Extraction of the microscopic properties of quasiparticles using deep neural networks

We use deep neural networks (DNNs) to obtain the properties of partons in terms of an off-shell quasiparticle description. We aim to infer masses and widths of quasigluons, up/down, and strange (anti)quarks using constraints on the macroscopic thermodynamic observables obtained by the first-principles lattice QCD (lQCD) calculations. In this study we use three independent dimensionless thermodynamic observables from lQCD for minimization as the ratio of entropy density to temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>s</a:mi><a:mo>/</a:mo><a:msup><a:mi>T</a:mi><a:mn>3</a:mn></a:msup></a:mrow></a:math>, baryon susceptibility <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msubsup><b:mi>χ</b:mi><b:mn>2</b:mn><b:mi>B</b:mi></b:msubsup></b:math>, and strangeness susceptibility <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msubsup><c:mi>χ</c:mi><c:mn>2</c:mn><c:mi>S</c:mi></c:msubsup></c:math>. First, we train our DNN using the DQPM (dynamical quasiparticle model) ansatz for the masses and widths. Furthermore, we use the DNN capabilities to generalize this ansatz, to evaluate which quasiparticle masses and widths are desirable to describe different thermodynamic functions simultaneously. To evaluate consistently the microscopic properties obtained by the DNN in the case of off-shell quarks and gluons, we compute transport coefficients using the spectral function within the Kubo-Zubarev formalism in different setups. In particular, we make a comprehensive comparison in the case of the dimensionless ratios of shear viscosity over entropy density <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>η</d:mi><d:mo>/</d:mo><d:mi>s</d:mi></d:mrow></d:math>, and electric conductivity over temperature <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>σ</e:mi><e:mi>Q</e:mi></e:msub><e:mo>/</e:mo><e:mi>T</e:mi></e:mrow></e:math>, which provide additional constraints for the parameter generalization of the considered model cases. We present the parameter settings found by the DNN which can improve the quasiparticle description of lQCD data on the susceptibility and electric conductivity of strange quarks.