Related papers: On the Thermodynamics of Global Optimization
Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can…
We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
Accurate, global Potential Energy Surfaces (PES) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the MCTDH method. This work introduces a methodology for…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity}…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that…
An energy functional for orbital based $O(N)$ calculations is proposed, which depends on a number of non orthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical…
Most noninvasive imaging techniques utilize electromagnetic or acoustic waves originating from multiple locations and directions to identify hidden geometrical structures. Surprisingly, it is also possible to image hidden voids and…
The energy landscapes of proteins have evolved to be different from most random heteropolymers. Many studies have concluded that evolutionary selection for rapid and reliable folding to a given structure that is stable at biological…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
Highly-optimized complex transport networks serve crucial functions in many man-made and natural systems such as power grids and plant or animal vasculature. Often, the relevant optimization functional is non-convex and characterized by…
The construction of the potential energy surface (PES) of even a medium-sized molecule employing correlated theory, such as CCSD(T), is an arduous task due to the high computational cost. In this Letter, we report the possibility of…
We dramatically improve convergence speed and global exploration capabilities of particle swarm optimization (PSO) through a targeted position-mutated elitism (PSO-TPME). The three key innovations address particle classification, elitism,…
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well known quantum mechanical tunneling property which enables small bodies to penetrate…
We propose a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing. The method is useful for studies involving large numbers of PES evaluations, such as the…
Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…
Efficient and reliable identification and optimization of transition state structures is a longstanding challenge in computational chemistry. Popular chain-of-states methods require hundreds if not thousands of ab initio calculations to…
Metasurfaces are subwavelength-structured artificial media that can shape and localize electromagnetic waves in unique ways. The inverse design of these devices is a non-convex optimization problem in a high dimensional space, making global…