研究笔记 · Research Note

Multi-Method Comparison Spine (2019-2025)

Zhenyu He · Jobs Stroustrup 阅读约 6 分钟

Multi-Method Comparison Spine (2019-2025)

页面用途

本页 articulate Zhenyu 跨 7 年至少 8 个 instances 的 systematic multi-method comparison pattern — 而非 single-method + 事后 sanity check 的 ad-hoc pattern. 这条 spine 是 cross-project methodology backbone, 从 2019 年 11 月大二 first long report (earliest evidence) 到 2025 ongoing methane regressions, 在完全独立的 domain (climate dynamics / quantitative finance / inverse problem theory / aerosol retrieval / spectral methods) 都 consistently 出现.

定义

Multi-method comparison = 对同一 scientific question, 从一开始就 set up ≥ 2 个 independent methods 并列执行 + 全部 preserve result, 不是 “1 method + 事后 sanity check” 的 ad-hoc pattern. 关键 distinguishing features:

Methods 独立 (不共享 core assumption 或 subroutine)
并列执行 (不是 fallback from failed method)
所有结果 preserved (即使某方法 disadvantageous to narrative)
Cross-validate 作为 discovery mechanism (不仅是 robustness check)

跨 7 年 ≥ 8 instances 总表

Year	Context	Methods compared	Outcome
2019-11-04	PKU Zhenyu 大二 first long report 43 slides `the impact on the strength of tropical circulations 2.pptx`	3 Walker strength 度量方式 (Tanaka 2004 velocity potential + ω-based + u-based / equivalent)	Earliest multi-method evidence — capability spine 起源
2020-2021	Walker paper v6 (PKU Ji Nie)	ω-based vs u-based stream function (`msf_top2bottom_omega2_WalkerStream.ncl` 63 lines + `msf_top2bottom_u2_Walker.ncl` 61 lines) 两 NCL module 并列 preserved	Methodology bug catch: ω-based 对”无散”条件满足不好 → switch to u-based for paper v6, 但 ω-based module 保留作为 failed approach evidence
Summer 2021	QLBS self-study + NSD Summer School Final Project (joint course project)	DP backward Bellman + FQI off-policy RL ( $η = 0.5$ ) + Black-Scholes closed-form benchmark — 3 solutions in single 780-line notebook + 1606-line Coursera independent path	780 lines of independent verification — earliest numerical multi-method instance, Summer 2021 (比 Caltech 早 3 月, 比 PhD 早 4 年)
2021-11	Caltech DSCOVR (Yuk Yung + King-Fai Li)	Pre-whitening L-curve + L-curve + GCV + Morozov + Hardened Balancing Principle + Tikhonov + TSVD + Kawahara Bayesian cost + discrepancy principle (7+ methods)	Structural limits diagnosed: Hansen σ² vs σ⁴ bug (80×) + Method B/C failure + axis-scale ambiguity + non-diagonal $S_{a}$ self-limit
2022-01	Phase 1 T,q vs h,q closure (PhD Nuclear Winter)	h-based RK4 + h-based forward Euler + T,q separate integrate + h_adj + T,q + cp_adj (4 Method variants) + conserved potential temperature 3rd-party ground truth	Root cause isolation (85 J/kg → 3 J/kg → 3.58e-5 J/kg), diagnosed hydrostatic balance violation as mechanism
2022-02	Aerosol joint retrieval (PKU 李婧 senior thesis)	Log scale height regression vs 1/e decay method — 两种 scale height 推算方法 + 系统 comparison across 12-month China LUT	Convention harmonization: log-linear full-profile regression chosen as primary method, 1/e preserved; test case 2019-08-01 Beijing (0.66 km vs 4.1 km) based on physical sanity check
2025-09	Phase 4.5 SWTG (PhD Nuclear Winter)	Spectral modes (Sturm-Liouville eigendecomposition) vs DAM 3-D LES ground truth + sanity-check experiments isolating mode evolution	1-D model 显著高估高度诊断: “failed cancellation” mechanism identified through multi-experiment comparison
Ongoing (2024-)	Methane mapping (UC Berkeley Inez Fung Lab)	Multiple regression types: quantile (upper 50% filter) + density (AvgHeadPer100Acres) + raw linear (MillionHeads)	Texas puzzle reformulation — recover positive slope in Nebraska/Idaho after density + quantile; raw linear preserved to show original negative slope artifact

Meta pattern (what makes this distinct from ad-hoc sanity check)

Characteristic 1: Upfront design, 不是 fallback

每 instance 的 methods 从一开始就是 parallel design, 不是 “method A 失败了 → 试 method B”
Evidence: QLBS single notebook 同时实现 3 solutions; Phase 1 4 method variants 并列从项目第一 phase 就存在

Characteristic 2: Independent methods (不 share core assumption)

DP + FQI + BS closed-form: 完全不同 mathematical framework (backward recursion / off-policy RL / analytical stochastic calculus)
ω-based vs u-based stream function: 不同 momentum variable + 不同 integration path
Phase 1: h-based vs T,q-based 是不同 state-variable choice

Characteristic 3: All results preserved, even disadvantageous

Walker v6 preserve ω-based NCL module 即使 methodology bug caught
Caltech preserve Hansen 原版 (σ²) 错误 PDF 并列 Hansen 学生正确版 (σ⁴) PDF
Phase 1+2 enforceEpsilon_z_iteration_v3.ipynb filename-as-failure-marker
Aerosol (supplementary inconvenient-evidence docx) preserve CALIPSO L2 4/4 优势

Characteristic 4: Cross-validate as discovery mechanism, 不只是 robustness

Caltech 7+ method comparison → Hansen textbook bug catch (80× overestimation)
Phase 1 T,q vs h,q comparison → hydrostatic balance violation mechanism identified
Methane density vs raw count → Texas free-range grazing hypothesis (Inez’s contribution)

与其他 cross-project patterns 的关系

与 Evidence Preservation Discipline (private companion) 的关系

Multi-method comparison 生成 inconvenient evidence 的 “source pool” (1 method “wins”, others 是 “losers” or “fails”) — Characteristic 3 与 inconvenient evidence 的 preservation discipline 直接 overlap
但 multi-method comparison focus 是 design-time upfront parallelism; inconvenient-evidence retention focus 是 result-time honest retention. 两个 pattern 是 complementary (前者 upstream, 后者 downstream)

与 PKU advisor methodology companion (private) 的关系

两者都是 methodology integrity 层面的 capability. methodology arc 是 advisor-level (credit honesty), multi-method spine 是 student-level (methodology honesty) — 两个 independent 证据 in same integrity cluster

与 Independent Judgment narrative (held until 2026-06-10) 的关系

Moment 3 (2022-01-23 refuse methodological-engineering pressure) 直接 rooted in multi-method comparison Characteristic 4: pre-whitening L-curve method 在 RBF kernel 下 showed non-monotonic behavior → Zhenyu articulate method self-limit, refuse tune 多 Sa/Se bundles. Multi-method discipline 使 Zhenyu able to diagnose method-level limit, 进而 refuse methodological-engineering pressure at methodology-integrity level.

Distinct signature: 大二 earliest evidence

Critical observation: capability spine 起源不是 PhD, 不是 Caltech, 也不是 senior thesis — 是大二 first long report (2019-11-04). 这意味着:

多 method comparison 不是研究 training 的 learned skill, 而是 Zhenyu personal epistemic habit — 从 entering 领域之初就存在
与 PhD-level multi-method training (通常 1-2 年 literature exposure 后 develop) 的 timeline 完全不 match
可以解释为什么 PhD 阶段 Caltech DSCOVR 7-method comparison 在本科 senior fall 就 emerge — 不是 “突然学会” 而是 “capability 已存在, domain 准备好才 fully expressed”

来源

research_wiki resume_angles/problem_solving.md 整页 (350+ 行, 所有 multi-method stories 完整 documented)
research_wiki resume_angles/technical_depth.md §1 Numerical Methods (7+ regularization methods + QLBS 3-way + Phase 1 4-method variants)
research_wiki projects/walker_hadley/overview.md §ω-based vs u-based 流函数 + 大二 2019-11-04 first long report
research_wiki projects/mcmc_retrieval/overview.md §Caltech DSCOVR 7-method systematic comparison
research_wiki projects/aerosol_retrieval/overview.md §log 拟合 vs 1/e 法 scale height
research_wiki projects/nuclear_winter/overview.md §Phase 1 T,q vs h,q + Phase 4.5 SWTG spectral modes
research_wiki projects/methane_mapping/overview.md §regression reformulation (density + quantile)
research_wiki projects/early_exploration/overview.md §2019-11-04 first long report 43 slides

Multi-Method Comparison Spine (2019-2025)

页面用途

定义

跨 7 年 ≥ 8 instances 总表

Meta pattern (what makes this distinct from ad-hoc sanity check)

与其他 cross-project patterns 的关系

与 Evidence Preservation Discipline (private companion) 的关系

与 PKU advisor methodology companion (private) 的关系

与 Independent Judgment narrative (held until 2026-06-10) 的关系

Distinct signature: 大二 earliest evidence

来源

相关页面