相关论文: Optimization Algorithms Based on Renormalization G…

The state transition algorithm (STA), as an intelligent optimization method grounded in constructivist learning, has been demonstrated to be highly effective in solving complex optimization problems. However, the standard STA suffers from…

In this article the most fundamental decomposition-based optimization method - block coordinate search, based on the sequential decomposition of problems in subproblems - and building performance simulation programs are used to reason about…

The field of algorithmic optimization has significantly advanced with the development of methods for the automatic configuration of algorithmic parameters. This article delves into the Algorithm Configuration Problem, focused on optimizing…

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…

Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…

A lot of real-world engineering problems represent dynamicity with nests of nonlinearities due to highly complex network of exponential functions or large number of differential equations interacting together. Such search spaces are…

Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that…

The tensor-entanglement renormalization group approach is applied to Hamiltonians that realize a class of topologically ordered states -- string-net condensed states. We analyze phase transitions between phases with and without string-net…

We update a one-dimensional chain of Ising spins of length $L$ with algorithms which are parameterized by the probability $p$ for a certain site to get updated in one time step. The result of the update event itself is determined by the…

The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, ...) and are decoded by linear-time iterative algorithms. Because of these features, they are remarkable examples of…

Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the…

The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on…

Optimization of non-convex loss surfaces containing many local minima remains a critical problem in a variety of domains, including operations research, informatics, and material design. Yet, current techniques either require extremely high…

The group synchronization problem involves estimating a collection of group elements from noisy measurements of their pairwise ratios. This task is a key component in many computational problems, including the molecular reconstruction…

Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…

Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful…