Lana I Geothermal Eval

---
name: lana-i-geothermal-eval
description: Evaluates a multimodal machine learning workflow's ability to predict 3D subsurface geological, hydrogeological, and geophysical features from sparse, heterogeneous field data. It tests the model's generalization capability using transductive learning and mutual information maximization across five cross-validation splits. Use when the user wants to benchmark on Lana'i 3D Subsurface Grid, or asks about evaluating this task. Reports R-squared.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2312.16194
  bibtex_key: friedel2023multimodal
  confidence: high
---

# lana-i-geothermal-eval

> Multimodal machine learning for 3-dimensional characterization of hidden groundwater and geothermal resources — Friedel et al. (2023) (arXiv:2312.16194, 2023)

## What this evaluates

Evaluates a multimodal machine learning workflow's ability to predict 3D subsurface geological, hydrogeological, and geophysical features from sparse, heterogeneous field data. It tests the model's generalization capability using transductive learning and mutual information maximization across five cross-validation splits.

## Datasets

- **Lana'i 3D Subsurface Grid** — total ?; splits: 5-fold cross-validation (-1)

## Metrics

- `R-squared` **(primary)** — range: [0, 1]
  - Coefficient of determination: 1 - (SS_res / SS_tot), where SS_res is the sum of squared residuals and SS_tot is the total sum of squares. Measures the proportion of variance in observed values explained by predicted values.
- `Kappa` — range: [-1, 1]
  - Cohen's kappa statistic for categorical agreement (dikes/basalt prediction), correcting for chance agreement.
- `Accuracy` — range: [0, 1]
  - Fraction of correctly classified instances out of total instances.

## Input / output format

**Input**: Sparse, heterogeneous field data including geophysical (resistivity, density), hydrogeological (head, temperature, chloride), and geological (basalt, dike) observations, normalized by data variance and presented sequentially to a toroidal hexagonal grid.

**Output**: Predicted 3D feature vectors (continuous values for physical/chemical properties, categorical labels for geology) mapped onto a 148×140 toroidal hexagonal neuron grid.

## Scoring recipe

```python
def r_squared(y_true, y_pred):
    mean_true = sum(y_true) / len(y_true)
    ss_res = sum((y - y_hat)**2 for y, y_hat in zip(y_true, y_pred))
    ss_tot = sum((y - mean_true)**2 for y in y_true)
    return 1 - (ss_res / ss_tot)

def kappa_score(y_true, y_pred, classes):
    n = len(y_true)
    observed_agree = sum(1 for yt, yp in zip(y_true, y_pred) if yt == yp)
    p0 = observed_agree / n
    # Expected agreement pe calculated from marginal totals
    return (p0 - pe) / (1 - pe)
```

## Common pitfalls

- Temperature predictions are only valid for depths ≤1 km; deeper temperatures are extrapolated or assumed based on Moho estimates.
- Predictions near the ocean-basalt interface exhibit bias due to large voxel sizes in deterministic inversions and limited grid resolution.
- Performance varies across the 5 cross-validation split sets, reflecting a random process for individual feature predictions.

## Evidence (verbatim from paper)

> The cross-validation statistics further reveal that the MSOM model has a moderate ability (kappa values >0.53) to predict dikes and basalt with strong prediction accuracies (accuracy values >0.99). ... The associated scatter plots (Figure 3) of observed versus predicted values for these features have reasonable R-squared values (resistivity, ohm-m = 89.9%; density, kg/m³ = 99.9%; chloride, mg/l = 68.8%; temperature, C = 92.8%) albeit with some bias at smallest values.

## Citation

```bibtex
@misc{friedel2023multimodal,
  title={Multimodal machine learning for 3-dimensional characterization of hidden groundwater and geothermal resources},
  author={Friedel et al. (2023)},
  year={2023},
  note={arXiv:2312.16194}
}
```

- arXiv: 2312.16194