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The deep connection among braids, knots and topological physics has providedvaluable insights into studying topological states in various physical systems.However, identifying distinct braid groups and knot topology embedded innon-Hermitian systems is challenging and requires significant efforts. Here, wedemonstrate that an unsupervised learning with the representation basis of$su(n)$ Lie algebra on $n$-fold extended non-Hermitian bands can fully classifybraid group and knot topology therein, without requiring any prior mathematicalknowledge or any pre-defined topological invariants. We demonstrate that theapproach successfully identifies different topological elements, such asunlink, unknot, Hopf link, Solomon ring, trefoil, and so on, by employinggeneralized Gell-Mann matrices in non-Hermitian models with $n$=2 and $n$=3energy bands. Moreover, since eigenstate information of non-Hermitian bands isincorporated in addition to eigenvalues, the approach distinguishes thedifferent parity-time symmetry and breaking phases, recognizes the oppositechirality of braids and knots, and identifies out distinct topological phasesthat were overlooked before. Our study shows significant potential of machinelearning in classification of knots, braid groups, and non-Hermitiantopological phases.

Machine Learning of Knot Topology in Non-Hermitian Band Braids