WillmorePINN
Physics-informed neural networks (PINNs) that learn surface embeddings minimising the Willmore energy.
Research
Our work
Here we gather papers, preprints, code and talks by lab members, organised by the four modes and by a fifth direction, geometry in the service of AI itself.
Research
9 items
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2026 Preprint
Optimal pruning for neural architectures using Fisher information distances
Geodesic distance in the Fisher-information metric on model space organises a hierarchy of pruning schemes for neural networks.
Geometry for AIarXiv:2609.16129
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2026 Talk
Digital tools and AI for contemporary mathematical productivity
Talk at CBG, Campinas · 17 Aug 2026
From reducing friction to changing the research frontier, the talk tells a “productivity story” and a “discovery story”.
AssistSlides
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2026 Preprint
Learning the graphical nature of symmetries
A census of 131,406 Cayley graphs for learning properties of finite groups from graph observables, which led to new conjectures and new OEIS sequences.
PredictarXiv:2607.12026
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2026 Preprint
Black hole black boxes: numerical black hole metrics via AInstein neural networks
The AInstein architecture, taken to Lorentzian signature, recovers the Schwarzschild geometry and searches for new Petrov type I Einstein metrics.
ApproximatearXiv:2607.05489
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2026 Proceedings
PINNs in more general geometry
An introduction to PINNs for differential geometry, showing how geometric functionals become loss functions.
ApproximatearXiv:2604.25020
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2026 Preprint
Minimising Willmore energy via neural flow
The neural Willmore flow recovers the round sphere (genus 0) and the Clifford torus (genus 1), and opens a new approach to the open genus-2 case.
ApproximatearXiv:2604.04321
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2026 Preprint
A penalised Saito functional for heuristic search of free line arrangements
A functional that vanishes exactly on free arrangements guides the search, and every example is certified in exact arithmetic. In total, 6,146 representatives were found up to n = 28.
SearcharXiv:2604.02995
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2026 Article
Neural and numerical methods for G2-structures on contact Calabi–Yau 7-manifolds
Physics Letters B 878, 140566
Neural Ricci-flat metrics on Calabi–Yau threefolds yield G2 3-forms on the 7-dimensional links, which are then learned directly by a network.
ApproximatearXiv:2602.12438DOI
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2025 Article
Metaheuristic generation of brane tilings
Physics Letters B 862, 139365
Simulated annealing constructs geometrically consistent brane tilings and finds a new example with 26 fields.
SearcharXiv:2412.19313DOI Code
Each member's full list is on their personal page.
Code & data
Open by default
FreeLineArrangements
Heuristic and reinforcement-learning search for free line arrangements in the projective plane, with a database of arrangements certified in exact arithmetic.
LearningG2
Neural networks that learn the 3-form φ and the metric of G2-structures on contact Calabi–Yau 7-manifolds.
NumericalExteriorDerivative
A SageMath demo implementation of the numerical exterior derivative in ℝ³, based on the mean value equality.
Metaheuristic brane tiling search
Simulated annealing to construct geometrically consistent brane tilings.
MLcCY7
Generates Calabi–Yau links from weighted projective spaces, computes their topological invariants (Sasakian Hodge numbers, Crowley–Nordström invariant) and studies them with machine learning.
You don't need to know AI. You need a good question.
If you work in geometry or in any other area of mathematics and have a problem with many examples, a hard computation or a pattern you can't yet explain, let's talk.