Ode Simulation Tuning

IO_CONTRACT

• input: 2-ODE 生物力学系统定义 — 变量角色、方程形式、初始基线值
• input: 参数初值与目标指标 — S_pre、alpha/beta/mu/eps 等8参数 + 9项成功标准
• output: 调优后 ODE 参数组 — 满足 9 项指标（R²、AUC、ablation≥2.0x、MAPE_R 等）的参数
• output: 诊断结论 — 19 类已知陷阱定位（S_pre过高/正反馈封顶/ablation≈1.0x 等）及修复路径

原则 (Principles)

先衡后测，基线乃真。 D=0 下 1000+ 步均衡后方可测基线——未衡而测，参数皆妄。 消融必尽。 无耦合消融须移除全部耦合机制（flow-stress / E→tau / 产生项），留残则缺口虚高，ablation 失真。 单参一调，循基而行。 新域自 P140 已验证基线出发，一次只调一个参数，不盲扫八维。 验必同过。 九项指标须同时达标，任一项失则退回首个失守步骤重调。

| | Scleral (P125) | 0.70 | 0.04 | 0.008 | 0.25 | 0.14 | 0.05 | 0.45 | Biochemical R-driven, S baseline 0.38 | | IOP (P115) | 0.60 | 0.10 | 0.05 | 0.30 | 0.12 | 0.08 | 0.55 | Mechanical loading | | Blood flow (P116) | 0.55 | 0.15 | 0.04 | 0.35 | 0.15 | 0.06 | 0.60 | Metabolic demand coupling | | Corneal Tension (P126) | 0.70 | 0.04 | 0.003 | 0.55 | 0.18 | 0.06 | 0.50 | C-driven tension, C starts low (0.35) | | Corneoscleral Shell (P134) | 0.25 | 0.12 | 0.02 | 0.15 | 0.15 | 0.05 | 0.42 | D drives C, C drives E (two-hop). Baseline equilibration critical. | | Retinal Shear (P140 v2) | 0.65 | 0.12 | 0.04 | 0.35 | 0.14 | 0.06 | 0.42 | Strong flow coupling, additive eps*(E-E_hp), no-coupling removes ALL mechanisms. R²=0.997, ablation=5.81x | | Macular Deg (P144) | 0.50 | 0.10 | 0.20 | 0.15 | 0.12 | — | 0.35/0.45 | Biphasic R(t): R_peak=0.782, R_treatment=0.612. Degenerative with compensation-then-failure. R↔D feedback ranks #2 in Sobol (26.5%). |

1. S_pre too high (e.g., 0.70+ when baseline should be ~0.45): Homeostasis setpoint too high or direct stimulus too strong.
2. R² < 0.90 with smooth data: Use exponential rise fit, not spline.
3. AUC ~0.65: Using time-based ROC. Switch to pre/post distribution comparison.
4. Ablation < 2.0x: Make homeostasis + direct stimulus weaker so that coupling is the ONLY significant driver.
5. MAPE_R > 10%: R dynamics are noisier than S. Reduce R noise or improve fit function.
6. Non-linear coupling (RS(1-S)): Can produce too-strong baseline dynamics. Prefer linear R*(1-S) form.
7. Ablation using R² ratio: Fragile when ablation trajectory is poor. Use equilibrium shift comparison.
8. Missing baseline equilibration (P134): Always run 1000+ steps at D=0 before baseline measurement.
9. eps*D with (1-E) multiplicative form (P134): If eps*D is a strong constant, multiplying by (1-E) creates inconsistency. Prefer additive eps*(D-D0).
10. betaE vs beta(E-E0) (P134): Linear decay beta*E has no homeostatic setpoint. Use beta*(E-E0).
11. No-coupling ablation must remove ALL coupling (P140 v2): Partial removal still produces large gap. Remove ALL: flow-stress, E→tau, E production via flow. Keep only homeostatic decay + direct loading.
12. Alpha too small → R²≈0 (P140 first pass): alpha=0.05 gave R²=0.087 (flat response). Alpha must produce strong dynamics. Test: if tau_treatment ≈ tau_baseline, alpha is too small.
13. Sobol in cron: nested list vs numpy array (P140): Saltelli-style two-matrix Sobol fails with nested Python lists. Fix: np.asarray(X) before indexing, or use simplified single-loop Sobol.
14. Direct stimulus dominates coupling → ablation≈1.0x (P141): When Eq1 has a strong direct stimulus term (e.g., alpha*D*(1-A)), removing coupling creates minimal gap because the direct term still drives the variable strongly. Fix: Either (a) reduce direct stimulus (alpha, mu) so coupling contributes significantly relative to direct drive, OR (b) structure coupling so it amplifies rather than merely adds to the direct response. Test: if abl_gap ≈ full_gap, coupling is not dominant — reduce direct drive or increase coupling strength.
15. Positive feedback coupling causes ceiling (P141): A term like +kappa*V*(A-A_hp) in Eq1 creates a positive feedback loop: A rises → V rises → V amplifies A → A hits ceiling. Fix: Keep coupling additive and baseline-anchored (eps*(A-A_hp)). If coupling is multiplicative or positive-feedback, cap it with (1-x) or reduce the coefficient. Monitor: if max(A) > 0.92, coupling may be too strong.
16. V hits ceiling while A doesn't (P141): Eq2 with production term alpha*D*(A-A_hp)*(1-V) can push V to 1.0 because the D×A product grows during treatment. Fix: Make Eq2 production depend primarily on coupling eps*(A-A_hp) rather than direct stimulus. Remove or minimize D-dependent production in Eq2.
17. MAPE computed as relative change ≠ P140 pattern (P141): Computing MAPE as |y_transition - y_baseline| / y_baseline gives ~60% for systems with large relative response. P140's MAPE was computed as curve-fit error (|y_fit - y_data| / y_data), giving ~0.7%. Use P140's method: fit exponential rise, compute MAPE on fit residuals, not on relative change.
18. R2 hits floor 0.90 from curve_fit bounds (P141): When bounds=([0,0.5,0.001],[1,1,0.1]), the curve_fit may return boundary values without warning, making R2 report exactly 0.90. Check: if R2 is exactly 0.90 for both variables, relax bounds (e.g., [0.7,0.9]) and verify the curve actually fits well visually.
19. Parameter sweep can be empty for novel domains (P141): For new 2-ODE domains not seen before, a brute-force grid sweep over 8 parameters × 1000 steps per sample may find no working combination. Strategy: Start with P140's proven baseline (alpha=0.65, beta=0.12, mu=0.04, eps=0.35, kappa=0.14, A_hp=0.42, E_hp=0.55), then iteratively adjust ONE parameter at a time. If the domain produces fundamentally different dynamics (e.g., V hits ceiling in all configs), consider the domain may not support clean 2-ODE separation and defer assembly.

Tension/Curvature Systems (P126+)

For tension/curvature systems, the variable roles differ from biochemical systems:

• T (tension): starts low (0.40–0.50), structural baseline — like S in biochemical systems
• C (curvature control): starts very low (0.05–0.35), "quiet" baseline — like R but more suppressed
• C dynamics equation is critical: production must overcome decay
• C starts near 0: Unlike biochemical systems where secondary variable starts at moderate values
• When ablation fails for tension systems: Reduce μ (direct stimulus) not α (coupling)

Success Criteria

All 9 metrics pass simultaneously. If any fail, go back to the step where it first started failing and adjust from there.

Genes (策略基因)

紧凑策略表示。条件→策略。需要深度时参考完整文档。

• [ODE-001] 测量基线前 → 必须在 D=0 条件下运行 1000+ 步以确保系统达到均衡，否则基线数据无效
• [ODE-002] 执行无耦合消融测试 → 必须移除所有耦合机制（如 flow-stress、E→tau、产生项），仅保留稳态衰减和直接加载，以防消融缺口虚高
• [ODE-003] 在新领域进行参数调优 → 从 P140 已验证的基线参数出发，每次仅调整一个参数，禁止对八维参数空间进行盲目网格扫描
• [ODE-004] 设计耦合项方程 → 必须采用加性且基线锚定的形式（如 eps*(X-X_hp)），严禁使用乘性正反馈项以避免变量冲顶或失真
• [ODE-005] 验证模型成功标准 → 九项指标（R²、AUC、ablation 等）须同时达标，若任一项失败则退回首个失守步骤重新调优
• [ODE-006] 计算 MAPE 指标 → 应使用曲线拟合残差法（|y_fit - y_data| / y_data）而非相对变化法，以准确反映拟合精度
• [ODE-007] 处理非线性耦合导致的基线动态过强 → 优先使用线性形式 R*(1-S) 替代非线性形式 R*S*(1-S)，以稳定基线动态

示例 · EXAMPLES

输入：Retinal Shear P140 v2 — alpha=0.65, beta=0.12, mu=0.04, eps=0.35, kappa=0.14, A_hp=0.42, E_hp=0.55 + D(t) 刺激信号 输出：9 项指标全过 — R²=0.997, AUC=0.93, ablation=5.81x, MAPE_R=0.7%（曲线拟合残差法）；Sobol: R↔D feedback 26.5% 排 #2

输入：P141 新域初扫 — alpha=0.65 基线直接应用，发现 max(A)=0.97（冲顶），ablation=1.2x 输出：诊断：耦合项 +kappa*V*(A-A_hp) 为正反馈 → 改为加性 eps*(A-A_hp) 且 kappa 0.14→0.08 → 重跑 max(A)=0.84, ablation=3.1x ✅

约束规则 · RULES

• D=0 下必须运行 1000+ 步均衡后方可测基线，未衡而测参数皆妄
• 无耦合消融须移除全部耦合机制（flow-stress / E→tau / 产生项），留残则 ablation 失真
• 新域从 P140 已验证基线出发，一次只调一个参数，不盲扫八维
• 耦合项必须加性且基线锚定（eps*(X-X_hp)），禁止乘性正反馈
• 9 项指标须同时达标，任一项失则退回首个失守步骤重调

Success Criteria

All 9 metrics pass simultaneously. If any fail, go back to the step where it first started failing and adjust from there.

Ode Simulation Tuning---

(P032 去重: 保留另一份 11 行独有内容)

验证清单 (Verification)

• 9 项指标同时通过；任一失败已回到首个失守步骤调整
• 基线均衡化已运行（D=0 下 1000+ 步）后才测基线（P134）
• 消融移除全部耦合机制（flow-stress / E→tau / flow 产生项），保留 homeostatic decay + direct loading（P140）
• R² 用指数上升拟合（平滑数据不用 spline）；R² 恰好 0.90 时已放宽 bounds 复核
• MAPE 按曲线拟合残差计算（|y_fit - y_data|/y_data），非相对变化
• 新域参数扫描从 P140 已验证基线出发、一次只调一个参数（P141）

Golden 集合 · GOLDEN SET

• Golden Input: Retinal Shear P140 v2 参数初值 — alpha=0.65, beta=0.12, mu=0.04, eps=0.35, kappa=0.14, A_hp=0.42, E_hp=0.55；含完整 2-ODE 方程定义与 D(t) 刺激信号。
• Golden Output: 9 项指标同时达标 — R²=0.997、AUC≥0.90、ablation=5.81x（≥2.0x）、MAPE_R≈0.7%（曲线拟合残差法），Sobol 排序输出，参数组可复现。
• Golden Error: 正反馈耦合 +kappa*V*(A-A_hp) 致 A 冲顶（max(A)>0.92），ablation 仅 1.2x（<2.0x）→ 诊断：耦合为乘性正反馈，修复为加性基线锚定 eps*(A-A_hp) 并降低 kappa，重跑后 ablation 回升。