Visualization (pypielm.visualization)

Visualisation utilities (requires pip install pypielm[viz]).

Public surface:

from pypielm.visualization import (
    plot_solution_1d,
    plot_solution_2d,
    plot_training_history,
    plot_pareto,
    plot_leaderboard_heatmap,
    save_figure,
)
pypielm.visualization.plot_solution_1d(x, u_pred, u_true=None, *, xlabel='x', ylabel='u(x)', title='Solution', figsize=(7, 4), ax=None)[source]

Plot a 1D PDE solution (predicted vs. reference).

Parameters:

  • x (Any) – Coordinate array, shape (N,).

  • u_pred (Any) – Predicted solution, shape (N,).

  • u_true (Any | None) – Optional reference solution for comparison.

  • xlabel (str) – X-axis label.

  • ylabel (str) – Y-axis label.

  • title (str) – Figure title.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when ax is provided).

  • ax (Any) – Existing Axes to draw on. If None a new figure is created.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plot_solution_2d(x, u_pred, u_true=None, *, nx=64, ny=64, cmap='viridis', title='Solution', figsize=(12, 4), fig=None)[source]

Plot a 2D PDE solution as colour maps.

Parameters:

  • x (Any) – Coordinate array, shape (N, 2). Columns are [x, y].

  • u_pred (Any) – Predicted solution, shape (N,) or (N, 1).

  • u_true (Any | None) – Optional reference solution, same shape as u_pred.

  • nx (int) – Grid resolution along x-axis for interpolation.

  • ny (int) – Grid resolution along y-axis for interpolation.

  • cmap (str) – Colour map name.

  • title (str) – Figure suptitle.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when fig is provided).

  • fig (Any) – Existing Figure. If None a new figure is created.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plot_training_history(losses, *, log_scale=True, title='Training History', figsize=(7, 4), ax=None)[source]

Plot training loss curves.

Parameters:

  • losses (dict[str, list[float]]) – Dict mapping loss component names to lists of per-epoch values. Example: {"total": [...], "pde": [...], "bc": [...]}.

  • log_scale (bool) – If True, use log scale on the y-axis.

  • title (str) – Figure title.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when ax is provided).

  • ax (Any) – Existing Axes.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plot_pareto(results, *, x_metric='fit_time_s', y_metric='rel_l2', label_key='model', log_x=False, log_y=True, figsize=(8, 5), ax=None)[source]

Pareto-front scatter plot: accuracy vs. runtime.

Parameters:

  • results (list[dict[str, Any]]) – List of dicts; each must contain x_metric, y_metric, and label_key.

  • x_metric (str) – Column name for the x-axis (default: fit time).

  • y_metric (str) – Column name for the y-axis (default: relative L² error).

  • label_key (str) – Column name used as point labels.

  • log_x (bool) – Log scale on x-axis.

  • log_y (bool) – Log scale on y-axis.

  • figsize (tuple[float, float]) – Figure size (ignored when ax is provided).

  • ax (Any) – Existing Axes.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plot_leaderboard_heatmap(df, *, metric='rel_l2', figsize=(12, 6), cmap='YlOrRd_r', title='Leaderboard Heatmap', fig=None)[source]

Heatmap of model × task performance.

Parameters:

  • df (Any) – A 2-D structure (numpy.ndarray, list[list], or pandas.DataFrame) with models as rows and tasks as columns, pre-aggregated to metric values. When a DataFrame is supplied, row/column labels are used.

  • metric (str) – Metric name used for the colour-bar label.

  • figsize (tuple[float, float]) – Figure size (ignored when fig is provided).

  • cmap (str) – Colour map (default green = good: YlOrRd_r).

  • title (str) – Figure title.

  • fig (Any) – Existing Figure.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.save_figure(fig, path, *, dpi=300, bbox_inches='tight')[source]

Save a matplotlib.figure.Figure to path.

Parameters:

  • fig (Any) – The figure to save.

  • path (str | Path) – Output file path. Extension determines format (.pdf, .png, .svg, …).

  • dpi (int) – Resolution (dots per inch).

  • bbox_inches (str) – Passed verbatim to savefig().

Return type:

None

Matplotlib-based visualisation utilities.

All functions accept torch.Tensor or NumPy arrays and produce matplotlib.figure.Figure objects that can be shown interactively, saved, or embedded in notebooks.

Requires: pip install pypielm[viz].

pypielm.visualization.plots.plot_solution_1d(x, u_pred, u_true=None, *, xlabel='x', ylabel='u(x)', title='Solution', figsize=(7, 4), ax=None)[source]

Plot a 1D PDE solution (predicted vs. reference).

Parameters:

  • x (Any) – Coordinate array, shape (N,).

  • u_pred (Any) – Predicted solution, shape (N,).

  • u_true (Any | None) – Optional reference solution for comparison.

  • xlabel (str) – X-axis label.

  • ylabel (str) – Y-axis label.

  • title (str) – Figure title.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when ax is provided).

  • ax (Any) – Existing Axes to draw on. If None a new figure is created.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plots.plot_solution_2d(x, u_pred, u_true=None, *, nx=64, ny=64, cmap='viridis', title='Solution', figsize=(12, 4), fig=None)[source]

Plot a 2D PDE solution as colour maps.

Parameters:

  • x (Any) – Coordinate array, shape (N, 2). Columns are [x, y].

  • u_pred (Any) – Predicted solution, shape (N,) or (N, 1).

  • u_true (Any | None) – Optional reference solution, same shape as u_pred.

  • nx (int) – Grid resolution along x-axis for interpolation.

  • ny (int) – Grid resolution along y-axis for interpolation.

  • cmap (str) – Colour map name.

  • title (str) – Figure suptitle.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when fig is provided).

  • fig (Any) – Existing Figure. If None a new figure is created.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plots.plot_training_history(losses, *, log_scale=True, title='Training History', figsize=(7, 4), ax=None)[source]

Plot training loss curves.

Parameters:

  • losses (dict[str, list[float]]) – Dict mapping loss component names to lists of per-epoch values. Example: {"total": [...], "pde": [...], "bc": [...]}.

  • log_scale (bool) – If True, use log scale on the y-axis.

  • title (str) – Figure title.

  • figsize (tuple[float, float]) – Figure size in inches (ignored when ax is provided).

  • ax (Any) – Existing Axes.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plots.plot_pareto(results, *, x_metric='fit_time_s', y_metric='rel_l2', label_key='model', log_x=False, log_y=True, figsize=(8, 5), ax=None)[source]

Pareto-front scatter plot: accuracy vs. runtime.

Parameters:

  • results (list[dict[str, Any]]) – List of dicts; each must contain x_metric, y_metric, and label_key.

  • x_metric (str) – Column name for the x-axis (default: fit time).

  • y_metric (str) – Column name for the y-axis (default: relative L² error).

  • label_key (str) – Column name used as point labels.

  • log_x (bool) – Log scale on x-axis.

  • log_y (bool) – Log scale on y-axis.

  • figsize (tuple[float, float]) – Figure size (ignored when ax is provided).

  • ax (Any) – Existing Axes.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plots.plot_leaderboard_heatmap(df, *, metric='rel_l2', figsize=(12, 6), cmap='YlOrRd_r', title='Leaderboard Heatmap', fig=None)[source]

Heatmap of model × task performance.

Parameters:

  • df (Any) – A 2-D structure (numpy.ndarray, list[list], or pandas.DataFrame) with models as rows and tasks as columns, pre-aggregated to metric values. When a DataFrame is supplied, row/column labels are used.

  • metric (str) – Metric name used for the colour-bar label.

  • figsize (tuple[float, float]) – Figure size (ignored when fig is provided).

  • cmap (str) – Colour map (default green = good: YlOrRd_r).

  • title (str) – Figure title.

  • fig (Any) – Existing Figure.

Return type:

Any

Returns:

matplotlib.figure.Figure.

pypielm.visualization.plots.save_figure(fig, path, *, dpi=300, bbox_inches='tight')[source]

Save a matplotlib.figure.Figure to path.

Parameters:

  • fig (Any) – The figure to save.

  • path (str | Path) – Output file path. Extension determines format (.pdf, .png, .svg, …).

  • dpi (int) – Resolution (dots per inch).

  • bbox_inches (str) – Passed verbatim to savefig().

Return type:

None