L1 ⚛ L1-436 ⊙ Testnet

Ensemble Kalman Filter (EnKF)

Control Theory · Ensemble data assimilation

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⬇ L1-436.md

# ⚛ L1 Principle — Ensemble Kalman Filter (EnKF) **ID:** `L1-436` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Control Theory — *Ensemble data assimilation* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** ensemble state distribution > **📡 Carrier:** N/A · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555258 --- ## 🧠 1. Introduction **Ensemble Kalman Filter (EnKF)** is a **parameter-estimation problem** whose unknown lives in **ensemble state distribution** space, within the **Ensemble data assimilation** sub-domain of **Control Theory**. Measurements consist of N/A via a **ensemble state estimation** sensing mechanism. The forward operator applies, in order: S · enkf · ensemble update operator; adds a prior term that biases the solution toward smoothness/sparsity; O · inflation · ensemble spread operator. Observations are corrupted by additive Gaussian noise. Existence of the recovered ensemble_state_distribution is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); sampling_error_finite_ensemble dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → S · enkf · ensemble update → O · inflation · ensemble spread → **y** (detector). ``` y = `O.inflation.ensemble_spread` `S.enkf.ensemble_update` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `S.enkf.ensemble_update` | S · enkf · ensemble update operator | | `O.inflation.ensemble_spread` | O · inflation · ensemble spread operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `O.regularize` | Adds a prior term that biases the solution toward smoothness/sparsity | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Control Theory | | Sub domain | Ensemble data assimilation | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | ensemble_state_distribution | | Noise model | gaussian | | Integration axis | assimilation_cycle | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered ensemble_state_distribution is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 500); sampling_error_finite_ensemble dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | spread_skill_ratio | | Secondary | RMSE_analysis_normalized | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `ensemble_state_estimation` **Center point:** | Parameter | Unit | Value | |---|---|---| | N e ensemble | — | 50 | | Localization km | km | 500 | | N state million | — | 1 | | Obs density per gridpt | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N e ensemble | — | 10 – 1000 | | Localization km | km | 50 – 5000 | | N state million | — | 0.001 – 100 | | Obs density per gridpt | — | 0.01 – 10.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.05 RMSE_analysis_normalized | Metric | Range | |---|---| | Rmse analysis normalized | 0.01 – 0.3 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **spread_skill_ratio**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9007e2f6a5fc7308d9ca5e457cceb718b8a8c4631fa95bb6faf3a502ae64ed00` - **Chain tx hash:** `0x0aedcdc01c4f114a8b81dde23900d09f2d90d0e5e47d90d3a70935b94361dd08` - **Chain block:** `41555258` --- ## File Mapping This bundle consists of: `L1-436.md`, `L1-436.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-436.md` | Source of truth — edit this | Human or LLM | | `L1-436.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-436`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-436.md).
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L2-436-001 Ensemble Kalman Filter (EnKF) — Nominal + Mismatch Specs

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📋 JSON metadata

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    "title": "Ensemble Kalman Filter (EnKF)"
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  "status": "testnet",
  "sub_domain": "Ensemble data assimilation",
  "title": "Ensemble Kalman Filter (EnKF)"
}

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