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Gavin Nop

Publications and source records attributed to Gavin Nop.

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Predicting quantum materials properties using novel faithful machine learning embeddings

Machine Learning (ML) is accelerating the progress of materials prediction and classification, with particular success in CGNN designs. While classical ML methods remain accessible, advanced deep networks are still challenging to build and train. We introduce two new adaptations and refine two existing ML networks for generic crystalline quantum materials properties prediction and optimization. These new models achieve state-of-the-art performance in predicting TQC classification and strong performance in predicting band gaps, magnetic classifications, formation energies, and symmetry group. All networks easily generalize to all quantum crystalline materials property predictions. To support this, full implementations and automated methods for data handling and materials predictions are provided, facilitating the use of deep ML methods in quantum materials science. Finally, dataset error rates are analyzed using an ensemble model to identify and highlight highly atypical materials for further investigations.

cond-mat.other

Random walk on the Poincaré disk induced by a group of Möbius transformations

We consider a discrete-time random motion, Markov chain on the Poincaré disk. In the basic variant of the model a particle moves along certain circular arcs within the disk, its location is determined by a composition of random Möbius transformations. We exploit an isomorphism between the underlying group of Möbius transformations and $\rr$ to study the random motion through its relation to a one-dimensional random walk. More specifically, we show that key geometric characteristics of the random motion, such as Busemann functions and bipolar coordinates evaluated at its location, and hyperbolic distance from the origin, can be either explicitly computed or approximated in terms of the random walk. We also consider a variant of the model where the motion is not confined to a single arc, but rather the particle switches between arcs of a parabolic pencil of circles at random times.

math.PR