mlsanityData to 14 Oct 2026

Can A Neural Network Hear the Shape of A Drum?

arXiv 2203.08073 ↗First posted 14 Mar 2022cs.SD cs.LG physics.data-ancited by 0

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Abstract (arXiv)

We have developed a deep neural network that reconstructs the shape of a polygonal domain given the first hundred of its Laplacian eigenvalues. Having an encoder-decoder structure, the network maps input spectra to a latent space and then predicts the discretized image of the domain on a square grid. We tested this network on randomly generated pentagons. The prediction accuracy is high and the predictions obey the Laplacian scaling rule. The network recovers the continuous rotational degree of freedom beyond the symmetry of the grid. The variation of the latent variables under the scaling transformation shows they are strongly correlated with Weyl' s parameters (area, perimeter, and a certain function of the angles) of the test polygons.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 42 references that are in the map. First posted on arXiv 14 Mar 2022.

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15 of 42 references.

References · 15

  1. 2019Expressive Body Capture: 3D Hands, Face, and Body from a Single Imagecited by 1,612
  2. 2016Generative Adversarial Text to Image Synthesiscited by 735
  3. 2016Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modelingcited by 558
  4. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
  5. 2017StackGAN++: Realistic Image Synthesis with Stacked Generative Adversarial Networkscited by 229
  6. 2017Learning Koopman Invariant Subspaces for Dynamic Mode Decompositioncited by 158
  7. 2017Linearly-Recurrent Autoencoder Networks for Learning Dynamicscited by 145
  8. 2018Discovering physical concepts with neural networkscited by 117
  9. 2018Tell, Draw, and Repeat: Generating and Modifying Images Based on Continual Linguistic Instructioncited by 61
  10. 2017SurfNet: Generating 3D shape surfaces using deep residual networkscited by 32
  11. 2019Geometric Disentanglement for Generative Latent Shape Modelscited by 30
  12. 2018Isospectralization, or how to hear shape, style, and correspondencecited by 18
3 more
  1. 2017Learning hard quantum distributions with variational autoencoderscited by 17
  2. 2018Unsupervised Learning of Latent Physical Properties Using Perception-Prediction Networkscited by 13
  3. 2014Enhanced Higgs to τ^+τ^- Searches with Deep Learningcited by 5

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