Related papers: Applications of the Perturbative Gradient Flow
The cut-off effects of the lattice gradient flow -- often called Wilson flow -- are calculated on a periodic 4-torus at leading order in the gauge coupling. A large class of discretizations is considered which includes all frequently used…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is…
Recent work shows that path gradient estimators for normalizing flows have lower variance compared to standard estimators for variational inference, resulting in improved training. However, they are often prohibitively more expensive from a…
The color-flavor transformation is a mathematical result that has applications to problems as diverse as lattice gauge theory, random network models, and dynamical systems. Several variants are described, and an outline of the proof is…
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…
The simulation of real-time dynamics in lattice gauge theories is particularly hard for classical computing due to the exponential scaling of the required resources. On the other hand, quantum algorithms can potentially perform the same…
We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions…
We use a lattice Boltzmann method to study pattern formation in chemically reactive binary fluids in the regime where hydrodynamic effects are important. The coupled equations solved by the method are a Cahn-Hilliard equation, modified by…
We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextet model using the finite volume gradient flow scheme. Our results, using clover improved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop…
We investigate the coupled dynamics of quantized vortices and normal fluid in superfluid $^4$He at finite temperatures using a numerical approach based on the vortex filament model (VFM) and lattice Boltzmann method (LBM). The LBM allows us…
We present the results of an experimental and numerical investigation of a turbulent flow over a backward-facing step in a channel. Experimental data are visualized using a Particle Image Velocimetry (PIV) device. As a mathematical model we…
Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open…
For quantum computing (QC) to emerge as a practically indispensable computational tool, there is a need for quantum protocols with an end-to-end practical applications -- in this instance, fluid dynamics. We debut here a high performance…
This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller - based on gradient flow dynamics…
Studies of strongly nonlinear dynamical systems such as turbulent flows call for superior computational prowess. With the advent of quantum computing, a plethora of quantum algorithms have demonstrated, both theoretically and…
Concepts from elementary quantum mechanics can be used to understand vortex line fluctuations in high-temperature superconductors. Flux lines are essentially classical objects, described by a string tension, their mutual repulsion, and…
Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…
Grad-div stabilization, adding a term -gamma grad div u, has proven to be a useful tool in the simulation of incompressible flows. Such a term requires a choice of the coefficient gamma and studies have begun appearing with various…
Normalizing flows have recently demonstrated the ability to learn the Boltzmann distribution of the Hubbard model, opening new avenues for generative modeling in condensed matter physics. In this work, we investigate the steps required to…