Chladni Plate Operator Learning Benchmark

This repository contains MATLAB code that generates a forced Chladni plate benchmark dataset for operator learning.

The code:

1. Defines a 2D rectangular domain ((0, L) \times (0, M)).
2. Randomly samples a forcing function (S(x,y)) in a Fourier-cosine basis via random coefficients (\alpha(n,m)).
3. Computes the corresponding plate displacement (Z(x,y)) at a fixed time (t_{\mathrm{fixed}}) by precomputing integrals associated with the PDE.
4. Stores the forcing fields ({S_k}) and the resulting solutions ({Z_k}) in a .mat file.

With these ({S,Z}) data pairs, you can train operator-learning models (e.g., Fourier Neural Operator, DeepONet, B2B, etc.) to learn the mapping (S \mapsto Z).

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Features

• Precomputation
  The script calculates and caches all terms independent of (\alpha) (cosines, time integrals, etc.) for speed.

• Easy Input/Output
  It stores the random coefficients (\alpha), forcing (S), solution (Z), and coordinate grids ((x,y)) in .mat format.

• Customizable

  • Domain dimensions ((L, M))
  • Grid resolution (numPoints)
  • Number of modes ((n_{\max}, m_{\max}))
  • Damping and wave parameters (\gamma, v, \omega)
  • Number of samples to generate (train/test splitting)