{ "cells": [ { "cell_type": "markdown", "id": "cell-0", "metadata": {}, "source": [ "# Multi-Resolution Component Separation with HEALPix ud_grade\n", "\n", "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/CMBSciPol/furax-cs/blob/main/notebooks/03_PTEP_Multi_Resolution_Component_Separation.ipynb)\n", "\n", "## Learning Objectives\n", "\n", "By the end of this notebook, you will:\n", "- Understand multi-resolution component separation using HEALPix ud_grade\n", "- Implement resolution-based parameter optimization for CMB analysis\n", "- Optimize spectral parameters at different spatial scales\n", "- Visualize how resolution-based parameterization improves computational efficiency\n", "\n", "## The Multi-Resolution Approach\n", "\n", "Traditional component separation uses uniform resolution across all parameters. The PTEP (LiteBIRD Physics, Technology, and Engineering Plan) approach recognizes that different astrophysical parameters vary at different spatial scales. This method uses HEALPix `ud_grade` to downsample parameter maps to appropriate resolutions.\n", "\n", "**Key Innovation**: Optimize spectral parameters at resolution scales matched to their astrophysical variation, reducing computational cost while maintaining accuracy." ] }, { "cell_type": "code", "execution_count": null, "id": "271a2d2f", "metadata": {}, "outputs": [], "source": [ "!pip install -q furax-cs\n", "!pip install -r https://raw.githubusercontent.com/CMBSciPol/furax-cs/main/requirements.txt" ] }, { "cell_type": "code", "execution_count": 2, "id": "cell-1", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "ERROR:2026-02-01 21:50:34,703:jax._src.xla_bridge:491: Jax plugin configuration error: Exception when calling jax_plugins.xla_cuda12.initialize()\n", "Traceback (most recent call last):\n", " File \"/home/wassim/micromamba/envs/fg/lib/python3.11/site-packages/jax/_src/xla_bridge.py\", line 489, in discover_pjrt_plugins\n", " plugin_module.initialize()\n", " File \"/home/wassim/micromamba/envs/fg/lib/python3.11/site-packages/jax_plugins/xla_cuda12/__init__.py\", line 328, in initialize\n", " _check_cuda_versions(raise_on_first_error=True)\n", " File \"/home/wassim/micromamba/envs/fg/lib/python3.11/site-packages/jax_plugins/xla_cuda12/__init__.py\", line 285, in _check_cuda_versions\n", " local_device_count = cuda_versions.cuda_device_count()\n", " ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n", "RuntimeError: jaxlib/cuda/versions_helpers.cc:113: operation cuInit(0) failed: CUDA_ERROR_UNKNOWN\n", "WARNING:2026-02-01 21:50:34,708:jax._src.xla_bridge:876: An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n", "/home/wassim/micromamba/envs/fg/lib/python3.11/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", " from .autonotebook import tqdm as notebook_tqdm\n" ] } ], "source": [ "# Setup and Data Loading\n", "\n", "\n", "# Core libraries\n", "# Data utilities\n", "from functools import partial\n", "\n", "import furax_cs as fcs\n", "import healpy as hp\n", "\n", "# JAX ecosystem\n", "import jax\n", "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# FURAX framework\n", "from furax import HomothetyOperator\n", "from furax.obs import negative_log_likelihood, sky_signal\n", "from furax.obs.stokes import Stokes\n", "\n", "# JAX-HEALPix for mask and map operations\n", "from jax_healpy.clustering import get_cutout_from_mask, get_fullmap_from_cutout\n", "\n", "# Configure JAX\n", "jax.config.update(\"jax_enable_x64\", True)" ] }, { "cell_type": "code", "execution_count": 3, "id": "c7948b87", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/wassim/Projects/CMB/furax-compsep-paper/src/furax_cs/data/instruments.py:41: UserWarning: A JAX array is being set as static! This can result in unexpected behavior and is usually a mistake to do.\n", " return FGBusterInstrument(frequency, depth_i, depth_p)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[INFO] Loaded freq_maps for nside 64 from cache with noise_ratio 0.0.\n", "[INFO] Loaded freq_maps for nside 64 from cache.\n", "Frequency maps shape: (15, 3, 49152)\n", "Frequencies: 15 bands from 40 to 402 GHz\n", "Sky coverage: 19.7% (9,695 pixels)\n", "Masked data shape: (15, 9695)\n" ] } ], "source": [ "# Load CMB and foreground data\n", "nside = 64\n", "npixels = 12 * nside**2\n", "\n", "# Generate and load multi-frequency data\n", "fcs.save_to_cache(nside, sky=\"c1d1s1\")\n", "nu, freq_maps = fcs.load_from_cache(nside, sky=\"c1d1s1\")\n", "print(f\"Frequency maps shape: {freq_maps.shape}\")\n", "print(f\"Frequencies: {len(nu)} bands from {nu[0]:.0f} to {nu[-1]:.0f} GHz\")\n", "\n", "# Convert to FURAX format (Q,U polarization)\n", "d = Stokes.from_stokes(Q=freq_maps[:, 1, :], U=freq_maps[:, 2, :])\n", "\n", "# Load galactic mask (cleanest 20% of sky)\n", "mask = fcs.get_mask(\"GAL020\", nside=nside)\n", "(indices,) = jnp.where(mask == 1)\n", "coverage = jnp.mean(mask) * 100\n", "print(f\"Sky coverage: {coverage:.1f}% ({len(indices):,} pixels)\")\n", "\n", "# Extract masked data for computation\n", "masked_d = get_cutout_from_mask(d, indices, axis=1)\n", "print(f\"Masked data shape: {masked_d.shape}\")" ] }, { "cell_type": "markdown", "id": "9b4x600oope", "metadata": {}, "source": [ "## Step 2: Multi-Resolution Patch Generation\n", "\n", "The PTEP method uses HEALPix `ud_grade` to create resolution-based patches:\n", "\n", "### How ud_grade Works\n", "1. **Downgrade**: Map pixels to lower resolution (fewer pixels)\n", "2. **Upgrade**: Map back to original resolution\n", "3. **Result**: Pixels that share the same low-res pixel become a patch\n", "\n", "### Resolution Choices\n", "- **beta_dust** (nside=64): Full resolution - varies pixel-by-pixel\n", "- **temp_dust** (nside=32): 4x fewer patches - varies more slowly\n", "- **beta_pl** (nside=16): 16x fewer patches - varies most slowly\n", "\n", "This reduces the parameter count significantly while preserving physical variation scales." ] }, { "cell_type": "code", "execution_count": 4, "id": "8e4d477f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Multi-resolution configuration:\n", " Dust spectral index (beta_dust): nside=64 (49,152 pixels)\n", " Dust temperature (temp_dust): nside=32 (12,288 pixels)\n", " Synchrotron index (beta_pl): nside=16 (3,072 pixels)\n", "\n", "Generating multi-resolution patches...\n", "Resolution patch counts:\n", " beta_dust: 9695 patches\n", " beta_pl: 682 patches\n", " temp_dust: 2516 patches\n" ] } ], "source": [ "# Multi-Resolution Patch Generation\n", "\n", "# Configure resolution parameters for different spectral indices\n", "target_ud_grade = {\n", " \"beta_dust\": 64,\n", " \"temp_dust\": 32,\n", " \"beta_pl\": 16,\n", "}\n", "ud_beta_d = target_ud_grade[\"beta_dust\"]\n", "ud_temp_d = target_ud_grade[\"temp_dust\"]\n", "ud_beta_pl = target_ud_grade[\"beta_pl\"]\n", "\n", "print(\"Multi-resolution configuration:\")\n", "print(f\" Dust spectral index (beta_dust): nside={ud_beta_d} ({12 * ud_beta_d**2:,} pixels)\")\n", "print(f\" Dust temperature (temp_dust): nside={ud_temp_d} ({12 * ud_temp_d**2:,} pixels)\")\n", "print(f\" Synchrotron index (beta_pl): nside={ud_beta_pl} ({12 * ud_beta_pl**2:,} pixels)\")\n", "\n", "# Generate resolution-based patch indices\n", "print(\"\\nGenerating multi-resolution patches...\")\n", "masked_patches = fcs.multires_clusters(mask, indices, target_ud_grade, nside)\n", "\n", "# Count unique patches for each parameter\n", "max_count = {\n", " key.replace(\"_patches\", \"\"): int(jnp.unique(val).size) for key, val in masked_patches.items()\n", "}\n", "\n", "print(\"Resolution patch counts:\")\n", "for param, count in max_count.items():\n", " print(f\" {param}: {count} patches\")" ] }, { "cell_type": "markdown", "id": "c4fe67d6", "metadata": {}, "source": [ "# Visualize Clusters\n", "\n", "Consider using `from jax_healpy.clustering._clustering import shuffle_labels` to shuffle cluster labels for better visualization.\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "cell-2", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_100842/3775188447.py:23: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", " plt.tight_layout()\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Multi-resolution patches ready for optimization\n" ] } ], "source": [ "# Visualize the multi-resolution patches\n", "fig = plt.figure(figsize=(15, 5))\n", "\n", "param_labels = [\n", " \"Dust Spectral Index\\n(nside=64)\",\n", " \"Dust Temperature\\n(nside=32)\",\n", " \"Synchrotron Index\\n(nside=16)\",\n", "]\n", "patch_maps = get_fullmap_from_cutout(masked_patches, indices, nside=nside)\n", "patch_maps = [\n", " patch_maps[\"beta_dust_patches\"],\n", " patch_maps[\"temp_dust_patches\"],\n", " patch_maps[\"beta_pl_patches\"],\n", "]\n", "\n", "for i, (label, patch_map) in enumerate(zip(param_labels, patch_maps)):\n", " n_unique = np.unique(patch_map).size\n", "\n", " hp.mollview(\n", " patch_map, title=f\"{label}\\n({n_unique} patches)\", sub=(1, 3, i + 1), bgcolor=(0.0,) * 4\n", " )\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(\"Multi-resolution patches ready for optimization\")" ] }, { "cell_type": "markdown", "id": "3lhk6gth6j8", "metadata": {}, "source": [ "## Step 3: Parameter Optimization\n", "\n", "With resolution-based patches defined, we optimize spectral parameters at each patch.\n", "\n", "### Computational Advantage\n", "- Full resolution: 49,152 parameters per spectral index\n", "- PTEP approach: 9,695 + 2,516 + 682 = 12,893 total parameters\n", "- **3.8x reduction** in parameter count\n", "\n", "### Physical Justification\n", "- Dust temperature varies on ~1° scales → nside=32 sufficient\n", "- Synchrotron index varies on ~3° scales → nside=16 sufficient\n", "- Dust spectral index has finer structure → nside=64 needed" ] }, { "cell_type": "code", "execution_count": 6, "id": "cell-3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Parameter initialization:\n", " beta_dust: 9695 patches at resolution, initial value = 1.54\n", " beta_pl: 682 patches at resolution, initial value = -3.0\n", " temp_dust: 2516 patches at resolution, initial value = 20.0\n", "\n", "Running multi-resolution optimization...\n", "This may take a few minutes...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "100.00%|██████████| [10:04<00:00, 6.05s/%]" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Optimization completed!\n", "Final function value: -7.39e+04\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# Parameter Optimization\n", "\n", "# Setup optimization parameters\n", "dust_nu0 = 160.0 # Dust reference frequency (GHz)\n", "synchrotron_nu0 = 20.0 # Synchrotron reference frequency (GHz)\n", "\n", "# Create objective function with fixed reference frequencies\n", "negative_log_likelihood_fn = partial(\n", " negative_log_likelihood,\n", " dust_nu0=dust_nu0,\n", " synchrotron_nu0=synchrotron_nu0,\n", " analytical_gradient=True,\n", ")\n", "\n", "sky_signal_fn = partial(sky_signal, dust_nu0=dust_nu0, synchrotron_nu0=synchrotron_nu0)\n", "\n", "# Initialize parameters for each resolution level (realistic starting values)\n", "base_params = {\n", " \"beta_dust\": 1.54, # Dust spectral index\n", " \"temp_dust\": 20.0, # 20K dust temperature\n", " \"beta_pl\": -3.0, # Synchrotron index\n", "}\n", "\n", "initial_params = jax.tree.map(lambda v, c: jnp.full((c,), v), base_params, max_count)\n", "\n", "print(\"Parameter initialization:\")\n", "for param, values in initial_params.items():\n", " print(f\" {param}: {len(values)} patches at resolution, initial value = {values[0]}\")\n", "\n", "# Create noise operator (simplified for demonstration)\n", "N = HomothetyOperator(jnp.ones(1), in_structure=masked_d.structure)\n", "\n", "print(\"\\nRunning multi-resolution optimization...\")\n", "print(\"This may take a few minutes...\")\n", "\n", "# Run optimization using unified minimize API\n", "final_params, final_state = fcs.minimize(\n", " fn=negative_log_likelihood_fn,\n", " init_params=initial_params,\n", " solver_name=\"optax_lbfgs\",\n", " max_iter=1000,\n", " rtol=1e-16,\n", " atol=1e-16,\n", " precondition=True,\n", " nu=nu,\n", " N=N,\n", " d=masked_d,\n", " patch_indices=masked_patches,\n", ")\n", "\n", "# Show optimization results\n", "print(\"\\nOptimization completed!\")\n", "print(f\"Final function value: {final_state.best_loss:.2e}\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "e6639d48", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "UnifiedState(\n", " best_loss=f64[],\n", " best_y={'beta_dust': f64[9695], 'beta_pl': f64[682], 'temp_dust': f64[2516]},\n", " iter_num=weak_i64[],\n", " solver_state=_BestSoFarState(\n", " best_y={'beta_dust': f64[9695], 'beta_pl': f64[682], 'temp_dust': f64[2516]},\n", " best_aux=None,\n", " best_loss=f64[],\n", " state=_OptaxState(\n", " step=weak_i64[],\n", " f=f64[],\n", " opt_state=(\n", " ScaleByLBFGSState(\n", " count=i32[],\n", " params={\n", " 'beta_dust': f64[9695], 'beta_pl': f64[682], 'temp_dust': f64[2516]\n", " },\n", " updates={\n", " 'beta_dust': f64[9695], 'beta_pl': f64[682], 'temp_dust': f64[2516]\n", " },\n", " diff_params_memory={\n", " 'beta_dust': f64[10,9695],\n", " 'beta_pl': f64[10,682],\n", " 'temp_dust': f64[10,2516]\n", " },\n", " diff_updates_memory={\n", " 'beta_dust': f64[10,9695],\n", " 'beta_pl': f64[10,682],\n", " 'temp_dust': f64[10,2516]\n", " },\n", " weights_memory=f64[10]\n", " ),\n", " EmptyState(),\n", " ScaleByZoomLinesearchState(\n", " learning_rate=f64[],\n", " value=f64[],\n", " grad={\n", " 'beta_dust': f64[9695], 'beta_pl': f64[682], 'temp_dust': f64[2516]\n", " },\n", " info=ZoomLinesearchInfo(\n", " num_linesearch_steps=i64[],\n", " decrease_error=f64[],\n", " curvature_error=f64[]\n", " )\n", " )\n", " ),\n", " terminate=bool[]\n", " )\n", " )\n", ")" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "final_state" ] }, { "cell_type": "code", "execution_count": 8, "id": "7f643826", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Optimized parameter ranges:\n", " beta_dust (nside=64): [1.366, 2.585], mean = 1.614 ± 0.054\n", " beta_pl (nside=16): [-3.163, -2.312], mean = -3.012 ± 0.056\n", " temp_dust (nside=32): [15.672, 26.297], mean = 20.856 ± 0.931\n", "\n", "CMB reconstruction completed\n", "CMB shape: Q=(9695,), U=(9695,)\n" ] } ], "source": [ "# Display optimized parameter statistics\n", "print(\"\\nOptimized parameter ranges:\")\n", "for param, values in final_params.items():\n", " resolution_info = {\n", " \"beta_dust\": f\"nside={ud_beta_d}\",\n", " \"temp_dust\": f\"nside={ud_temp_d}\",\n", " \"beta_pl\": f\"nside={ud_beta_pl}\",\n", " }\n", " print(\n", " f\" {param} ({resolution_info[param]}): [{jnp.min(values):.3f}, {jnp.max(values):.3f}], \"\n", " f\"mean = {jnp.mean(values):.3f} ± {jnp.std(values):.3f}\"\n", " )\n", "\n", "# Compute CMB reconstruction with optimized parameters\n", "reconstructed_signal = sky_signal_fn(\n", " final_params, nu=nu, d=masked_d, N=N, patch_indices=masked_patches\n", ")\n", "cmb_reconstruction = reconstructed_signal[\"cmb\"]\n", "print(\"\\nCMB reconstruction completed\")\n", "print(f\"CMB shape: Q={cmb_reconstruction.q.shape}, U={cmb_reconstruction.u.shape}\")" ] }, { "cell_type": "markdown", "id": "i673urhbxr", "metadata": {}, "source": [ "## Step 4: Parameter Map Reconstruction\n", "\n", "The optimized parameters are mapped back to full resolution:\n", "1. Each pixel gets the value from its resolution patch\n", "2. The result shows the multi-resolution structure\n", "3. Lower-resolution parameters appear as larger uniform regions" ] }, { "cell_type": "code", "execution_count": 9, "id": "a73d1b62", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reconstructing full-sky parameter maps...\n", "Parameter map reconstruction completed!\n", "CMB maps reconstructed to full sky\n", "Parameter maps available: ['temp_dust', 'beta_dust', 'beta_pl']\n", "\\nFull-sky parameter statistics:\n", " temp_dust: [15.672, 26.297], mean = 20.866 ± 0.937\n", " beta_dust: [1.366, 2.585], mean = 1.614 ± 0.054\n", " beta_pl: [-3.163, -2.312], mean = -3.015 ± 0.048\n" ] } ], "source": [ "# Parameter Map Reconstruction\n", "\n", "# Map cluster parameters back to full sky maps\n", "print(\"Reconstructing full-sky parameter maps...\")\n", "\n", "param_maps = {}\n", "for param_name in [\"temp_dust\", \"beta_dust\", \"beta_pl\"]:\n", " # Get optimized parameter values for each cluster\n", " param_values = final_params[param_name]\n", " cluster_indices = masked_patches[f\"{param_name}_patches\"]\n", "\n", " # Map parameter values to masked pixels using cluster assignments\n", " param_map_masked = param_values[cluster_indices]\n", "\n", " # Convert back to full HEALPix map\n", " full_param_map = get_fullmap_from_cutout(param_map_masked, indices, nside=nside)\n", " param_maps[param_name] = full_param_map\n", "\n", "print(\"Parameter map reconstruction completed!\")\n", "\n", "# Also reconstruct CMB maps for visualization\n", "cmb_q_full = get_fullmap_from_cutout(cmb_reconstruction.q, indices, nside=nside)\n", "cmb_u_full = get_fullmap_from_cutout(cmb_reconstruction.u, indices, nside=nside)\n", "\n", "print(\"CMB maps reconstructed to full sky\")\n", "print(f\"Parameter maps available: {list(param_maps.keys())}\")\n", "\n", "# Display parameter statistics\n", "print(\"\\\\nFull-sky parameter statistics:\")\n", "for param_name, param_map in param_maps.items():\n", " valid_data = param_map[param_map != hp.UNSEEN]\n", " if len(valid_data) > 0:\n", " print(\n", " f\" {param_name}: [{jnp.min(valid_data):.3f}, {jnp.max(valid_data):.3f}], \"\n", " f\"mean = {jnp.mean(valid_data):.3f} ± {jnp.std(valid_data):.3f}\"\n", " )\n", " else:\n", " print(f\" {param_name}: No valid data\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "cell-5", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_100842/1189568572.py:11: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", " plt.tight_layout()\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Results Visualization\n", "fig = plt.figure(figsize=(15, 5))\n", "\n", "# Plot the three parameter maps only\n", "hp.mollview(param_maps[\"temp_dust\"], title=\"Dust Temperature\", sub=(1, 3, 1), bgcolor=(0.0,) * 4)\n", "\n", "hp.mollview(param_maps[\"beta_dust\"], title=\"Dust Spectral Index\", sub=(1, 3, 2), bgcolor=(0.0,) * 4)\n", "\n", "hp.mollview(param_maps[\"beta_pl\"], title=\"Synchrotron Index\", sub=(1, 3, 3), bgcolor=(0.0,) * 4)\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cell-6", "metadata": {}, "source": [ "## Command-Line Tool for Large-Scale Analysis\n", "\n", "The complete workflow demonstrated above is implemented in the production script `05-PTEP-model.py` for large-scale analysis on HPC clusters.\n", "\n", "### Basic Usage\n", "\n", "```bash\n", "# Run multi-resolution PTEP component separation\n", "!pip install furax-cs\n", "ptep-model -n 64 -ud 64 32 16 -tag c1d1s1 -m GAL020 -i LiteBIRD\n", "\n", "```\n", "\n", "### Key Parameters\n", "\n", "- `-n 64`: HEALPix resolution (nside=64 → ~55 arcmin pixels)\n", "- `-ud 64 32 16`: Target nside values for [dust_beta, dust_temp, sync_beta] resolutions\n", "- `-tag c1d1s1`: Sky simulation (CMB + dust + synchrotron)\n", "- `-m GAL020`: Galactic mask (20% cleanest sky)\n", "- `-i LiteBIRD`: Instrument configuration\n", "\n", "### Output Structure\n", "\n", "Results are saved to `results/PTEP_{config}_BD{ud1}_TD{ud2}_BS{ud3}_{instrument}_{mask}_{noise}/`:\n", "- `best_params.npz`: Optimized spectral parameters per resolution\n", "- `results.npz`: Full optimization results with resolution patches\n", "- `mask.npy`: Sky mask used for analysis\n", "\n", "### Scaling to Large Problems\n", "\n", "The command-line tool provides:\n", "- **Resolution flexibility**: Adjust parameter resolutions based on astrophysical scales\n", "- **Computational efficiency**: Lower resolution for slowly-varying parameters\n", "- **Monte Carlo analysis**: Multiple noise realizations (`-ns` parameter)\n", "- **SLURM integration**: Distributed computing for GPU clusters\n", "- **Memory optimization**: Reduced parameter space compared to full-resolution methods\n", "\n", "## Key Benefits\n", "\n", "1. **Computational Efficiency**: Parameters optimized at appropriate spatial scales\n", "2. **Physical Realism**: Resolution matched to astrophysical variation scales\n", "3. **Memory Optimization**: Reduced parameter space for slowly-varying components\n", "4. **Baseline Compatibility**: Based on LiteBIRD PTEP methodology\n", "\n", "This multi-resolution approach provides a computationally efficient alternative to adaptive clustering, particularly effective when astrophysical parameter variation scales are well understood." ] } ], "metadata": { "kernelspec": { "display_name": "fg", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 5 }