Benchmark: distance localization, a smoother case, and a quick run

benchmarks/minires/RESULTS.md

@@ -7,22 +7,24 @@ and which score matters is for the reader to judge.
 
 ## Case `coarse`: 25 x 25 cells
 
-20 truths, 50 members; history of 16 of 40 steps, observed at steps [4, 8, 12, 16]. PET at `b731be7`, 2026-10-27.
+20 truths, 50 members; history of 16 of 40 steps, observed at steps [4, 8, 12, 16]. PET at `2fe3aba`, 2026-10-28.
 
-| | misfit | RMSE forecast WWCT | logK RMSE | logK corr | logK spread | sor error | sor spread | vo error | vo spread | simulations |
-|---|---|---|---|---|---|---|---|---|---|---|
-| prior | 91.7 ± 4.2 | 0.221 ± 0.021 | 0.783 ± 0.019 | 0.0201 ± 0.027 | 0.8 ± 0.0028 | 0.0314 ± 0.0058 | 0.0383 ± 0.00077 | 0.676 ± 0.15 | 1.02 ± 0.023 |  |
-| ES-MDA (4 steps, α = 4) | 1.68 ± 0.083 | 0.0847 ± 0.013 | 0.829 ± 0.016 | 0.205 ± 0.037 | 0.526 ± 0.0041 | 0.0349 ± 0.0059 | 0.0221 ± 0.0007 | 0.602 ± 0.094 | 0.469 ± 0.012 | 250 |
-| ES-MDA (4 steps, α = 4), adaptive localization (universal threshold) | 29.6 ± 1.7 | 0.146 ± 0.02 | 0.779 ± 0.019 | 0.122 ± 0.024 | 0.773 ± 0.0031 | 0.0302 ± 0.0052 | 0.0339 ± 0.001 | 0.531 ± 0.08 | 0.894 ± 0.025 | 250 |
-| ES-MDA (4 steps, α = 4), adaptive localization (3σ threshold) | 17.7 ± 0.91 | 0.123 ± 0.018 | 0.777 ± 0.019 | 0.167 ± 0.024 | 0.752 ± 0.0029 | 0.0253 ± 0.0053 | 0.0329 ± 0.00071 | 0.43 ± 0.083 | 0.773 ± 0.022 | 250 |
+| | misfit | RMSE forecast WWCT | logK RMSE | logK corr | logK spread | sor error | sor spread | simulations |
+|---|---|---|---|---|---|---|---|---|
+| prior | 99.2 ± 5 | 0.242 ± 0.023 | 0.78 ± 0.026 | 0.0299 ± 0.036 | 0.802 ± 0.0037 | 0.0314 ± 0.0058 | 0.0383 ± 0.00077 |  |
+| ES-MDA (4 steps, α = 4) | 1.71 ± 0.095 | 0.092 ± 0.015 | 0.763 ± 0.029 | 0.299 ± 0.043 | 0.494 ± 0.0058 | 0.0362 ± 0.0058 | 0.0212 ± 0.00071 | 250 |
+| ES-MDA (4 steps, α = 4), adaptive localization (universal threshold) | 20.6 ± 1.9 | 0.153 ± 0.023 | 0.758 ± 0.025 | 0.21 ± 0.031 | 0.744 ± 0.0038 | 0.0257 ± 0.0049 | 0.0327 ± 0.00083 | 250 |
+| ES-MDA (4 steps, α = 4), adaptive localization (3σ threshold) | 13.5 ± 1.2 | 0.124 ± 0.019 | 0.75 ± 0.024 | 0.262 ± 0.032 | 0.719 ± 0.0042 | 0.0288 ± 0.0051 | 0.0316 ± 0.00071 | 250 |
+| ES-MDA (4 steps, α = 4), distance localization (Gaspari-Cohn, 300 m) | 8.96 ± 0.96 | 0.101 ± 0.017 | 0.718 ± 0.023 | 0.337 ± 0.039 | 0.678 ± 0.0035 | 0.0303 ± 0.0046 | 0.0236 ± 0.00071 | 250 |
 
 ## Case `fine`: 50 x 50 cells
 
-8 truths, 50 members; history of 16 of 40 steps, observed at steps [4, 8, 12, 16]. PET at `b731be7`, 2026-10-27.
+8 truths, 50 members; history of 16 of 40 steps, observed at steps [4, 8, 12, 16]. PET at `2fe3aba`, 2026-10-28.
 
-| | misfit | RMSE forecast WWCT | logK RMSE | logK corr | logK spread | sor error | sor spread | vo error | vo spread | simulations |
-|---|---|---|---|---|---|---|---|---|---|---|
-| prior | 97 ± 7.6 | 0.243 ± 0.029 | 0.815 ± 0.022 | -0.0673 ± 0.03 | 0.793 ± 0.0038 | 0.0282 ± 0.008 | 0.0402 ± 0.0012 | 0.583 ± 0.12 | 1.03 ± 0.035 |  |
-| ES-MDA (4 steps, α = 4) | 1.9 ± 0.21 | 0.0867 ± 0.015 | 0.869 ± 0.035 | 0.179 ± 0.059 | 0.511 ± 0.0037 | 0.0326 ± 0.01 | 0.0253 ± 0.001 | 0.356 ± 0.14 | 0.47 ± 0.015 | 250 |
-| ES-MDA (4 steps, α = 4), adaptive localization (universal threshold) | 47.7 ± 5.4 | 0.2 ± 0.026 | 0.806 ± 0.021 | 0.0307 ± 0.042 | 0.777 ± 0.0026 | 0.0328 ± 0.0082 | 0.0364 ± 0.00088 | 0.476 ± 0.15 | 0.926 ± 0.039 | 250 |
-| ES-MDA (4 steps, α = 4), adaptive localization (3σ threshold) | 20.2 ± 3.5 | 0.144 ± 0.021 | 0.794 ± 0.019 | 0.151 ± 0.04 | 0.745 ± 0.0018 | 0.0358 ± 0.0099 | 0.0355 ± 0.0013 | 0.495 ± 0.12 | 0.766 ± 0.035 | 250 |
+| | misfit | RMSE forecast WWCT | logK RMSE | logK corr | logK spread | sor error | sor spread | simulations |
+|---|---|---|---|---|---|---|---|---|
+| prior | 99 ± 5.2 | 0.247 ± 0.035 | 0.817 ± 0.029 | -0.0719 ± 0.047 | 0.793 ± 0.0058 | 0.0282 ± 0.008 | 0.0402 ± 0.0012 |  |
+| ES-MDA (4 steps, α = 4) | 1.83 ± 0.16 | 0.0984 ± 0.02 | 0.793 ± 0.059 | 0.355 ± 0.07 | 0.489 ± 0.0055 | 0.0308 ± 0.01 | 0.0231 ± 0.00081 | 250 |
+| ES-MDA (4 steps, α = 4), adaptive localization (universal threshold) | 33.3 ± 3.6 | 0.173 ± 0.039 | 0.793 ± 0.027 | 0.153 ± 0.032 | 0.752 ± 0.0046 | 0.0306 ± 0.0089 | 0.0342 ± 0.0024 | 250 |
+| ES-MDA (4 steps, α = 4), adaptive localization (3σ threshold) | 16.4 ± 2.4 | 0.158 ± 0.032 | 0.761 ± 0.03 | 0.29 ± 0.043 | 0.711 ± 0.0039 | 0.0335 ± 0.0086 | 0.0317 ± 0.0014 | 250 |
+| ES-MDA (4 steps, α = 4), distance localization (Gaspari-Cohn, 300 m) | 12.4 ± 2.4 | 0.112 ± 0.029 | 0.732 ± 0.036 | 0.402 ± 0.047 | 0.675 ± 0.0048 | 0.0338 ± 0.011 | 0.0249 ± 0.00089 | 250 |

benchmarks/minires/cases.py

@@ -5,8 +5,8 @@
 pressure, 40 report steps of 60 days. The producers' rates, and when they water out, are
 therefore outcomes of the permeability around them.
 
-The unknowns are the log-permeability field and two scalars of the fluid, the residual oil
-saturation ``sor`` and the oil viscosity ``vo``. Each twin experiment draws its truth from
+The unknowns are the log-permeability field and a scalar of the fluid, the residual oil
+saturation ``sor``; the oil viscosity is known. Each twin experiment draws its truth from
 the same prior as the ensemble, simulates it to the end, and perturbs the history part into
 observations; the forecast part is what the posterior is scored against, unseen.
 """
@@ -36,12 +36,12 @@
 # Observation error, as (relative, absolute): the larger applies.
 OBS_ERROR = {"WWCT": (0.05, 0.02), "WOPR": (0.10, 5.0), "WBHP": (0.01, 1.0)}
 
-# The prior. log K about log(200 mD), sd 0.8, spherical variogram of range RANGE metres.
+# The prior. log K about log(200 mD), sd 0.8, with a smooth variogram of range RANGE metres:
+# PET's "exp" is exp(-3 (h/range)^1.9), i.e. all but Gaussian.
 LOGK_MEAN, LOGK_SD, RANGE = np.log(200.0), 0.8, 300.0
 SCALARS = {
     #       mean   sd     limits
     "sor": (0.22, 0.04, [0.05, 0.40]),
-    "vo": (5.0, 1.0, [1.5, 10.0]),
 }
 
 
@@ -63,7 +63,7 @@ def model(self) -> dict:
         return {
             "Lx": LX, "Ly": LX, "Nx": self.n, "Ny": self.n,
             "por": 0.2, "ct": 1e-5, "cdarcy": 0.008527,
-            "fluid": {"vw": 1.0, "vo": SCALARS["vo"][0], "swc": 0.2, "sor": SCALARS["sor"][0]},
+            "fluid": {"vw": 1.0, "vo": 5.0, "swc": 0.2, "sor": SCALARS["sor"][0]},
             "wells": wells,
         }
 
@@ -81,14 +81,24 @@ def ensemble(self, ne: int, seed: int, mean_file: str) -> dict:
             "ne": ne, "seed": seed, "disable_tqdm": True, "save_prior": False,
             "state": ["permx", *SCALARS],
             "prior_permx": {
-                "vario": "sph", "mean": mean_file, "var": LOGK_SD**2,
+                "vario": "exp", "mean": mean_file, "var": LOGK_SD**2,
                 "range": RANGE / self.dx, "aniso": 1.0, "angle": 0.0, "grid": [self.n, self.n, 1],
             },
         }
         for name, (mean, sd, limits) in SCALARS.items():
             ens[f"prior_{name}"] = {"mean": mean, "var": sd**2, "limits": limits}
         return ens
 
+    def distance_entries(self, radius: float) -> list:
+        """Distance-localization entries: a taper of ``radius`` metres on the field, at each datum's well."""
+        cells = {w["name"]: [int(w["xy"][0] // self.dx), int(w["xy"][1] // self.dx)] for w in self.model()["wells"]}
+        return [
+            {"x": x, "y": y, "z": 0, "radius": int(round(radius / self.dx)), "z_range": ":", "aniso": 1.0,
+             "rotation": 0.0, "data_type": d, "time": "*", "param": "permx"}
+            for d in DATATYPES
+            for x, y in [cells[d.split(":")[1]]]
+        ]
+
     def write_prior_mean(self, path: str) -> None:
         np.savez(path, permx=np.full(self.n**2, LOGK_MEAN))
 

benchmarks/minires/methods.py

@@ -1,7 +1,9 @@
 """The methods compared: each a label and its ``[dataassim]`` settings.
 
-The settings are PET's own, as a config would give them. Unless a row says it is tuned,
-they are defaults or the textbook choice, the same for every case.
+The settings are PET's own, as a config would give them, except that a distance localization
+gives its ``radius`` in metres: ``run.py`` places a taper of that radius at each datum's well,
+on the case's grid. Unless a row says it is tuned, the settings are defaults or the textbook
+choice, the same for every case.
 """
 
 COMMON = {"energy": 99.0, "obsname": "steps"}
@@ -33,4 +35,14 @@
             "localization": {"name": "autoadaloc", "threshold": "adaptive", "cutoff": 3.0, "type": "hard"},
         },
     },
+    {
+        # The radius, in metres, is the prior's correlation range; the scalars have no position
+        "label": "ES-MDA (4 steps, α = 4), distance localization (Gaspari-Cohn, 300 m)",
+        "dataassim": {
+            "scheme": "esmda",
+            "analysis": "approx",
+            "mda": {"tot_assim_steps": 4, "inflation_param": [4, 4, 4, 4]},
+            "localization": {"name": "distance_loc", "taper_func": "gc", "radius": 300.0, "unlocalized": ["sor"]},
+        },
+    },
 ]