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20132026
most citedTowards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

50 citations · 193 across the 27 of their papers we have counts for

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Showing 2018Show all

3 papers · 1 filter

math.DG2018

Confined elasticae and the buckling of cylindrical shells

Stephan Wojtowytsch

For curves of prescribed length embedded into the unit disc in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds and in the l…

math.AP2018★ 2 cited

Approximation of the relaxed perimeter functional under a connectedness constraint by phase-fields

Patrick Dondl, Matteo Novaga, Benedikt Wirth +1

We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional…

math.NA2018★ 1 cited

Keeping it together: a phase field version of path-connectedness and its implementation

Patrick Dondl, Stephan Wojtowytsch

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the pha…