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name: gnnwr description: | Spatial and spatiotemporal regression with GNNWR (Geographically Neural Network Weighted Regression). Use when the agent needs to: (1) Build spatially varying coefficient regression models, (2) Analyze geographic non-stationarity in spatial data, (3) Generate spatial coefficient maps for publication, (4) Run spatiotemporal regression with GTNNWR, (5) Scale geographically weighted regression to large datasets (N > 10k) with KNN mode, (6) Diagnose spatial model performance with F-tests, AIC, and residual maps. license: MIT metadata: version: 1.0.1 author: Geoscience Skills tags: '["Spatial Regression", "GNNWR", "GTNNWR", "GWR", "Non-Stationarity", "Coefficient Mapping", "Spatial Analysis", "Geographic Weighting"]' dependencies: '["gnnwr>=0.1.0", "pandas", "torch"]' complements: '["verde", "geostatspy", "scikit-gstat", "pyvista", "xarray"]' workflow_role: analysis skill_type: domain

GNNWR - Geographically Neural Network Weighted Regression

Quick Reference

from gnnwr import models, datasets, utils
import pandas as pd

data = pd.read_csv("data.csv")

train, val, test = datasets.init_dataset(
    data=data, test_ratio=0.2, valid_ratio=0.1,
    x_column=["x1", "x2", "x3"], y_column=["y"],
    spatial_column=["lon", "lat"],  # REQUIRED: geographic coords
    batch_size=32, process_fn="minmax_scale"
)

model = models.GNNWR(train, val, test, use_gpu=True, optimizer="Adam", start_lr=0.01)
model.run(max_epoch=200, early_stop=30)

result = model.reg_result(only_return=True)  # DataFrame: coef_x1, coef_x2, ..., Pred_y
print(model.result())                         # R², AIC, RMSE, F-tests summary

Spatiotemporal (GTNNWR)

train, val, test = datasets.init_dataset(
    data=data, ...,
    spatial_column=["lon", "lat"],
    temp_column=["year", "month"],  # add temporal coords
    use_model="gtnnwr"
)
model = models.GTNNWR(train, val, test, use_gpu=True)

Large-Scale (N > 10k) — KNN Mode

train, val, test = datasets.init_dataset(
    data=data, ..., knn_k=500  # only k nearest neighbor distances
)
# Memory: N=100k full=55GB → knn_k=2000 only 763MB

Key Classes

Class	Purpose
models.GNNWR	Spatial regression with neural network geographic weighting
models.GTNNWR	Spatiotemporal regression with temporal + spatial weighting
datasets.init_dataset	Data splitting, normalization, distance matrix construction
utils.Visualize	Built-in folium interactive maps for coefficients and predictions

Essential Operations

init_dataset Parameters

Parameter	Default	Notes
knn_k	None	KNN sparse distance; None=full matrix
process_fn	"minmax_scale"	or "standard_scale"
spatial_fun	BasicDistance	Euclidean; or ManhattanDistance
Reference	None	"train", "train_val", or custom DataFrame
sample_seed	42	Reproducibility

Model Hyperparameters

Parameter	Recommended	Notes
optimizer	"Adam"	Also: SGD, AdamW, Adagrad, RMSprop
start_lr	0.01–0.1	Critical tuning point
drop_out	0.2	0.0–0.5
dense_layers	None (auto)	Auto: power-of-2 sequence from input_dim to n_coef
early_stop	20–50	Patience; -1=disabled
batch_norm	True	Stabilizes training
use_ols	True	OLS-initialized output layer

Diagnostics

diag = model._test_diagnosis
diag.R2()           # always available
diag.RMSE()         # always available
diag.AIC()          # needs lite=False (auto for N<10k)
diag.AICc()         # corrected AIC
diag.F1_Global()    # GNNWR vs OLS significance
diag.F2_Global()    # spatial weight significance
diag.F3_Local()     # per-variable significance → (dict1, dict2)

lite=True (auto when N>10k): only R²/RMSE; Hat-matrix diagnostics skipped.

Visualization Patterns

Folium Interactive Maps (built-in)

viz = utils.Visualize(model, lon_lat_columns=["lon", "lat"], zoom=5)
m1 = viz.display_dataset(name="all", y_column="y")
m1.save("dataset_map.html")

for col in [c for c in result.columns if c.startswith("coef_")]:
    m = viz.coefs_heatmap(data_column=col, steps=20)
    m.save(f"map_{col}.html")

Matplotlib Static Maps (publication-ready)

import matplotlib.pyplot as plt

fig, axes = plt.subplots(2, 3, figsize=(18, 12))
coef_cols = [c for c in result.columns if c.startswith("coef_")]

for ax, col in zip(axes.flat, coef_cols):
    sc = ax.scatter(
        result["lon"], result["lat"],
        c=result[col], cmap="RdYlBu_r", s=5, alpha=0.8,
        vmin=result[col].quantile(0.02), vmax=result[col].quantile(0.98)
    )
    ax.set_title(col.replace("coef_", "β_"), fontsize=14)
    plt.colorbar(sc, ax=ax, shrink=0.8)

plt.suptitle("Spatially Varying Coefficients (GNNWR)", fontsize=16)
plt.tight_layout()
plt.savefig("coefficients_map.png", dpi=300, bbox_inches="tight")

GeoPandas + Contextily (with basemap)

import geopandas as gpd
import contextily as ctx

gdf = gpd.GeoDataFrame(result, geometry=gpd.points_from_xy(result.lon, result.lat), crs="EPSG:4326")
gdf_web = gdf.to_crs(epsg=3857)

fig, ax = plt.subplots(figsize=(12, 10))
gdf_web.plot(column="coef_x1", ax=ax, cmap="RdYlBu_r", legend=True,
             markersize=5, alpha=0.7, legend_kwds={"shrink": 0.6})
ctx.add_basemap(ax, source=ctx.providers.CartoDB.Positron)
ax.set_title("β_x1 Spatial Variation")
ax.set_axis_off()
plt.savefig("coef_basemap.png", dpi=300, bbox_inches="tight")

When to Use vs Alternatives

Use Case	Tool	Why
Spatially varying coefficients (neural net)	GNNWR	Non-linear weighting, scalable, coefficient maps
Classical geographically weighted regression	mgwr / GWR4	Traditional bandwidth-based, well-established theory
Spatial interpolation (no covariates)	verde / scikit-gstat	Gridding / kriging without regression
Global regression baseline	statsmodels / scikit-learn	No spatial non-stationarity assumed
Spatiotemporal varying coefficients	GTNNWR	GNNWR extended with temporal dimension
Large-scale spatial regression (N > 100k)	GNNWR + knn_k	Sparse distance matrix, O(n·k²) diagnostics
Geostatistical simulation	geostatspy / SGeMS	Stochastic realizations, uncertainty quantification

Choose GNNWR when: You need spatially varying regression coefficients with neural network-based geographic weighting, especially for large datasets where classical GWR is computationally infeasible.

Choose classical GWR when: You need well-established inferential statistics, bandwidth-based weighting, and simpler model interpretation.

Choose verde/kriging when: You need spatial interpolation without explanatory variables — pure spatial prediction from observed values.

Common Workflows

Spatial Regression Analysis

• EDA: Check spatial distribution, feature correlations, OLS baseline
• Data split: init_dataset with appropriate ratios and sample_seed=42
• Train: Start with defaults, tune start_lr and early_stop
• Diagnose: R², RMSE, F1 (GNNWR vs OLS), F2 (spatial weight significance)
• Visualize: Coefficient maps, residual spatial distribution, pred vs obs
• Interpret: Where do coefficients vary most? Which variables show strongest non-stationarity? (F3_Local)
• Report: Model summary table + coefficient maps + diagnostic statistics

Common Issues

Issue	Solution
Model degenerates to global regression	Forgot spatial_column — always pass it
OOM on distance matrix	N > 10k without knn_k; use knn_k=500–2000
Loss explodes during training	start_lr too high; start with 0.01
Overfitting	No early_stop; always set 20–50
Coefficients on wrong scale	Use reg_result() for denormalized predictions
GTNNWR behaves like GNNWR	Missing temp_column; silently falls back

References

• Diagnostics — DIAGNOSIS methods, F-tests, residual analysis
• Visualization — Detailed visualization patterns and publication figures