03-EFT.WP.Core.Parameters v1.0 | 第2章 参数目录与分类

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第2章 参数目录与分类

I. 目录说明与分类口径

• 本章提供跨卷一致的参数词条卡片，覆盖 env/const/proc/obs/num/drv 六类；字段统一为英文字段与纯文本公式，便于工具链解析与跨卷引用。
• 每个词条包含：Code，Role，Type，Unit，Definition，Default，Bounds，Prior，Transform，See，Notes，Misuse。
• 量纲、到达时与路径相关表达严格使用括号体并显式 gamma(ell) 与 d ell；涉及冲突名的避免规则与编号体系遵循第1章（P31-1…P31-3）。

II. 物理与环境参数（env）

1. Code: env.c_ref.si
   • Role: env；Type: scalar；Unit: m/s
   • Definition: Reference propagation upper bound used in arrival-time formula T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
   • Default: 2.99792458e8；Bounds: (1.0e8, 4.0e8)
   • Prior: LogNormal(mu=19.5, sigma=0.05)；Transform: None
   • See: ["S20-1","Core.Terms:c_ref","I20 4"]
   • Notes: Do not use bare c anywhere.
   • Misuse: Setting c_ref in km/s without rescaling.
2. Code: env.L0.ref
   • Role: env；Type: scalar；Unit: m
   • Definition: Reference length scale for nondimensionalization bar_x = x / L0.
   • Default: 1.0；Bounds: (1.0e-9, 1.0e9)
   • Prior: LogUniform(a=1.0e-6, b=1.0e3)；Transform: log
   • See: ["S70-1","Core.Equations:weak-form","I30 10:check_dim"]
   • Notes: Single length family per derivation domain.
   • Misuse: Mixing L0 with a grid spacing h in the same symbol.
3. Code: env.t0.ref
   • Role: env；Type: scalar；Unit: s
   • Definition: Reference time scale for nondimensionalization bar_t = t / t0.
   • Default: 1.0；Bounds: (1.0e-9, 1.0e9)
   • Prior: LogUniform(a=1.0e-6, b=1.0e3)；Transform: log
   • See: ["S70-1","I30 10:check_dim"]
   • Notes: Keep consistent with solver dt.
   • Misuse: Choosing t0 smaller than machine timestep.
4. Code: env.T0.ref
   • Role: env；Type: scalar；Unit: N
   • Definition: Reference tension scale used to form bar_T = T_fil / T0.
   • Default: 1.0；Bounds: (1.0e-6, 1.0e6)
   • Prior: LogUniform(a=1.0e-3, b=1.0e3)；Transform: log
   • See: ["S40-1","Core.Terms:T_fil"]
   • Notes: Chosen for stable conditioning in constitutive maps.
   • Misuse: Using data maximum as T0 without robustness check.
5. Code: env.rho0.si
   • Role: env；Type: scalar；Unit: kg/m^3
   • Definition: Background mass density entering transport or coupling closures.
   • Default: 1.0；Bounds: (1.0e-6, 1.0e6)
   • Prior: LogNormal(mu=0.0, sigma=2.0)；Transform: log
   • See: ["S50-1","Core.Terms:rho"]
   • Notes: Distinct from number density n(x,t).
   • Misuse: Equating rho0 with n_bg without conversion.
6. Code: env.n_bg.ref
   • Role: env；Type: scalar；Unit: 1/m^3
   • Definition: Background number density baseline for n(x,t).
   • Default: 1.0e20；Bounds: (1.0e10, 1.0e30)
   • Prior: LogUniform(a=1.0e12, b=1.0e28)；Transform: log
   • See: ["S50-1","Core.Terms:n"]
   • Notes: Never confuse with n_eff.
   • Misuse: Using n_bg inside arrival-time integrand.
7. Code: env.path.ds_ref
   • Role: env；Type: scalar；Unit: m
   • Definition: Reference path discretization step for gamma_ref(ell) used in path averages.
   • Default: 0.01；Bounds: (1.0e-6, 1.0)
   • Prior: None；Transform: log
   • See: ["S20-2","I20 2:discretize_path"]
   • Notes: Controls quadrature resolution, not a physical parameter.
   • Misuse: Calibrating ds_ref against data.

III. 本构参数（const）

1. Code: const.n_eff.alpha0
   • Role: const；Type: scalar；Unit: 1
   • Definition: Offset in n_eff def= alpha0 + alpha1 * bar_T + beta_grad * |grad(bar_T)|.
   • Default: 0.0；Bounds: (-0.5, 0.5)
   • Prior: Normal(mu=0.0, sigma=0.1)；Transform: None
   • See: ["S30-1","Core.Terms:n_eff","Core.Terms:T_fil"]
   • Notes: Keeps n_eff dimensionless.
   • Misuse: Giving alpha0 units.
2. Code: const.n_eff.alpha1
   • Role: const；Type: scalar；Unit: 1
   • Definition: Linear sensitivity of n_eff to bar_T = T_fil / T0.
   • Default: 0.1；Bounds: (-2.0, 2.0)
   • Prior: Normal(mu=0.0, sigma=0.5)；Transform: None
   • See: ["S30-1","S40-1"]
   • Notes: Identifiability improves with tension excitation.
   • Misuse: Using raw T_fil without scaling by T0.
3. Code: const.n_eff.beta_grad
   • Role: const；Type: scalar；Unit: 1
   • Definition: Gradient sensitivity in n_eff, with |grad(bar_T)| = |grad(T_fil)| * (L0 / T0).
   • Default: 0.0；Bounds: (0.0, 5.0)
   • Prior: HalfNormal(sigma=1.0)；Transform: softplus
   • See: ["S30-2","I30 10:check_dim"]
   • Notes: Ensures dimensionless gradient term.
   • Misuse: Omitting L0/T0 normalization.
4. Code: const.tension.tau_relax
   • Role: const；Type: scalar；Unit: s
   • Definition: Relaxation time constant in tension dynamics closures.
   • Default: 1.0；Bounds: (1.0e-6, 1.0e6)
   • Prior: LogNormal(mu=0.0, sigma=2.0)；Transform: log
   • See: ["S40-2"]
   • Notes: Affects stiffness of the PDE.
   • Misuse: Setting tau_relax <= 0.
5. Code: const.coupling.k_T
   • Role: const；Type: scalar；Unit: 1
   • Definition: Dimensionless coupling coefficient linking constitutive map and tension gradient effects.
   • Default: 1.0；Bounds: (0.0, 10.0)
   • Prior: HalfNormal(sigma=2.0)；Transform: softplus
   • See: ["S30-3","S40-1"]
   • Notes: Kept dimensionless to avoid hidden unit conversions.
   • Misuse: Treating k_T as a mass or energy scale.

IV. 过程与动力学参数（proc）

1. Code: proc.transport.kappa
   • Role: proc；Type: scalar；Unit: m^2/s
   • Definition: Effective diffusivity in transport terms.
   • Default: 1.0e-3；Bounds: (1.0e-6, 1.0)
   • Prior: LogNormal(mu=-6.9, sigma=1.0)；Transform: log
   • See: ["S50-1","I20 2:assemble_operator"]
   • Notes: Enters stability via CFL-like conditions.
   • Misuse: Negative kappa.
2. Code: proc.transport.u_x
   • Role: proc；Type: scalar；Unit: m/s
   • Definition: x-component of advection velocity.
   • Default: 0.0；Bounds: (-100.0, 100.0)
   • Prior: Normal(mu=0.0, sigma=10.0)；Transform: None
   • See: ["S50-1"]
   • Notes: Use vector components, not boldface arrows.
   • Misuse: Using |u| here and repeating magnitude in u_y,u_z.
3. Code: proc.transport.u_y
   • Role: proc；Type: scalar；Unit: m/s
   • Definition: y-component of advection velocity.
   • Default: 0.0；Bounds: (-100.0, 100.0)
   • Prior: Normal(mu=0.0, sigma=10.0)；Transform: None
   • See: ["S50-1"]
   • Notes: Same scaling as u_x.
   • Misuse: Units in km/s.
4. Code: proc.transport.u_z
   • Role: proc；Type: scalar；Unit: m/s
   • Definition: z-component of advection velocity.
   • Default: 0.0；Bounds: (-100.0, 100.0)
   • Prior: Normal(mu=0.0, sigma=10.0)；Transform: None
   • See: ["S50-1"]
   • Notes: Optional in 2-D setups.
   • Misuse: Leaving unconstrained with strong advection.
5. Code: proc.reaction.lambda_decay
   • Role: proc；Type: scalar；Unit: 1/s
   • Definition: First-order decay rate in auxiliary or source dynamics.
   • Default: 0.0；Bounds: (0.0, 1.0e6)
   • Prior: HalfNormal(sigma=1.0)；Transform: softplus
   • See: ["S40-3","S50-2"]
   • Notes: Interacts with time stepping stability.
   • Misuse: Negative rate.
6. Code: proc.source.S0
   • Role: proc；Type: scalar；Unit: N/s
   • Definition: Source magnitude scale entering S_src(x,t).
   • Default: 0.0；Bounds: (-1.0e6, 1.0e6)
   • Prior: Normal(mu=0.0, sigma=1.0e3)；Transform: None
   • See: ["S40-1"]
   • Notes: Sign defines injection vs removal.
   • Misuse: Treating S0 as dimensionless.

V. 观测与测量参数（obs）

1. Code: obs.arrival.sigma_Tarr
   • Role: obs；Type: scalar；Unit: s
   • Definition: Standard deviation of arrival-time measurement noise for T_arr.
   • Default: 1.0e-4；Bounds: (1.0e-6, 1.0)
   • Prior: HalfNormal(sigma=1.0e-3)；Transform: log
   • See: ["S20-1","I20 4:propagate_time"]
   • Notes: Noise is additive in time domain.
   • Misuse: Modeling noise on n_eff instead.
2. Code: obs.arrival.bias_Tarr
   • Role: obs；Type: scalar；Unit: s
   • Definition: Additive bias in arrival-time measurement.
   • Default: 0.0；Bounds: (-1.0, 1.0)
   • Prior: Normal(mu=0.0, sigma=1.0e-3)；Transform: None
   • See: ["S20-2"]
   • Notes: Bias is identifiable only with references.
   • Misuse: Folding bias into c_ref.
3. Code: obs.field.sigma_Tfil
   • Role: obs；Type: scalar；Unit: N
   • Definition: Standard deviation of tension field measurement noise.
   • Default: 1.0；Bounds: (1.0e-6, 1.0e6)
   • Prior: HalfNormal(sigma=10.0)；Transform: log
   • See: ["S40-1","Core.Terms:T_fil"]
   • Notes: Relative to T0 for scaling diagnostics.
   • Misuse: Expressing as percent without converting.
4. Code: obs.sampler.rate_hz
   • Role: obs；Type: scalar；Unit: 1/s
   • Definition: Sampling rate of the acquisition system.
   • Default: 1000.0；Bounds: (1.0, 1.0e9)
   • Prior: LogUniform(a=10.0, b=1.0e6)；Transform: log
   • See: ["S60-2","I20 3:solve_*"]
   • Notes: Align with dt_base to avoid aliasing.
   • Misuse: Using milliseconds but tagging unit as seconds.
5. Code: obs.sampler.window_dt
   • Role: obs；Type: scalar；Unit: s
   • Definition: Time window used in avg_t[·; Δt] estimators.
   • Default: 0.01；Bounds: (1.0e-6, 10.0)
   • Prior: None；Transform: log
   • See: ["S80-1","Core.Equations:statistics"]
   • Notes: Declare explicitly with each statistic.
   • Misuse: Implicit, undocumented windowing.

VI. 数值与求解器参数（num）

1. Code: num.solver.tol_newton
   • Role: num；Type: scalar；Unit: 1
   • Definition: Convergence tolerance for nonlinear solves.
   • Default: 1.0e-8；Bounds: (1.0e-12, 1.0e-2)
   • Prior: None；Transform: log
   • See: ["I20 3:solve_nonlinear"]
   • Notes: Monotone with residual norm definition.
   • Misuse: Mixing absolute and relative tolerances.
2. Code: num.solver.tol_linear
   • Role: num；Type: scalar；Unit: 1
   • Definition: Inner linear solver tolerance.
   • Default: 1.0e-10；Bounds: (1.0e-14, 1.0e-2)
   • Prior: None；Transform: log
   • See: ["I20 3:solve_linear"]
   • Notes: Should be tighter than tol_newton.
   • Misuse: Looser inner tolerance causing stagnation.
3. Code: num.solver.maxit_newton
   • Role: num；Type: scalar；Unit: 1
   • Definition: Maximum Newton iterations.
   • Default: 50；Bounds: (1, 500)
   • Prior: DiscreteUniform(10, 100)；Transform: None
   • See: ["I20 3"]
   • Notes: Impacts runtime, not physics.
   • Misuse: Calibrating iterations to fit data.
4. Code: num.time.dt_base
   • Role: num；Type: scalar；Unit: s
   • Definition: Base timestep for time integration.
   • Default: 1.0e-4；Bounds: (1.0e-9, 1.0)
   • Prior: None；Transform: log
   • See: ["S40-2","S50-1"]
   • Notes: Respect CFL-like constraints with kappa and u.
   • Misuse: Using adaptive dt without logging effective steps.
5. Code: num.mesh.h_base
   • Role: num；Type: scalar；Unit: m
   • Definition: Base mesh spacing for spatial discretization.
   • Default: 0.01；Bounds: (1.0e-6, 1.0)
   • Prior: None；Transform: log
   • See: ["I20 2:assemble_operator"]
   • Notes: Tie to L0 for nondimensional studies.
   • Misuse: Changing h_base mid-calibration unseen.
6. Code: num.cfl.safety
   • Role: num；Type: scalar；Unit: 1
   • Definition: Safety factor in explicit stability criteria.
   • Default: 0.5；Bounds: (0.1, 0.9)
   • Prior: Beta(a=2.0, b=2.0)；Transform: logit
   • See: ["S50-1","I20 3"]
   • Notes: Purely numerical, never inferred from physics.
   • Misuse: Treating as transport parameter.

VII. 派生参数（drv）

1. Code: drv.pathavg.n_eff
   • Role: drv；Type: scalar；Unit: 1
   • Definition: Path-averaged effective index avg_gamma[n_eff] def= ( 1 / L_gamma ) * ( ∫ n_eff d ell ) along declared gamma(ell).
   • Default: computed；Bounds: (0.0, inf)
   • Prior: None；Transform: None
   • See: ["S20-1","I20 4:propagate_time"]
   • Notes: Requires explicit gamma(ell) and d ell.
   • Misuse: Averaging over spatial grid instead of path.
2. Code: drv.T_arr.ref
   • Role: drv；Type: scalar；Unit: s
   • Definition: Reference arrival time computed via propagate_time(n_eff_path, ds, c_ref).
   • Default: computed；Bounds: (0.0, inf)
   • Prior: None；Transform: None
   • See: ["S20-2","I20 4"]
   • Notes: Used as regression metric T_arr.
   • Misuse: Using constant-segment approximation without ds.
3. Code: drv.advection.Pe
   • Role: drv；Type: scalar；Unit: 1
   • Definition: Péclet number Pe def= |u| * L0 / kappa with |u| = sqrt(u_x^2 + u_y^2 + u_z^2).
   • Default: computed；Bounds: (0.0, inf)
   • Prior: None；Transform: None
   • See: ["S50-1"]
   • Notes: Guides scheme selection and stabilization.
   • Misuse: Using kappa in cm^2/s without rescale.
4. Code: drv.noise.SNR_Tfil
   • Role: drv；Type: scalar；Unit: 1
   • Definition: Signal-to-noise ratio for tension field SNR_Tfil def= rms(T_fil) / sigma_Tfil.
   • Default: computed；Bounds: (0.0, inf)
   • Prior: None；Transform: None
   • See: ["S40-1","obs.field.sigma_Tfil"]
   • Notes: Requires consistent window avg_t[·; Δt].
   • Misuse: Mixing different Δt across datasets.

VIII. 误用与冲突示例（按类汇总）

• env 类
  误用：c_ref 写成 c；L0 与 h_base 混用；n_bg 误作 n_eff。
• const 类
  误用：alpha1 直接乘以 T_fil；beta_grad 未含 L0/T0；将 k_T 赋予单位。
• proc 类
  误用：负扩散系数；速度单位错配；未给 lambda_decay 下界。
• obs 类
  误用：把到达时噪声建模在积分核 ( n_eff / c_ref ) 上；遗漏 bias_Tarr。
• num 类
  误用：把 tol_* 当作可校准物理量；dt_base 未满足稳定条件。
• drv 类
  误用：avg_gamma[·] 未声明 gamma(ell) 与 d ell；Pe 用标量 u 替代范数。

IX. 导出与索引视图建议

• 参数清单视图：export_params(format="yaml")，按 role.family.name 排序并携带 see。
• 识别度视图：基于样本 posterior_sample_mcmc 的 Cov[theta] 与 Corr[theta] 概览，附派生 Pe 与 T_arr 指标。

X. 小结