Spectral Shape Lab

01 / MODELLoading

Ten-eigenvalue ensemble

Preparing the saved network…

Saved model

02 / OBJECTIVE Choose a saved function F(x₁, …, x₁₀)

x1…x10 are eigenvalues at the chosen area. Use + − * / ^ and parentheses.

Functions & symbolic derivatives

Supported: sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (or ln), sqrt; constants pi and e. Write multiplication explicitly, for example 2*x5. No abs, min, max or arbitrary code.

Your formula should be C¹ on the spectra explored. Undefined values or derivatives trigger backtracking. Regularity is not proved automatically.

03 / SEARCH

Direction

Fixed area

Starting shapes

Steps per start

Random seed

✓

Area fixed. Boundary stays simple.Positive radius and harmonic caps are enforced at every step.

Starts are the disk and seeded random feasible shapes. No training shapes or previous optimizers are used. A run may take minutes; you can pause or stop and save the best shape.

SHAPE EXPLORER

Ready to explore

Initializing

Loading the model…0.0 s

Fixed-area Fourier boundary
15 harmonics · positive radial graph

Best so farCurrent iterateEqual-area disk

Best predicted F—

Current predicted F—

Area1.0000

Certified r / a₀≥ 0.2500

Objective history

No iterations yet

Current objective in blue; best so far in teal. Values shown are raw F, including during maximization.

Best-shape spectrum

Predicted

Keep your result

Save the best shape, its coefficients, or the full reproducible run.

All displayed spectra and objectives are neural predictions. This app performs no PDE solve. All models use the same random-start rule. Ensemble spread is not an accuracy guarantee; stopping does not certify a global optimum.