Curve Fit BenchTested where fitting tools fail.
Ten deliberately hard datasets from a live conference demo, then a thousand random complex spectra with known truth. A correct model gives a reduced χ² near 1 and a curve closer to the truth than the noise.
Ten hard datasets: best reduced χ²
Before and after adaptive decomposition, log scale. Hover a row for values.
The same results as a table
Each dataset has σy; the noiseless truth was never shown to the fitter.
| Dataset | Before | Now |
|---|---|---|
| Multi-scale resonance | 5.71 | 1.04 |
| Two overlapping resonances | 5.43 | 0.96 |
| Threshold cusp + oscillations | 8.21 | 1.18 |
| Log-periodic power law | 217 | 1.10 |
| Fano interference | 36.9 | 1.13 |
| Damped chirp | 4.68 | 0.93 |
| Double sigmoid + dip | 4.04 | 0.97 |
| Broad peak + narrow spike | 3.35 | 1.21 |
| Rational crossover + ripple | 43.6 | 1.04 |
| Hard composite | 5.07 | 1.05 |
How the 1000 spectra were made
Each synthetic spectrum stacks 2 to 6 features — Lorentzian, Gaussian, Voigt and Fano bands, dips, steps, cusps, damped and chirped oscillations, wave packets, Shubnikov–de Haas oscillations periodic in 1/x and log-periodic terms — on a linear, quadratic, exponential, power-law, activated or logarithmic background. Grids are linear or logarithmic with 120 to 900 points; noise is 0.4–4 % of the range, constant or growing along x; 61 % of the spectra carry σ and the rest do not.
Two numbers are scored against the known truth: the reduced χ² of the fit to the noisy data, and the RMS distance between the fitted curve and the noiseless curve in units of σ. Below 1 means the fit recovered the underlying function better than any single measurement could.
What it is and is not. An adaptive decomposition is an accurate description of the data — positions, widths, frequencies and a curve you can trust — not an identification of the physics. When you know the mechanism, fit the named model for it; the bench shows both.
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