PINNs approximate near-minimal surfaces bounding knots in S^3; their self-intersection numbers align with Fine's conjecture predictions derived from the HOMFLY polynomial.
Metric flows with neural networks
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math.DG 2years
2026 2verdicts
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Neural networks minimize Willmore energy on embedded surfaces, recovering the round sphere and Clifford torus while supplying a search procedure for genus-2 minimal surfaces.
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Minimal surfaces, Knots, and Neural Networks
PINNs approximate near-minimal surfaces bounding knots in S^3; their self-intersection numbers align with Fine's conjecture predictions derived from the HOMFLY polynomial.
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Minimising Willmore Energy via Neural Flow
Neural networks minimize Willmore energy on embedded surfaces, recovering the round sphere and Clifford torus while supplying a search procedure for genus-2 minimal surfaces.