Final Sprint

README.md

@@ -57,6 +57,28 @@ uv run mlflow ui
 # https://kni.dk/mlflow-ana-p3/
 ```
 
+## Hyperparameter Optimization
+
+Optimize `corner_smoothing` using [Optuna](https://optuna.org/) + Hydra:
+
+```bash
+# Minimize L2 error vs FV reference (default objective)
+uv run python main.py -m +experiment/optimization=corner_smoothing \
+    'solver.corner_smoothing=interval(0.02,0.35)' Re=1000 N=30
+
+# Minimize vortex error vs Botella & Peyret reference
+uv run python main.py -m +experiment/optimization=corner_smoothing \
+    'solver.corner_smoothing=interval(0.02,0.35)' Re=1000 N=30 \
+    optuna.objective=botella_vortex
+
+# Customize trials and parallelism
+uv run python main.py -m +experiment/optimization=corner_smoothing \
+    'solver.corner_smoothing=interval(0.02,0.35)' Re=1000 N=30 \
+    hydra.sweeper.n_trials=20 hydra.sweeper.n_jobs=8
+```
+
+View results in MLflow under `Optuna-CornerSmoothing-{objective}`. See [docs/optuna_optimization.md](docs/optuna_optimization.md) for details.
+
 ## References
 
 - [High-Re solutions for incompressible flow (Ghia et al.)](https://www.sciencedirect.com/science/article/pii/0021999182900584)

conf/config.yaml

@@ -18,7 +18,7 @@ N: 32
 
 # Solver control
 tolerance: 1.0e-6
-max_iterations: 500000
+max_iterations: 10000000
 
 # Experiment naming
 experiment_name: LDC-Dev

conf/experiment/benchmarking/timings.yaml

@@ -9,7 +9,7 @@ defaults:
 
 # MLflow experiment
 experiment_name: LDC-Benchmarking
-sweep_name: multigrid-comparison-Re${Re}
+sweep_name: Benchmarking
 
 # Benchmarking parameters
 Re: 100
@@ -21,6 +21,4 @@ hydra:
       # Sweep over spectral solver variants
       # sg: Single Grid (no multigrid)
       # fsg: Full Single Grid
-      # vmg: V-cycle MultiGrid
-      # fmg: Full MultiGrid
-      solver: spectral/sg,spectral/fsg,spectral/vmg,spectral/fmg
+      solver: spectral/sg,spectral/fsg

conf/experiment/optimization/corner_smoothing.yaml

@@ -0,0 +1,57 @@
+# @package _global_
+#
+# Optuna optimization of corner_smoothing parameter
+#
+# Supported objectives (override with optuna.objective=...):
+#   - fv_l2_error: Minimize L2 error vs FV reference (default)
+#   - botella_vortex: Minimize vortex metric error vs Botella & Peyret
+#
+# Note: Multi-objective optimization is not supported by hydra-optuna-sweeper 1.x
+#
+# Usage:
+#   # FV L2 error (default)
+#   uv run python main.py -m +experiment/optimization=corner_smoothing \
+#       'solver.corner_smoothing=interval(0.02,0.35)'
+#
+#   # Botella vortex metrics
+#   uv run python main.py -m +experiment/optimization=corner_smoothing \
+#       'solver.corner_smoothing=interval(0.02,0.35)' optuna.objective=botella_vortex
+#
+#   # Custom Re/N
+#   uv run python main.py -m +experiment/optimization=corner_smoothing \
+#       'solver.corner_smoothing=interval(0.02,0.35)' Re=1000 N=32
+
+defaults:
+  - override /solver: spectral/fsg
+  - override /hydra/sweeper: optuna_corner
+
+# Experiment name (dynamically includes objective type)
+experiment_name: Optuna-CornerSmoothing
+sweep_name: corner-smoothing-${optuna.objective}
+# Grid and physics
+N: 30
+Re: 1000
+
+# Solver settings (strict convergence)
+# Note: Early NaN/Inf detection exits diverging runs quickly
+tolerance: 1.0e-6
+max_iterations: 500000
+
+# Validation against non-regularized FV (true LDC solution)
+validation:
+  reference_dir: data/validation/fv
+
+# Optimization settings
+# Override objective with: optuna.objective=botella_vortex
+optuna:
+  objective: fv_l2_error  # Options: fv_l2_error, botella_vortex
+
+# Optuna sweeper settings
+hydra:
+  sweeper:
+    study_name: corner_smoothing_${optuna.objective}_Re${Re}_N${N}
+    n_trials: 15
+    n_jobs: 5
+    params:
+      N: 30, 40, 50
+      solver.corner_smoothing: interval(0.01, 0.10)

conf/experiment/validation/ghia/fv.yaml

@@ -6,12 +6,13 @@ defaults:
   - override /solver: fv
 
 # MLflow experiment
-experiment_name: LDC-Validation
-sweep_name: ghia-Re${Re}
+experiment_name: LDC-GHIA-PLOTS
+
+sweep_name: ghia-plots
 
 hydra:
   sweeper:
     params:
       # Sweep over FV grid sizes
-      N: 64
-      Re: 100
+      N: 128
+      Re: 1000

conf/experiment/validation/ghia/spectral.yaml

@@ -6,8 +6,12 @@ defaults:
   - override /solver: spectral/sg
 
 # MLflow experiment
-experiment_name: LDC-Validation
-sweep_name: ghia-HPC
+experiment_name: LDC-GHIA-PLOTS
+sweep_name: ghia-plots
+
+solver: 
+  corner_treatment: smoothing
+  corner_smoothing: 0.15   # smoothing width (fraction of domain) for smoothing method
 
 # Validation parameters
 
@@ -16,5 +20,5 @@ hydra:
     params:
       # Sweep over spectral solver types
       solver: spectral/fsg #,spectral/vmg #, spectral/vmg
-      Re: 400, 1000
-      N: 12, 14, 16, 18, 20, 24, 28, 32, 36, 40, 46, 50, 56, 60, 64, 68, 74, 82, 86, 90
+      Re: 1000
+      N: 16, 20, 32 

conf/experiment/validation/convergence/spectral-regu-400.yaml → conf/experiment/validation/saad-regu/spectral.yaml

@@ -7,8 +7,8 @@ defaults:
   - override /validation: fv-regu
 
 # MLflow experiment
-experiment_name: LDC-Convergence
-sweep_name: regu-Re400
+experiment_name: LDC-Saad-Regu
+sweep_name: regu-Re1000
 
 # Use Saad/polynomial corner treatment for regularized problem
 solver:
@@ -17,5 +17,5 @@ solver:
 hydra:
   sweeper:
     params:
-      Re: 400
-      N: 12, 14, 16, 18, 24, 32, 40, 48, 56, 64
+      Re: 1000
+      N: 16, 32, 64, 128

conf/experiment/validation/convergence/spectral-regu-1000.yaml → conf/experiment/validation/saad/spectral.yaml

@@ -1,21 +1,21 @@
 # @package _global_
-# Convergence test - Spectral solver with Saad regularization at Re=1000
+# Convergence test - Spectral solver with Saad regularization at Re=400
 # Sweep over N values with polynomial corner treatment
 
 defaults:
   - override /solver: spectral/fsg
-  - override /validation: fv-regu
+  - override /validation: fv
 
 # MLflow experiment
-experiment_name: LDC-Convergence
-sweep_name: regu-Re1000-b
+experiment_name: LDC-Saad
+sweep_name: Re1000
 
 # Use Saad/polynomial corner treatment for regularized problem
 solver:
-  corner_treatment: saad
+  corner_smoothing: 0.15   # smoothing width (fraction of domain) for smoothing method
 
 hydra:
   sweeper:
     params:
       Re: 1000
-      N: 26, 28, 32, 36, 40, 44, 48, 64, 80, 96, 112, 128
+      N: 16, 32, 64, 128

conf/hydra/sweeper/optuna_corner.yaml

@@ -0,0 +1,28 @@
+# @package hydra.sweeper
+#
+# Optuna Sweeper Configuration for corner_smoothing optimization
+# Usage: python main.py -m hydra/sweeper=optuna_corner
+#
+# For parallel execution, set n_jobs > 1 (requires storage to be set)
+# Example: hydra.sweeper.n_jobs=4 hydra.sweeper.storage="sqlite:///optuna.db"
+
+_target_: hydra_plugins.hydra_optuna_sweeper.optuna_sweeper.OptunaSweeper
+
+defaults:
+  - sampler: tpe
+
+# Optimization direction (minimize L2 error)
+direction: minimize
+
+# Study configuration
+study_name: corner_smoothing_optimization
+storage: null  # Set to "sqlite:///optuna.db" for parallel execution
+
+# Number of trials and parallel jobs
+n_trials: 15
+n_jobs: 1  # Set > 1 for parallel trials (requires storage)
+
+# Required fields
+search_space: null
+custom_search_space: null
+params: null

conf/solver/spectral/fsg.yaml

@@ -11,7 +11,7 @@ name: spectral_fsg
 
 # FSG Multigrid settings
 multigrid: fsg
-n_levels: 3
+n_levels: 2
 coarse_tolerance_factor: 1.0
 prolongation_method: fft
 restriction_method: fft

conf/solver/spectral/sg.yaml

@@ -17,7 +17,7 @@ max_iterations: ${max_iterations}
 
 # Spectral-specific parameters
 basis_type: chebyshev    # "chebyshev" or "legendre"
-CFL: 2.0
+CFL: 1.5
 beta_squared: 5.0        # artificial compressibility parameter
 
 # Corner singularity treatment

data/validation/botella/botella_Re1000_vortex.csv

@@ -0,0 +1,14 @@
+# Botella & Peyret (1998) - Benchmark spectral solution for lid-driven cavity
+# Reference: J. Comp. Phys. 179, 439-468 (2002)
+# Primary and secondary vortex characteristics at Re=1000 with regularized lid velocity
+# N=160 polynomial order (highest resolution benchmark)
+#
+# Primary vortex (PV): |psi| = magnitude of streamfunction at vortex center
+# BL (bottom-left): secondary vortex in bottom-left corner
+# BR (bottom-right): secondary vortex in bottom-right corner
+#
+# Note: psi values are absolute magnitudes (|ψ|), omega values are absolute magnitudes (|ω|)
+# Sign conventions vary between papers; we compare magnitudes.
+#
+Re,psi_primary,omega_primary,x_primary,y_primary,psi_BL,omega_BL,x_BL,y_BL,psi_BR,omega_BR,x_BR,y_BR
+1000,0.1189366,2.067753,0.4692,0.5652,2.3072e-4,1.109789,0.1360,0.1118,1.7297e-3,1.112030,0.8640,0.1118

data/validation/botella/botella_Re100_vortex.csv

@@ -0,0 +1,11 @@
+# Botella & Peyret (1998) - Benchmark spectral solution for lid-driven cavity
+# Reference: J. Comp. Phys. 179, 439-468 (2002) - Table II
+# Primary and secondary vortex characteristics at Re=100 with regularized lid velocity
+# N=128 polynomial order
+#
+# Primary vortex (PV): global minimum of streamfunction
+# BR (bottom-right): secondary vortex in bottom-right corner
+# BL (bottom-left): secondary vortex in bottom-left corner (very weak at Re=100)
+#
+Re,psi_min,psi_min_x,psi_min_y,omega_center,psi_BR,psi_BR_x,psi_BR_y,psi_BL,psi_BL_x,psi_BL_y
+100,-0.1034339,0.6188,0.7344,3.166577,1.4235e-8,0.9453,0.0625,0.0,0.0,0.0

data/validation/botella/botella_Re400_vortex.csv

@@ -0,0 +1,11 @@
+# Botella & Peyret (1998) - Benchmark spectral solution for lid-driven cavity
+# Reference: J. Comp. Phys. 179, 439-468 (2002) - Table V
+# Primary and secondary vortex characteristics at Re=400 with regularized lid velocity
+# N=128 polynomial order
+#
+# Primary vortex (PV): global minimum of streamfunction
+# BR (bottom-right): secondary vortex in bottom-right corner
+# BL (bottom-left): secondary vortex in bottom-left corner
+#
+Re,psi_min,psi_min_x,psi_min_y,omega_center,psi_BR,psi_BR_x,psi_BR_y,psi_BL,psi_BL_x,psi_BL_y
+400,-0.1139600,0.5547,0.6055,2.295353,6.4157e-7,0.8906,0.1250,5.1567e-6,0.0508,0.0469