arXiv subjects

Gert Aarts

Publications and source records attributed to Gert Aarts.

At least 55 records · Page 3Linked to original sources

arXiv2023

Recent Results from the FASTSUM Collaboration

The FASTSUM Collaboration has developed a comprehensive research programme in thermal QCD using 2+1 flavour, anisotropic ensembles. In this talk, we summarise some of our recent results including thermal hadron spectrum calculations using our ``Generation 2L'' ensembles which have pion masses of 239(1) MeV. These include open charm mesons and charm baryons. We also summarise our work using the Backus Gilbert approach to determining the spectral function of the NRQCD bottomonium system. Finally, we review our determination of the interquark potential in the same system, but using our ``Generation 2'' ensembles which have heavier pion masses of 384(4) MeV.

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arXiv2022

Charm baryons at finite temperature on anisotropic lattices

Singly, doubly and triply charmed baryons are investigated at multiple temperatures using the anisotropic FASTSUM 'Generation 2L' ensembles. We discuss the temperature dependence of these baryons' spectra in both parity channels with a focus on the confining phase. To further qualify the behaviour of these states around the pseudocritical temperature, we investigate the effect of chiral symmetry restoration for light quarks. We find that an estimate of the pseudocritical temperature can still be found from positive and negative-parity charmed baryon correlators, even when parity doubling itself is not very evident (as expected).

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arXiv2022

Hadrons at high temperature: an update from the FASTSUM collaboration

We present the most recent results from the FASTSUM collaboration for hadron properties at high temperature. This includes the temperature dependence of the light and charmed meson and baryon spectrum, as well as properties of heavy quarkonia. The results are obtained using anisotropic lattices with a fixed scale approach. We also present the status of our next generation gauge ensembles.

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arXiv2022

Lattice QCD at finite temperature: some aspects related to chiral symmetry

Out of the many exciting results obtained with the lattice approach to QCD under extreme conditions, I discuss a few selected items related to chiral symmetry: the chiral condensate as an approximate order parameter, meson screening masses, and masses of baryons and mesons, including D(s) mesons, when approaching the crossover from the hadronic side.

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arXiv2022

Open charm mesons at nonzero temperature: results in the hadronic phase from lattice QCD

We study what happens to D and D_s mesons as the temperature increases, using lattice QCD simulations with N_f=2+1 dynamical flavours on anistropic lattices. We have access to five temperatures in the hadronic phase. Using the determined groundstate mass at the lowest temperature, we investigate the effect of rising temperature by analysing ratios of mesonic correlators, without the need for further fitting or spectral reconstruction. In the pseudoscalar and vector channels, we demonstrate that temperature effects are at the percent level and can be captured by a reduction of the groundstate mass as the thermal crossover is approached. In the axial-vector and scalar channels on the other hand, temperature effects are prominent throughout the hadronic phase.

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arXiv2022

Quantum field theories, Markov random fields and machine learning

The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the $ϕ^{4}$ lattice field theory on a square lattice, are mathematically equivalent to Markov fields, a notable class of probabilistic graphical models with applications in a variety of research areas, including machine learning. The results are established based on the Hammersley-Clifford theorem. We will then derive neural networks from quantum field theories and discuss applications pertinent to the minimization of the Kullback-Leibler divergence for the probability distribution of the $ϕ^{4}$ machine learning algorithms and other probability distributions.

cs.LG↗

arXiv2022

Inverse Renormalization Group in Quantum Field Theory

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional $ϕ^{4}$ scalar field theory on sizes as small as $V=8^{2}$, we apply the inverse transformations to produce rescaled systems of size up to $V'=512^{2}$ which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

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arXiv2022

Applications of Machine Learning to Lattice Quantum Field Theory

There is great potential to apply machine learning in the area of numerical lattice quantum field theory, but full exploitation of that potential will require new strategies. In this white paper for the Snowmass community planning process, we discuss the unique requirements of machine learning for lattice quantum field theory research and outline what is needed to enable exploration and deployment of this approach in the future.

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arXiv2022

Towards a Shapley Value Graph Framework for Medical peer-influence

eXplainable Artificial Intelligence (XAI) is a sub-field of Artificial Intelligence (AI) that is at the forefront of AI research. In XAI, feature attribution methods produce explanations in the form of feature importance. People often use feature importance as guidance for intervention. However, a limitation of existing feature attribution methods is that there is a lack of explanation towards the consequence of intervention. In other words, although contribution towards a certain prediction is highlighted by feature attribution methods, the relation between features and the consequence of intervention is not studied. The aim of this paper is to introduce a new framework, called a peer influence framework to look deeper into explanations using graph representation for feature-to-feature interactions to improve the interpretability of black-box Machine Learning models and inform intervention.

cs.AI↗

arXiv2021

Spectral reconstruction in NRQCD via the Backus-Gilbert method

We present progress results from the FASTSUM collaboration's programme to determine the spectrum of the bottomonium system as a function of temperature using a variety of approaches. In this contribution, the Backus Gilbert method is used to reconstruct spectral functions from NRQCD meson correlator data from FASTSUM's anisotropic ensembles at nonzero temperature. We focus in particular on the resolving power of the method, providing a demonstration of how the underlying resolution functions can be probed by exploiting the Laplacian nature of the NRQCD kernel. We conclude with estimates of the bottomonium ground state mass and widths at nonzero temperature.

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arXiv2021

Bottomonium spectral widths at nonzero temperature using maximum likelihood

We present progress results from the Fastsum collaboration's programme to determine the spectrum of the bottomonium system as a function of temperature using a variety of approaches. In these proceedings, the Maximum Likelihood approach is used with an Ansatz comprising of a Gaussian spectral function for the ground state. Fastsum anisotropic lattices with 2+1 dynamical quark flavours were used with temperatures ranging from 47 to 375 MeV.

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arXiv2021

A comparison of spectral reconstruction methods applied to non-zero temperature NRQCD meson correlation functions

We present results from the fastsum collaboration's programme to determine the spectrum of the bottomonium system as a function of temperature. Three different methods of extracting spectral information are discussed: a Maximum Likelihood approach using a Gaussian spectral function for the ground state, the Backus Gilbert method, and the Kernel Ridge Regression machine learning procedure. We employ the fastsum anisotropic lattices with 2+1 dynamical quark flavours, with temperatures ranging from 47 to 375 MeV.

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arXiv2021

Reconstruction of bottomonium spectral functions in thermal QCD using Kernel Ridge Regression

We discuss results for bottomonium at nonzero temperature obtained using NRQCD on Fastsum Generation 2L ensembles, as part of the Fastsum collaboration's programme to determine the spectrum of the bottomonium system as a function of temperature using a variety of approaches. Here we give an update on results for spectral functions obtained using Kernel Ridge Regression. We pay in particular attention to the generation of training data and introduce the notion of using lattice QCD ensembles to learn how to improve the generation of training data. A practical implementation is given.

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arXiv2021

Meson thermal masses at different temperatures

We determine the ground state meson masses at low temperature using simulations with $2+1$ flavours of improved Wilson-clover fermions. Subsequently we study the effect of increasing the temperature of the hadron gas, including the transition to the quark-gluon plasma, as well as the restoration of $SU(2)_A$ chiral symmetry. We use the FASTSUM anisotropic, fixed-scale Generation2L ensembles and consider mesons with light, strange and charm content.

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arXiv2021

Interpreting machine learning functions as physical observables

We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size scaling, to analyse phase transitions quantitatively. In addition we incorporate predictive functions as conjugate variables coupled to an external field within the Hamiltonian of a system, allowing to induce order-disorder phase transitions in a novel manner. A noteworthy feature of this approach is that no knowledge of the symmetries in the Hamiltonian is required.

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arXiv2021

Machine learning with quantum field theories

The precise equivalence between discretized Euclidean field theories and a certain class of probabilistic graphical models, namely the mathematical framework of Markov random fields, opens up the opportunity to investigate machine learning from the perspective of quantum field theory. In this contribution we will demonstrate, through the Hammersley-Clifford theorem, that the $ϕ^{4}$ scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the $ϕ^{4}$ theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures. Finally, we will conclude by presenting applications based on the minimization of an asymmetric distance between the probability distribution of the $ϕ^{4}$ machine learning algorithms and target probability distributions.

cs.LG↗

arXiv2021

Quantum field-theoretic machine learning

We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $ϕ^{4}$ scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the $ϕ^{4}$ theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural network architectures are additionally derived from the $ϕ^{4}$ theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.

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arXiv2021

Adding machine learning within Hamiltonians: Renormalization group transformations, symmetry breaking and restoration

We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system. Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied by proposing a Hamiltonian-agnostic reweighting approach and forming a renormalization group mapping on quantities derived from the neural network. Accurate estimates of the critical point and of the critical exponents related to the operators that govern the divergence of the correlation length are provided. We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.

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