We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parametrized in terms of a permutationally invariant part described by the Deep Sets neural-network architecture. The input coordinates to the Deep Sets are periodically transformed such that they are suitable to directly describe periodic bosonic systems. We show example applications to both one- and two-dimensional interacting quantum gases with Gaussian interactions, as well as to $^{4}\mathrm{He}$ confined in a one-dimensional geometry. For the one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles. In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods. 

/pdf/neural-network-quantum-states-for-periodic-systems-in-2jqcli7w.pdf

Neural-network quantum states for periodic systems in continuous space

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations (ODEs) to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Spin-Neural ODEs an acceleration factor over 200 compared to micromagnetic simulations for a complex problem -- the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Spin-Neural ODEs on five milliseconds of their measured response to different excitations. Spin-Neural ODE is a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Spin-Neural ODE can also be generalized to other electronic devices involving dynamics.

/pdf/forecasting-the-outcome-of-spintronic-experiments-with-4q1nu27img.pdf

Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations.

Critical properties of the frustrated Ising model on a honeycomb lattice: A Monte Carlo study

Deep learning has an increasing impact to assist research, allowing, for example, the discovery of novel materials. Until now, however, these artificial intelligence techniques have fallen short of discovering the full differential equation of an experimental physical system. Here we show that a dynamical neural network, trained on a minimal amount of data, can predict the behavior of spintronic devices with high accuracy and an extremely efficient simulation time, compared to the micromagnetic simulations that are usually employed to model them. For this purpose, we re-frame the formalism of Neural Ordinary Differential Equations to the constraints of spintronics: few measured outputs, multiple inputs and internal parameters. We demonstrate with Neural Ordinary Differential Equations an acceleration factor over 200 compared to micromagnetic simulations for a complex problem - the simulation of a reservoir computer made of magnetic skyrmions (20 minutes compared to three days). In a second realization, we show that we can predict the noisy response of experimental spintronic nano-oscillators to varying inputs after training Neural Ordinary Differential Equations on five milliseconds of their measured response to a different set of inputs. Neural Ordinary Differential Equations can therefore constitute a disruptive tool for developing spintronic applications in complement to micromagnetic simulations, which are time-consuming and cannot fit experiments when noise or imperfections are present. Our approach can also be generalized to other electronic devices involving dynamics. 

/pdf/forecasting-the-outcome-of-spintronic-experiments-with-1gkz2j7i.pdf

Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations

The recent renaissance in machine learning has brought about a plethora of new techniques in the study of condensed matter and statistical physics In particular, artificial neural networks (ANNs) have been used extensively in the classification and identification of phase transitions in spin models; however, their applicability is typically limited to the spin models they are trained with and little is known about their generalizability Here, we propose a method that resembles the introduction of sparsity, by which simple ANNs trained with the two-dimensional ferromagnetic Ising model can be applied to the ferromagnetic $q$-state Potts model in different dimensions for $q \geq 2$ We establish the generalizability of the ANNs by showing that critical properties are correctly reproduced, and show that the same method can also be applied to the highly nontrivial case of the antiferromagnetic $q$-state Potts model Furthermore, we demonstrate that similar results can be obtained by reducing the exponentially large state space spanned by the training data to one that comprises only three representative spin configurations artificially constructed through symmetry considerations Our findings suggest that nontrivial information of multiple-state systems can be encoded in a representation of far fewer states, and the amount of ANNs required in the study of spin models can potentially be reduced We anticipate our methodology will invigorate the application and understanding of machine learning techniques to spin models and related fields

On the generalizability of artificial neural networks in spin models

Exploring neural network training strategies to determine phase transitions in frustrated magnetic models

The transfer learning of a neural network is one of its most outstanding aspects, and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting many-body systems. By means of case studies, we show the potential of this deep learning technique to detect phases and their transitions in frustrated spin systems, using dense and convolutional neural networks. In addition, we explore a recently-introduced technique, which is at the middle point of supervised and unsupervised learning. It consists in evaluating the performance of a neural network which has been deliberately 'confused' during its training. To properly demonstrate the capability of the 'confusion' and transfer learning techniques, we apply them to a paradigmatic model of frustrated magnetism in two dimensions, to determine its phase diagram and compare it with high-performance Monte Carlo simulations.

Transfer and confusion deep learning in frustrated spin systems

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Exploring neural network training strategies to determine phase transitions in frustrated magnetic models

Transfer and confusion deep learning in frustrated spin systems