Related papers: Optimisation of the exact renormalisation group
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the…
The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its…
Coarse graining techniques offer a promising alternative to large-scale simulations of complex dynamical systems, as long as the coarse-grained system is truly representative of the initial one. Here, we investigate how the dynamical…
Graph coarsening is a widely used dimensionality reduction technique for approaching large-scale graph machine learning problems. Given a large graph, graph coarsening aims to learn a smaller-tractable graph while preserving the properties…
Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
A regularization algorithm (AR1pGN) for unconstrained nonlinear minimization is considered, which uses a model consisting of a Taylor expansion of arbitrary degree and regularization term involving a possibly non-smooth norm. It is shown…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
We formulate a method of performing non-perturbative calculations in quantum field theory, based upon a derivative expansion of the exact renormalization group. We then proceed to apply this method to the calculation of critical exponents…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…
Dissipative particle dynamics (DPD) is now a well-established method for simulating soft matter systems. However, its applicability was recently questioned because some investigations showed an upper coarse-graining limit that would prevent…
This Note gives conditions that must be imposed to algebraic multilevel discretizations involving at the same time nodal and edge elements so that a gradient-prolongation commutativity condition will be satisfied; this condition is very…
The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Modern distribution grids with high penetration of renewable generation provide substantial flexibility through distributed reactive power sources and transformer tap changers. This high degree of freedom can be exploited for optimisation.…
We formulate the problem of finding the low-energy limit of spin foam models as a coarse-graining problem in the sense of statistical physics. This suggests that renormalization group methods may be used to find that limit. However, since…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…