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3D Surface & Uncertainty Plots

Surface plots provide an intuitive three-dimensional view of the surrogate model's predictions and uncertainty estimates across two input dimensions. They complement the standard 2D contour plots, offering a more visually expressive way to communicate model landscapes.

3D Prediction Surface

The prediction surface renders the surrogate model's mean prediction as a continuous 3D surface over a two-variable grid, with experimental observations and (optionally) acquisition suggestions overlaid as scatter points.

When to use: - Communicating optimization results to stakeholders who find 3D plots more intuitive - Identifying curvature and interaction structure between two key variables - Presentations and publications

The surface is colored by predicted output value (using a diverging colormap), and experiment points are shown as markers above or below the surface at their actual output values.

3D Uncertainty Surface

The uncertainty surface shows the surrogate model's predictive standard deviation (epistemic uncertainty) across the variable space — the same information shown in the 2D uncertainty contour, but rendered as a 3D surface.

When to use: - Identifying regions of high uncertainty that are candidates for active learning - Verifying that the model is well-calibrated (low uncertainty near data, high away from data) - Communicating where the model is most confident vs. most uncertain

Web UI

After training a model, open the Visualizations panel and select:

  • 3D Surface Plot — predicted mean surface
  • 3D Uncertainty Surface — predictive uncertainty surface

Use the variable dropdowns to select which two variables appear on the X and Y axes. All other variables are held at their midpoints.

Python API

from alchemist_core import OptimizationSession
from alchemist_core.visualization.plots import create_surface_plot, create_uncertainty_surface_plot
import numpy as np

session = OptimizationSession()
# ... load variables, data, train model ...

# Get grid data from session
grid_data = session.compute_contour_data(x_var="Temperature", y_var="Pressure")

# 3D prediction surface
fig, ax, cbar = create_surface_plot(
    x_grid=grid_data["x_grid"],
    y_grid=grid_data["y_grid"],
    predictions_grid=grid_data["predictions_grid"],
    x_var="Temperature",
    y_var="Pressure",
    output_label="Predicted Yield",
    exp_x=grid_data.get("exp_x"),
    exp_y=grid_data.get("exp_y"),
    exp_output=grid_data.get("exp_output"),
)
fig.savefig("surface_plot.png", dpi=150)

# 3D uncertainty surface
fig2, ax2, cbar2 = create_uncertainty_surface_plot(
    x_grid=grid_data["x_grid"],
    y_grid=grid_data["y_grid"],
    uncertainty_grid=grid_data["uncertainty_grid"],
    x_var="Temperature",
    y_var="Pressure",
)
fig2.savefig("uncertainty_surface.png", dpi=150)

Interpretation

Prediction Surface

  • Peaks (high values) indicate predicted optimum regions — potential targets for the next experiment
  • Valleys may represent unfavorable conditions or constraints
  • Curvature reveals quadratic structure — steep surfaces suggest strong variable effects
  • Experimental points shown above/below the surface reveal how well the model fits the data

Uncertainty Surface

  • High peaks near unexplored regions → model is uncertain, good candidates for exploration
  • Low, flat regions near your data → model is confident here
  • If uncertainty is high everywhere: You may need more experiments before the model is reliable