Toot, Jacob (2026) Machine learning quasisymmetries. Master's Thesis / Essay, Physics.
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Abstract
Symmetries are central in physics: exact symmetries generate conservation laws, constrain interactions, and classify phases of matter. Breaking of exact symmetries also proves to be an important instrument in many theories, showing that symmetries need not hold or be exact to be physically relevant. This raises a broader question of whether approximate symmetries, named quasisymmetries throughout this thesis, can play an important role as do the exact ones, and if so, what tools are needed to detect and characterise them. This thesis develops such tools by using cut-and-project sets in one and two dimensions as a model of approximate translational symmetry, and by applying machine-learning architectures to five tasks: classification, parameter reconstruction, and continuation in 1D, and dimensional identification and basis-vector reconstruction in 2D. In 1D, a convolutional network separates cut-and-project sequences from unrelated aperiodic sequences, but cannot distinguish rational-slope (periodic) from irrational-slope (quasiperiodic) instances once noise is added, a limitation expected for finite sequences. The model is effective at separating cut-and-project from other types of sequences. A neural spline flow (NSF) recovers the generating slope and acceptance window from noisy sequences at, and above, noise levels where an exact algorithmic model fails; multimodal posteriors that appear at high noise are shown to correspond to regions with similar tile lengths. A gated recurrent unit predicts the next tile correctly in 99.7 % of cases and produces valid 150-step continuations in 75 % of rollouts, outperforming both transformer configurations tested. In 2D, a convolutional network identifies the parent-lattice dimension N ∈ {4, . . . , 9} of a rhombus tiling from its diffraction pattern at 89.4 % accuracy. For N = 5, an NSF conditioned on the diffraction pattern and a edge-length histogram recovers the ten basis-vector components with posteriors whose calibration remains stable under vertex corruption. Machine learning can recognise, reconstruct and extend structure carrying approximate translational symmetry from finite observations, but distinguishing true quasiperiodicity from long-period periodicity remains fundamentally hard in noisy, finite sequences.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Boer, D. and Aalbers, J. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 11 Aug 2026 11:27 |
| Last Modified: | 11 Aug 2026 11:27 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37499 |
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