## Line Graph: Performance Comparison of Baselines and Models ### Overview The image is a logarithmic line graph comparing three performance metrics across a range of input values (x-axis: 10¹ to 10⁵). The y-axis represents a normalized metric (10⁻¹ to 10⁻⁴). Three lines are plotted: a constant baseline (dashed black), PIKL baseline (solid blue), and PINN (solid orange), with shaded regions indicating uncertainty. ### Components/Axes - **Y-axis**: Logarithmic scale labeled 10⁻¹ (top) to 10⁻⁴ (bottom), with gridlines at 10⁻² and 10⁻³. - **X-axis**: Logarithmic scale labeled 10¹ (left) to 10⁵ (right), with gridlines at 10², 10³, 10⁴. - **Legend**: Positioned at the bottom-left corner, with three entries: - Dashed black: "Constant baseline" - Solid blue: "PIKL baseline" - Solid orange: "PINN" - **Shaded Regions**: Light blue (PIKL) and light orange (PINN) bands around the lines, representing uncertainty. ### Detailed Analysis 1. **Constant Baseline (Dashed Black)**: - Horizontal line at y = 10⁻² (0.01) across all x-values. - No variation or uncertainty shading. 2. **PIKL Baseline (Solid Blue)**: - Starts at ~10⁻¹.⁵ (≈3×10⁻²) at x = 10¹. - Declines steeply, crossing the PINN line near x = 10². - Continues declining to ~10⁻³.⁵ (≈3×10⁻⁴) at x = 10⁵. - Shaded region widens at lower x-values, narrowing as x increases. 3. **PINN (Solid Orange)**: - Starts at ~10⁻².⁵ (≈3×10⁻³) at x = 10¹. - Rises slightly to ~10⁻² at x = 10², then plateaus. - Remains above the PIKL line after x = 10². - Shaded region is narrower than PIKL’s, indicating lower uncertainty. ### Key Observations - **Crossover Point**: PIKL and PINN intersect near x = 10², after which PINN outperforms PIKL. - **Uncertainty**: PIKL’s uncertainty is higher at lower x-values (10¹–10²) but decreases as x increases. - **Baseline Stability**: The constant baseline remains unchanged, serving as a reference for relative performance. ### Interpretation The graph demonstrates that PINN outperforms the PIKL baseline for x > 10², suggesting improved performance or stability at higher input scales. The constant baseline (10⁻²) may represent a theoretical or empirical threshold. The narrowing uncertainty bands for both models at higher x-values imply increased confidence in their predictions as input magnitude grows. This could indicate that PINN is better suited for high-scale applications, while PIKL’s variability at lower scales might limit its reliability. The constant baseline’s fixed value highlights a potential target or benchmark for both models.