## 1. 核心功能模块 ### 1.1 ODE模型定义 - **Case A**: 结构性不可识别 ODE python def ode_caseA(t, x0, theta): theta1, theta2 theta lam theta1 theta2 return x0 * np.exp(-lam * t)Case B: 先验截断 ODEdef ode_caseB(t, x0, theta): theta theta[0] return x0 * np.exp(-theta * t)Case C: 病态尺度参数 ODEdef ode_caseC(t, x0, theta): theta1, theta2 theta lam theta1 * theta2 return x0 * np.exp(-lam * t)Case D: 反向山脊标本 ODEdef ode_caseD(t, x0, theta): theta1, theta2 theta lam theta1 - theta2 return x0 * np.exp(-lam * t)1.2 损失函数构建def build_dels_loss(t_obs, y_obs, ode_model, x0, prior_mean, prior_cov): inv_prior_cov np.linalg.inv(prior_cov) def loss(theta): x_hat ode_model(t_obs, x0, theta) resid y_obs - x_hat ll_resid -0.5 * np.sum(resid**2) ll_prior -0.5 * (theta - prior_mean).T inv_prior_cov (theta - prior_mean) return -(ll_resid ll_prior) return loss1.3 剖面似然扫描def profile_likelihood_scan( param_idx: int, param_name: str, theta_prior_low: float, theta_prior_high: float, mle_point: np.ndarray, mcmc_post_std: float, hessian_full: np.ndarray, dels_loss_fn, base_bounds: List[Tuple[float,float]], specimen_id: str, extrap_fraction: float EXTRAP_FRACTION, use_spline_ci: bool True, multi_restart: bool True ) - ProfileResult: # 实现细节略1.4 山脊方向检测def ridge_direction(profile_list:List[ProfileResult]) - np.ndarray: dir_signs [] for pr in profile_list: grad np.gradient(pr.profile_ll, pr.scan_grid) flat_idx np.where(pr.profile_ll pr.profile_ll.max() - DELTA_LOG_L)[0] if len(flat_idx) 2: continue mean_grad np.mean(grad[flat_idx]) s np.sign(mean_grad) dir_signs.append(s) return np.array(dir_signs)1.5 跨标本聚合def cross_specimen_aggregate(profile_results:List[ProfileResult], enable_ridge_check:boolTrue) - ProfileResult: n_escaping sum(1 for r in profile_results if r.boundary_extrap_test escaping) agg profile_results[0] if n_escaping 2: if enable_ridge_check: signs ridge_direction(profile_results) if len(signs) 2: agg.cross_specimen_verdict inconsistent_numerical agg.verdict NUMERICAL_COUPLING else: if np.all(signs signs[0]): agg.cross_specimen_verdict consistent_structural agg.verdict STRUCTURAL_UNIDENTIFIABLE else: agg.cross_specimen_verdict opposite_ridge agg.verdict NUMERICAL_COUPLING else: agg.cross_specimen_verdict consistent_structural agg.verdict STRUCTURAL_UNIDENTIFIABLE else: agg.cross_specimen_verdict inconsistent_numerical agg.verdict NUMERICAL_COUPLING return agg2. 测试用例分析2.1 Case A: 结构性不可识别ODE:dx/dt -(θ1 θ2) x结果:STRUCTURAL_UNIDENTIFIABLE断言:assert prA.verdict STRUCTURAL_UNIDENTIFIABLE assert prA.boundary_extrap_test escaping2.2 Case B: 先验截断ODE:dx/dt -θ x结果:PRIOR_TRUNCATED断言:assert prB.verdict PRIOR_TRUNCATED assert prB.boundary_extrap_test stable2.3 Case C: 优化器失效ODE:dx/dt -θ1 * θ2 * x结果:OPT_FAILURE断言:assert prC.verdict OPT_FAILURE2.4 Case D: 反向山脊双标本ODE:dx/dt -(θ1 − θ2) x结果:NUMERICAL_COUPLING生产模式或STRUCTURAL_UNIDENTIFIABLE反事实模式断言:assert aggD_prod.verdict NUMERICAL_COUPLING assert aggD_counterfact.verdict STRUCTURAL_UNIDENTIFIABLE3. 关键技术点技术点描述增量更新使用--update和--cluster-only实现知识图谱的最小代价维护山脊方向校验通过梯度符号判断参数空间中的逃逸方向避免误判跨标本聚合通过cross_specimen_aggregate实现多标本的一致性验证剖面似然扫描通过自适应网格生成和多初值重启提高优化稳定性4. 总结该代码实现了对不同ODE模型的参数可识别性分析通过剖面似然扫描、山脊方向检测和跨标本聚合等方法能够准确判断模型的可识别性。在实际应用中需注意先验设置、优化器配置和网格生成策略以确保结果的可靠性 。参考来源graphify 增量更新运行手册--update 增量重建与 --cluster-only 仅重聚类全流程解析AI空间思维Placement与Direction决定落地成败Graphify 增量更新与重聚类完全指南--update 增量重抽取与 --cluster-only 重聚类的完整工作流与源码解析graphify 增量更新机制实战/graphify --update 与 --cluster-only 的完整流程与源码解析graphify 增量更新与 cluster-only 实战指南--update 如何以最小代价维护知识图谱