17 research outputs found
Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics
Next Generation Reservoir Computing (NG-RC) is a modern class of model-free
machine learning that enables an accurate forecasting of time series data
generated by dynamical systems. We demonstrate that NG-RC can accurately
predict full many-body quantum dynamics in both integrable and chaotic systems.
This is in contrast to the conventional application of reservoir computing that
concentrates on the prediction of the dynamics of observables. In addition, we
apply a technique which we refer to as skipping ahead to predict far future
states accurately without the need to extract information about the
intermediate states. However, adopting a classical NG-RC for many-body quantum
dynamics prediction is computationally prohibitive due to the large Hilbert
space of sample input data. In this work, we propose an end-to-end quantum
algorithm for many-body quantum dynamics forecasting with a quantum
computational speedup via the block-encoding technique. This proposal presents
an efficient model-free quantum scheme to forecast quantum dynamics coherently,
bypassing inductive biases incurred in a model-based approach.Comment: 15 pages, 5 figures. v2: additional forecasting results for a chaotic
quantum syste
StrainNet: Predicting crystal structure elastic properties using SE(3)-equivariant graph neural networks
Accurately predicting the elastic properties of crystalline solids is vital
for computational materials science. However, traditional atomistic scale ab
initio approaches are computationally intensive, especially for studying
complex materials with a large number of atoms in a unit cell. We introduce a
novel data-driven approach to efficiently predict the elastic properties of
crystal structures using SE(3)-equivariant graph neural networks (GNNs). This
approach yields important scalar elastic moduli with the accuracy comparable to
recent data-driven studies. Importantly, our symmetry-aware GNNs model also
enables the prediction of the strain energy density (SED) and the associated
elastic constants, the fundamental tensorial quantities that are significantly
influenced by a material's crystallographic group. The model consistently
distinguishes independent elements of SED tensors, in accordance with the
symmetry of the crystal structures. Finally, our deep learning model possesses
meaningful latent features, offering an interpretable prediction of the elastic
properties.Comment: 25 pages, 15 figure
Biologically Plausible Sequence Learning with Spiking Neural Networks
Motivated by the celebrated discrete-time model of nervous activity outlined
by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the
McCulloch-Pitts network (MPN), for sequence learning in spiking neural
networks. Our model has a local learning rule, such that the synaptic weight
updates depend only on the information directly accessible by the synapse. By
exploiting asymmetry in the connections between binary neurons, we show that
MPN can be trained to robustly memorize multiple spatiotemporal patterns of
binary vectors, generalizing the ability of the symmetric Hopfield network to
memorize static spatial patterns. In addition, we demonstrate that the model
can efficiently learn sequences of binary pictures as well as generative models
for experimental neural spike-train data. Our learning rule is consistent with
spike-timing-dependent plasticity (STDP), thus providing a theoretical ground
for the systematic design of biologically inspired networks with large and
robust long-range sequence storage capacity.Comment: Accepted for publication in the Proceedings of the 34th AAAI
Conference on Artificial Intelligence (AAAI-20
Family of chaotic maps from game theory
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal, on which a two-parameter family of bimodal interval maps exhibits periodic orbits and chaos. While the fixed point b corresponding to a Nash equilibrium of such map f is usually repelling, it is globally Cesà ro attracting on the diagonal, that is,
limn→∞1n∑n−1k=0fk(x)=b for every x∈(0,1). This solves a known open question whether there exists a ‘natural’ nontrivial smooth map other than x↦axe−x with centres of mass of all periodic orbits coinciding. We also study the dependence of the dynamics on the two parameters