt)
+
+    K_inv = np.linalg.inv(K)
+
+    mu = Kt.T @ K_inv @ y
+    cov = Ktt - Kt.T @ K_inv @ Kt
+
+    mu = mu.ravel()  # Ensure 1D array
+
+    posterior = np.random.multivariate_normal(
+        mean=mu,
+        cov=cov,
+        size=n_samples,
+    )
+    return posterior
+
+
+class PoissonDataset(IterableDataset):
+    """
+    Dataset for 2D Poisson equation with mixed boundary conditions.
+    
+    Generates random smooth forcing functions using Gaussian processes
+    and solves: ∇²u = f(x,y) with u(x,0) = g(x) and ∂u/∂y(x,Ly) = h(x).
+    """
+    def __init__(
+        self,
+        Lx=2*np.pi,              # Domain length in x-direction
+        Ly=np.pi,                # Domain length in y-direction  
+        Nx=256,                  # Grid points in x-direction
+        Ny=128,                  # Grid points in y-direction
+        dtype=np.float64,
+    ):
+        """
+        Initialize 2D Poisson equation dataset.
+        
+        Args:
+            Lx: Domain length in x-direction
+            Ly: Domain length in y-direction  
+            Nx: Number of grid points in x-direction
+            Ny: Number of grid points in y-direction
+            dtype: Data type for computations
+        """
+        super().__init__()
+        
+        # Store domain and grid parameters
+        self.Lx = Lx
+        self.Ly = Ly
+        self.Nx = Nx  
+        self.Ny = Ny
+        self.dtype = dtype
+        
+        # Setup Dedalus solver components
+        self.coords = d3.CartesianCoordinates('x', 'y')
+        self.dist = d3.Distributor(self.coords, dtype=dtype)
+        self.xbasis = d3.RealFourier(self.coords['x'], size=Nx, bounds=(0, Lx))
+        self.ybasis = d3.Chebyshev(self.coords['y'], size=Ny, bounds=(0, Ly))
+        
+        # Create coordinate grids
+        self.x, self.y = self.dist.local_grids(self.xbasis, self.ybasis)
+        
+        # Setup fields
+        self.u = self.dist.Field(name='u', bases=(self.xbasis, self.ybasis))
+        self.tau_1 = self.dist.Field(name='tau_1', bases=self.xbasis)
+        self.tau_2 = self.dist.Field(name='tau_2', bases=self.xbasis)
+        self.f = self.dist.Field(bases=(self.xbasis, self.ybasis))
+        self.g = self.dist.Field(bases=self.xbasis)
+        self.h = self.dist.Field(bases=self.xbasis)
+        
+        # Setup operators and namespace for boundary value problem
+        dy = lambda A: d3.Differentiate(A, self.coords['y'])
+        lift_basis = self.ybasis.derivative_basis(2)
+        lift = lambda A, n: d3.Lift(A, lift_basis, n)
+        f = self.f
+        g = self.g  
+        h = self.h
+        u = self.u
+        tau_1 = self.tau_1
+        tau_2 = self.tau_2
+        Ly = self.Ly
+        
+        self.problem = d3.LBVP([self.u, self.tau_1, self.tau_2], namespace=locals())
+        self.problem.add_equation("lap(u) + lift(tau_1,-1) + lift(tau_2,-2) = f")
+        self.problem.add_equation("u(y=0) = g")
+        self.problem.add_equation("dy(u)(y=Ly) = h")
+
+    def __iter__(self):
+        """Generate infinite samples from the dataset."""
+        while True:
+            # Generate random forcing function using filtered noise
+            self.f.fill_random('g', seed=np.random.randint(0, 2**31))
+            filter_x = np.random.randint(32, 128)
+            filter_y = np.random.randint(16, 64)
+            self.f.low_pass_filter(shape=(filter_x, filter_y))
+            
+            # Generate random Dirichlet boundary condition using GP
+            # Get x-coordinates for bottom boundary (1D array)
+            x_boundary = self.dist.local_grid(self.xbasis)
+            sigma_g = 0.2 * self.Lx
+            gamma_g = 1 / (2 * sigma_g**2)
+            g_sample = sample_gp_posterior(
+                kernel=partial(rbf_kernel, gamma=gamma_g),
+                X=np.array([0, self.Lx]),
+                y=np.array([0, 0]),
+                xt=x_boundary.ravel(),
+                n_samples=1
+            )[0]
+            self.g['g'] = (np.random.uniform(0.01, 0.1) * g_sample).reshape(-1, 1)
+            
+            # Generate random Neumann boundary condition using GP  
+            sigma_h = 0.3 * self.Lx
+            gamma_h = 1 / (2 * sigma_h**2)
+            h_sample = sample_gp_posterior(
+                kernel=partial(rbf_kernel, gamma=gamma_h),
+                X=np.array([0, self.Lx]),
+                y=np.array([0, 0]),
+                xt=x_boundary.ravel(),
+                n_samples=1
+            )[0]
+            self.h['g'] = (np.random.uniform(0.005, 0.05) * h_sample).reshape(-1, 1)
+            
+            yield self.solve()
+
+    def solve(self):
+        """
+        Solve the 2D Poisson boundary value problem.
+        
+        The forcing function and boundary conditions have already been set in __iter__.
+        
+        Returns:
+            A dictionary containing the solution and related data.
+        """
+        
+        # Build and solve the LBVP
+        solver = self.problem.build_solver()
+        solver.solve()
+        
+        # Gather global data for return
+        x_global = self.xbasis.global_grid(self.dist, scale=1)
+        y_global = self.ybasis.global_grid(self.dist, scale=1) 
+        u_global = self.u.allgather_data('g')
+        f_global = self.f.allgather_data('g')
+        g_global = self.g.allgather_data('g')
+        h_global = self.h.allgather_data('g')
+        
+        # Create coordinate meshgrids
+        X, Y = np.meshgrid(x_global.ravel(), y_global.ravel(), indexing='ij')
+
+        return {
+            # Combined spatial coordinates
+            "spatial_coordinates": np.array([X, Y]),  # Shape: (2, Nx, Ny)
+            
+            # Solution field
+            "solution_field": u_global,  # Shape: (Nx, Ny)
+            
+            # Forcing function 
+            "forcing_function": f_global,  # Shape: (Nx, Ny)
+            
+            # Boundary conditions
+            "boundary_condition_bottom": g_global,  # Shape: (Nx,)
+            "boundary_condition_top_gradient": h_global,  # Shape: (Nx,)
+        }

generate_data.py

@@ -0,0 +1,76 @@
+#!/usr/bin/env python3
+"""
+Generate 2D Poisson equation dataset and save to parquet files in chunks.
+"""
+
+import os
+import numpy as np
+import pyarrow as pa
+import pyarrow.parquet as pq
+from dataset import PoissonDataset
+
+
+def generate_dataset_split(
+    split_name="train", num_samples=1000, chunk_size=100, output_dir="data"
+):
+    """
+    Generate a dataset split and save as chunked parquet files.
+    """
+
+    os.makedirs(output_dir, exist_ok=True)
+
+    # Create PoissonDataset instance
+    dataset = PoissonDataset()
+    
+    num_chunks = (num_samples + chunk_size - 1) // chunk_size  # Ceiling division
+
+    print(f"Generating {num_samples} {split_name} samples in {num_chunks} chunks...")
+
+    dataset_iter = iter(dataset)
+    chunk_data = None
+
+    for i in range(num_samples):
+        sample = next(dataset_iter)
+
+        if chunk_data is None:
+            # Initialize chunk data on first sample
+            chunk_data = {key: [] for key in sample.keys()}
+
+        # Add sample to current chunk
+        for key, value in sample.items():
+            chunk_data[key].append(value)
+
+        # Save chunk when full or at end
+        if (i + 1) % chunk_size == 0 or i == num_samples - 1:
+            chunk_idx = i // chunk_size
+
+            # Convert numpy arrays to lists for PyArrow compatibility
+            table_data = {}
+            for key, values in chunk_data.items():
+                table_data[key] = [arr.tolist() for arr in values]
+
+            # Convert to PyArrow table
+            table = pa.table(table_data)
+
+            # Save chunk
+            filename = f"{split_name}-{chunk_idx:05d}-of-{num_chunks:05d}.parquet"
+            filepath = os.path.join(output_dir, filename)
+            pq.write_table(table, filepath)
+
+            print(f"Saved chunk {chunk_idx + 1}/{num_chunks}: {filepath}")
+
+            # Reset for next chunk
+            chunk_data = {key: [] for key in sample.keys()}
+
+    print(f"Generated {num_samples} {split_name} samples")
+    return num_samples
+
+
+if __name__ == "__main__":
+    np.random.seed(42)
+
+    # Generate train split
+    generate_dataset_split("train", num_samples=1000, chunk_size=100)
+
+    # Generate test split
+    generate_dataset_split("test", num_samples=200, chunk_size=100)

plot_sample.py

@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""
+Plot a single sample from the 2D Poisson equation dataset.
+
+Visualizes the forcing function, solution field, and boundary conditions
+for a single randomly generated Poisson boundary value problem.
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from dataset import PoissonDataset
+
+
+def plot_poisson_sample(sample, save_path="sample_plot.png"):
+    """
+    Plot a single sample from the 2D Poisson equation dataset.
+
+    Creates a 3-panel visualization showing:
+    1. Forcing function f(x,y)
+    2. Solution field u(x,y)
+    3. Boundary conditions
+    """
+    fig = plt.figure(figsize=(15, 5))
+    ax1 = plt.subplot(1, 3, 1)
+    ax2 = plt.subplot(1, 3, 2)
+    ax3 = plt.subplot(1, 3, 3)
+
+    # Extract data from dataset return dictionary
+    X, Y = sample["spatial_coordinates"]  # Shape: (2, Nx, Ny)
+    solution = sample["solution_field"]  # Shape: (Nx, Ny)
+    forcing = sample["forcing_function"]  # Shape: (Nx, Ny)
+    bc_bottom = sample["boundary_condition_bottom"]  # Shape: (Nx,)
+    bc_top_grad = sample["boundary_condition_top_gradient"]  # Shape: (Nx,)
+
+    # Plot 1: Forcing function f(x,y)
+    im1 = ax1.pcolormesh(
+        X, Y, forcing, cmap="RdBu_r", shading="gouraud", rasterized=True
+    )
+    ax1.set_xlabel("x")
+    ax1.set_ylabel("y")
+    ax1.set_title("Forcing Function f(x,y)")
+    ax1.set_aspect("equal")
+    plt.colorbar(im1, ax=ax1, label="f(x,y)")
+
+    # Plot 2: Solution field u(x,y)
+    im2 = ax2.pcolormesh(
+        X, Y, solution, cmap="viridis", shading="gouraud", rasterized=True
+    )
+    ax2.set_xlabel("x")
+    ax2.set_ylabel("y")
+    ax2.set_title("Solution u(x,y)")
+    ax2.set_aspect("equal")
+    plt.colorbar(im2, ax=ax2, label="u(x,y)")
+
+    # Plot 3: Boundary conditions
+    # X has shape (Nx, Ny), we want x-coordinates along boundaries
+    x_bottom = X[:, 0]  # x-coordinates along bottom boundary (y=0)
+    x_top = X[:, -1]  # x-coordinates along top boundary (y=Ly)
+
+    # Flatten boundary condition arrays if needed
+    bc_bottom_flat = bc_bottom.ravel() if bc_bottom.ndim > 1 else bc_bottom
+    bc_top_grad_flat = bc_top_grad.ravel() if bc_top_grad.ndim > 1 else bc_top_grad
+
+    ax3.plot(x_bottom, bc_bottom_flat, "b-", linewidth=2, label="u(x,0) = g(x)")
+    ax3.plot(x_top, bc_top_grad_flat, "r--", linewidth=2, label="∂u/∂y(x,Ly) = h(x)")
+    ax3.set_xlabel("x")
+    ax3.set_ylabel("Boundary values")
+    ax3.set_title("Boundary Conditions")
+    ax3.legend()
+    ax3.grid(True, alpha=0.3)
+
+    plt.tight_layout()
+    plt.savefig(save_path, dpi=200, bbox_inches="tight")
+    plt.close()
+
+    print(f"Sample visualization saved to {save_path}")
+
+
+if __name__ == "__main__":
+    # Set random seed for reproducibility
+    np.random.seed(42)
+
+    # Create dataset instance
+    dataset = PoissonDataset()
+
+    # Generate a single sample
+    dataset_iter = iter(dataset)
+    sample = next(dataset_iter)
+    sample = next(dataset_iter)
+
+    print("Sample keys:", list(sample.keys()))
+    for key, value in sample.items():
+        if hasattr(value, "shape"):
+            print(f"{key}: shape {value.shape}")
+        else:
+            print(f"{key}: {type(value)} - {value}")
+
+    # Plot the sample
+    plot_poisson_sample(sample)

requirements.txt

@@ -0,0 +1,6 @@
+numpy
+torch
+scikit-learn
+matplotlib
+pyarrow
+pillow