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.
Non-uniqueness and symmetries for the nirenberg problem using computer assistance
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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.
PINNs can address differential geometry problems by training neural networks to minimize functionals that encode geometric conditions, as shown through summaries of three related studies.
citing papers explorer
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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.
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PINNs in More General Geometry
PINNs can address differential geometry problems by training neural networks to minimize functionals that encode geometric conditions, as shown through summaries of three related studies.