Related papers: Analysis and Development of Stochastic Multigrid M…
We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length,…
We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric nonlinear $\sigma$-model [= SU(2) principal chiral model], on lattices…
Four-dimensional gauge theories based on symplectic Lie groups provide elegant realisations of the microscopic origin of several new physics models. Numerical studies pursued on the lattice provide quantitative information necessary for…
Non-equilibrium Markov Chain Monte Carlo (NE-MCMC) simulations provide a well-understood framework based on Jarzynski's equality to sample from a target probability distribution. By driving a base probability distribution out of…
Understanding the non-equilibrium dynamics of gauge theories remains a fundamental challenge in high-energy physics. Indeed, most large scale experiments on gauge theories intrinsically rely on very far-from equilibrium dynamics, from…
The Sweeny algorithm for the $Q$-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As $Q$ decreases, the so-called critical speeding-up for non-local quantities becomes…
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's `Global Drifter Program', this paper develops data-driven…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
Standard sampling algorithms for lattice QCD suffer from topology freezing (or critical slowing down) when approaching the continuum limit, thus leading to poor sampling of the distinct topological sectors. I will present a modified…
The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…
We investigate lattice simulations of scalar and nonabelian gauge fields in Minkowski space-time. For SU(2) gauge-theory expectation values of link variables in 3+1 dimensions are constructed by a stochastic process in an additional (5th)…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
This thesis is concerned with two topics in Hamiltonian lattice gauge theory: improvement and the application of analytic techniques. On the topic of improvement, we develop a direct method for improving lattice Hamiltonians for gluons, in…
Symplectic gauge theories coupled to matter fields lead to symmetry enhancement phenomena that have potential applications in such diverse contexts as composite Higgs, top partial compositeness, strongly interacting dark matter, and…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
We present a theoretical analysis of some popular adaptive Stochastic Gradient Descent (SGD) methods in the small learning rate regime. Using the stochastic modified equations framework introduced by Li et al., we derive effective…
The multigrid methodology is reviewed. By integrating numerical processes at all scales of a problem, it seeks to perform various computational tasks at a cost that rises as slowly as possible as a function of $n$, the number of degrees of…
Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these…
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…