Atomizer/studies/m1_mirror_adaptive_V15/STUDY_REPORT.md

M1 Mirror Adaptive V15 - NSGA-II Multi-Objective Optimization Report

Study: m1_mirror_adaptive_V15 Algorithm: NSGA-II (Multi-Objective Genetic Algorithm) Status: Completed Created: 2025-12-12 Completed: 2025-12-15

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Executive Summary

V15 applied NSGA-II multi-objective optimization to explore the Pareto front of design trade-offs, seeded with 494 valid trials from V14. The campaign completed 126 new FEA evaluations but did not find improvements over the V14-optimized designs.

Metric	Value
Total Trials in DB	644
Seeded from V14	494
New V15 FEA Trials	126
Failed Trials	24
Pareto Front Size	2
Best Weighted Sum	121.72 (from V14 seed)
Best V15 FEA Weighted Sum	127.35

Key Finding: NSGA-II exploration confirmed that V14 TPE optimization had already converged to the optimal region. No V15 FEA trial improved upon the seeded V14 data.

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1. Optimization Configuration

1.1 Algorithm Settings

Parameter	Value
Algorithm	NSGA-II
Population Size	50
Crossover Probability	0.9
Mutation	Adaptive
Seed	42

1.2 Design Variables (11 total)

Variable	Min	Max	Baseline	Best Value	Units
lateral_inner_angle	25.0	30.0	26.79	27.88	deg
lateral_outer_angle	11.0	17.0	14.64	13.19	deg
lateral_outer_pivot	9.0	12.0	10.40	11.53	mm
lateral_inner_pivot	5.0	12.0	10.07	7.41	mm
lateral_middle_pivot	15.0	27.0	20.73	22.95	mm
lateral_closeness	9.5	12.5	11.02	9.93	mm
whiffle_min	30.0	72.0	40.55	58.90	mm
whiffle_outer_to_vertical	60.0	80.0	75.67	77.84	deg
whiffle_triangle_closeness	50.0	80.0	60.00	66.88	mm
blank_backface_angle	4.1	4.5	4.15	4.30	deg
inner_circular_rib_dia	480.0	620.0	534.00	505.89	mm

1.3 Objectives

Objective	Description	Target	Direction	Weight
rel_filtered_rms_40_vs_20	40° tracking error vs 20° ref	4.0 nm	minimize	5
rel_filtered_rms_60_vs_20	60° tracking error vs 20° ref	10.0 nm	minimize	5
mfg_90_optician_workload	Manufacturing deformation (J1-J3 filtered)	20.0 nm	minimize	1

Weighted Sum Formula: 5 × obj_40 + 5 × obj_60 + 1 × obj_mfg

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2. Results Analysis

2.1 Best Design (Global - from V14 Seed)

Trial #445 (originally V14 Trial #725)

Objective	Value	Target	Status
40° vs 20° tracking	5.99 nm	4.0 nm	❌ Above target
60° vs 20° tracking	13.10 nm	10.0 nm	❌ Above target
Manufacturing (90°)	26.28 nm	20.0 nm	❌ Above target
Weighted Sum	121.72	-	Best achieved

2.2 Best V15 FEA Design

Trial #631 (New V15 FEA evaluation)

Objective	Value	vs Best	Delta
40° vs 20° tracking	5.92 nm	5.99 nm	-1.2% ✓
60° vs 20° tracking	13.78 nm	13.10 nm	+5.2% ✗
Manufacturing (90°)	28.83 nm	26.28 nm	+9.7% ✗
Weighted Sum	127.35	121.72	+4.6% ✗

2.3 Top 10 Designs Overall

Rank	Trial	Source	40°/20° (nm)	60°/20° (nm)	Mfg (nm)	WS
1	#445	V14_FEA_725	5.99	13.10	26.28	121.72
2	#444	V14_FEA_724	6.05	13.17	26.42	122.54
3	#274	V14_FEA_550	5.76	13.27	27.53	122.69
4	#440	V14_FEA_720	6.09	13.34	26.96	124.12
5	#438	V14_FEA_716	6.08	13.37	27.17	124.42
6	#271	V14_FEA_547	5.81	13.43	28.36	124.57
7	#290	V14_FEA_566	5.85	13.48	28.03	124.66
8	#275	V14_FEA_551	5.83	13.50	28.06	124.67
9	#487	V14_FEA_778	6.24	13.41	26.55	124.77
10	#364	V14_FEA_642	5.89	13.50	27.95	124.91

Observation: All top 10 designs are from V14 seeded data. No V15 FEA trial made it into the top 10.

2.4 Top 5 V15 FEA Trials

Rank	Trial	40°/20° (nm)	60°/20° (nm)	Mfg (nm)	WS
1	#631	5.92	13.78	28.83	127.35
2	#540	6.60	14.08	27.82	131.21
3	#621	6.01	14.10	31.08	131.63
4	#570	6.07	14.31	31.35	133.28
5	#624	5.98	14.47	32.22	134.45

2.5 Pareto Front Analysis

The true Pareto front (non-dominated solutions) contains only 2 designs:

Trial	Source	40°/20° (nm)	60°/20° (nm)	Mfg (nm)	WS
#445	V14_FEA_725	5.99	13.10	26.28	121.72
#274	V14_FEA_550	5.76	13.27	27.53	122.69

Interpretation: The small Pareto front indicates the objectives are not strongly conflicting in the optimal region. Trial #274 trades slightly worse 60° performance and manufacturing for better 40° performance.

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3. Source Distribution

Source	Count	Percentage
V14 Seeded	494	76.7%
V15 FEA (new)	126	19.6%
V15 FEA (failed)	24	3.7%
Total	644	100%

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4. Why NSGA-II Did Not Improve

1. V14 TPE Was Highly Effective: The 785 TPE trials in V14 (including V11-V13 seeds) already explored the design space extensively and found a strong local/global optimum.

2. Converged Design Space: The best designs cluster tightly in parameter space, indicating convergence to an optimal region.

3. NSGA-II Exploration vs Exploitation: NSGA-II prioritizes Pareto front diversity over single-objective convergence. It sampled widely but the promising regions were already well-explored.

4. Small Pareto Front: With only 2 truly non-dominated solutions, there's limited trade-off space to explore.

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5. Comparison with Prior Versions

Version	Algorithm	FEA Trials	Best WS	Best 40°	Best 60°	Best Mfg
V11	GNN + TuRBO	107	129.33	6.34	13.81	28.54
V12	GNN + TuRBO	5131*	129.33	6.34	13.81	28.54
V13	TPE	291	129.33	6.34	13.81	28.54
V14	TPE (adaptive)	785	121.72	5.99	13.10	26.28
V15	NSGA-II	126	121.72**	5.99**	13.10**	26.28**

* V12 includes 5000+ surrogate predictions ** Best from seeded V14 data, not new V15 FEA

Campaign Improvement: From V11 baseline to V14/V15 best:

• 40° tracking: 6.34 → 5.99 nm (-5.5%)
• 60° tracking: 13.81 → 13.10 nm (-5.1%)
• Manufacturing: 28.54 → 26.28 nm (-7.9%)
• Weighted Sum: 129.33 → 121.72 (-5.9%)

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6. Best Design Summary

6.1 Recommended Configuration

The best design found across the entire M1 mirror optimization campaign (V11-V15):

Trial: V14 #725 (V15 #445)
Source: FEA Validated

Design Variables:
  lateral_inner_angle:        27.8846°
  lateral_outer_angle:        13.1862°
  lateral_outer_pivot:        11.5290 mm
  lateral_inner_pivot:         7.4063 mm
  lateral_middle_pivot:       22.9518 mm
  lateral_closeness:           9.9300 mm
  whiffle_min:                58.8986 mm
  whiffle_outer_to_vertical:  77.8388°
  whiffle_triangle_closeness: 66.8829 mm
  blank_backface_angle:        4.3030°
  inner_circular_rib_dia:    505.8876 mm

Performance:
  40° vs 20° tracking:     5.99 nm (target: 4.0 nm)
  60° vs 20° tracking:    13.10 nm (target: 10.0 nm)
  Manufacturing (90°):    26.28 nm (target: 20.0 nm)
  Weighted Sum:          121.72

6.2 Target Achievement Status

Objective	Target	Achieved	Gap	Status
40° tracking	4.0 nm	5.99 nm	+50%	❌ Not met
60° tracking	10.0 nm	13.10 nm	+31%	❌ Not met
Manufacturing	20.0 nm	26.28 nm	+31%	❌ Not met

Conclusion: Current design space constraints cannot achieve the specified targets. Consider:

1. Expanding design variable bounds
2. Adding new design variables
3. Relaxing targets based on physical limitations
4. Design modifications (geometry changes, materials)

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7. Conclusions and Recommendations

7.1 Key Conclusions

1. Optimization Converged: The M1 mirror optimization campaign has effectively converged after ~1,400 total FEA evaluations across V11-V15.

2. V14 TPE Found Optimal: The V14 TPE optimization found the best design; V15 NSGA-II exploration confirmed this optimum.

3. Limited Trade-offs: The small Pareto front (2 solutions) indicates the three objectives are not strongly conflicting in the optimal region.

4. Targets Not Achievable: Current design space cannot achieve the specified targets. The best achievable performance is ~50% above targets.

7.2 Recommendations

1. Accept Current Best: Trial #725 (V14) / #445 (V15) represents the optimal design within current constraints.

2. Archive for Production: Run python tools/archive_best_design.py m1_mirror_adaptive_V15 to archive the best design.

3. Future Work Options:

   • Expand design space (new variables, wider bounds)
   • Alternative support structures
   • Material optimization
   • Active correction systems

4. No Further Optimization Needed: Additional trials are unlikely to find significant improvements without design space changes.

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Appendix A: File Locations

studies/m1_mirror_adaptive_V15/
├── 1_setup/
│   ├── optimization_config.json    # Study configuration
│   └── model/                      # NX model files
├── 2_iterations/
│   └── iter*/                      # FEA iteration folders
├── 3_results/
│   ├── study.db                    # Optuna database
│   ├── pareto_front.json           # Pareto front data
│   └── optimization.log            # Execution log
├── run_optimization.py             # Main optimization script
└── STUDY_REPORT.md                 # This report

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Appendix B: Zernike Analysis

Subcase Configuration

Subcase	Angle	Description
1	90°	Manufacturing/polishing position
2	20°	Reference position (minimum gravity)
3	40°	Operational tracking position
4	60°	Operational tracking position

Filtering Strategy

• Tracking (40°, 60° vs 20°): Filter Zernike modes J0-J3 (piston, tip/tilt, focus)
• Manufacturing (90° vs 20°): Filter only J1-J3 (tip/tilt, focus)
• Number of Zernike modes: 50

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Report generated by Atomizer. Last updated: 2025-12-15