scholarly journals Machine learning entanglement freedom

2018 ◽  
Vol 16 (08) ◽  
pp. 1840002 ◽  
Author(s):  
Samuel Spillard ◽  
Christopher J. Turner ◽  
Konstantinos Meichanetzidis
Keyword(s):  
Machine Learning ◽  
Optimization Problem ◽  
Alternative Measure ◽  
Free Fermion ◽  
Many Body ◽  
Entanglement Spectrum ◽  
Emergent Phenomena ◽  
Interaction Distance ◽  
Many Body Systems ◽  
The Given

Quantum many-body systems realize many different phases of matter characterized by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies that the physics is dictated by an interacting Hamiltonian. The interaction distance has been successfully used to quantify the effect of interactions in a variety of states of matter via the entanglement spectrum [C. J. Turner, K. Meichanetzidis, Z. Papic and J. K. Pachos, Nat. Commun. 8 (2017) 14926, Phys. Rev. B 97 (2018) 125104]. The computation of the interaction distance reduces to a global optimization problem whose goal is to search for the free-fermion entanglement spectrum closest to the given entanglement spectrum. In this work, we employ techniques from machine learning in order to perform this same task. In a supervised learning setting, we use labeled data obtained by computing the interaction distance and predict its value via linear regression. Moving to a semi-supervised setting, we train an autoencoder to estimate an alternative measure to the interaction distance, and we show that it behaves in a similar manner.

scholarly journals Machine learning outperforms thermodynamics in measuring how well a many-body system learns a drive

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Weishun Zhong ◽  
Jacob M. Gold ◽  
Sarah Marzen ◽  
Jeremy L. England ◽  
Nicole Yunger Halpern
Keyword(s):  
Machine Learning ◽  
Novelty Detection ◽  
Representation Learning ◽  
Many Body ◽  
Discrimination Ability ◽  
Machine Learning Model ◽  
Systems Learning ◽  
Statistical Mechanical ◽  
Far From Equilibrium ◽  
Many Body Systems

AbstractDiverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems’ learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

scholarly journals Machine learning active-nematic hydrodynamics

2021 ◽  
Vol 118 (10) ◽  
pp. e2016708118
Author(s):  
Jonathan Colen ◽  
Ming Han ◽  
Rui Zhang ◽  
Steven A. Redford ◽  
Linnea M. Lemma ◽  
...  
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Initial Conditions ◽  
Molecular Motor ◽  
Machine Learning Algorithms ◽  
Many Body ◽  
Hydrodynamic Parameters ◽  
Many Body Systems ◽  
And Control ◽  
Macroscopic Parameters

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

scholarly journals Quantifying the effect of interactions in quantum many-body systems

2018 ◽  
Author(s):  
Jiannis Pachos ◽  
Zlatko Papic
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
High Temperature Superconductivity ◽  
Quantum Hall ◽  
Quantum Spin ◽  
Many Body ◽  
Theoretical Understanding ◽  
Integer Quantum Hall Effect ◽  
Interaction Distance ◽  
Many Body Systems

Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture by giving rise to emerging physics that may not resemble free fermions. Examples of such phenomena include high-temperature superconductivity, fractional quantum Hall effect, Kondo effect and quantum spin liquids. The non-perturbative behaviour of such systems remains a major obstacle to their theoretical understanding that could unlock further technological applications. Here, we present a pedagogical review of “interaction distance" [Nat. Commun. 8, 14926 (2017)] – a systematic method that quantifies the effect interactions can have on the energy spectrum and on the quantum correlations of generic many-body systems. In particular, the interaction distance is a diagnostic tool that identifies the emergent physics of interacting systems. We illustrate this method on the simple example of a two-site Fermi-Hubbard model.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems

scholarly journals Discretization and machine learning approximation of BSDEs with a constraint on the Gains-process

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Idris Kharroubi ◽  
Thomas Lim ◽  
Xavier Warin
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Neural Networks ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Learning Approach ◽  
The Neural Network ◽  
Machine Learning Approach ◽  
Mesh Grid

AbstractWe study the approximation of backward stochastic differential equations (BSDEs for short) with a constraint on the gains process. We first discretize the constraint by applying a so-called facelift operator at times of a grid. We show that this discretely constrained BSDE converges to the continuously constrained one as the mesh grid converges to zero. We then focus on the approximation of the discretely constrained BSDE. For that we adopt a machine learning approach. We show that the facelift can be approximated by an optimization problem over a class of neural networks under constraints on the neural network and its derivative. We then derive an algorithm converging to the discretely constrained BSDE as the number of neurons goes to infinity. We end by numerical experiments.

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