Related papers: Hyperspatial optimisation of structures
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
In this paper, we study the construction of structural models for the description of substitutional defects in crystalline materials. Predicting and designing the atomic structures in such systems is highly challenging due to the…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Machine Learning algorithms have been extensively researched throughout the last decade, leading to unprecedented advances in a broad range of applications, such as image classification and reconstruction, object recognition, and text…
Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the…
This paper presents a genetic-based hybrid algorithm that combines the exploration power of Genetic Algorithm (GA) with the exploitation capacity of a phenotypical probabilistic local search algorithm. Though not limited to a certain class…
We develop and analyze stochastic optimization algorithms for problems in which the expected loss is strongly convex, and the optimum is (approximately) sparse. Previous approaches are able to exploit only one of these two structures,…
Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is…
Randomized Fast Subspace Descent (RFASD) Methods are developed and analyzed for smooth and non-constraint convex optimization problems. The efficiency of the method relies on a space decomposition which is stable in $A$-norm, and meanwhile,…
We study Crystal Structure Prediction, one of the major problems in computational chemistry. This is essentially a continuous optimization problem, where many different, simple and sophisticated, methods have been proposed and applied. The…
This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…
Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
This paper presents a novel approach to the optimisation of structures using a Tabu search (TS) method. TS is a metaheuristic which is used to guide local search methods towards a globally optimal solution by using flexible memory cycles of…
Low-rank matrix sensing is a fundamental yet challenging nonconvex problem whose optimization landscape typically contains numerous spurious local minima, making it difficult for gradient-based optimizers to converge to the global optimum.…