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This paper proposes a new view to algorithms, Algorithms as defining dynamic systems. This view extends the traditional, deterministic view that an algorithm is a step by step procedure with nondeterminism. As a dynamic system can be…
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…
We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of "live points" varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation…
We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…
In a world made of atoms, the computer simulation of molecular systems, such as proteins in water, plays an enormous role in science. Software packages that perform these computations have been developed for decades. In molecular…
In this paper, we present a novel Newton-based extremum seeking controller for the solution of multivariable model-free optimization problems in static maps. Unlike existing asymptotic and fixed-time results in the literature, we present a…
This paper outlines a numerical algorithm that could be used for simulating full 3D dynamics of magnetic fluid droplet shapes in external magnetic fields, by solving boundary integral equations. The algorithm works with arbitrary droplet…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
Matching pursuit algorithms are an important class of algorithms in signal processing and machine learning. We present a blended matching pursuit algorithm, combining coordinate descent-like steps with stronger gradient descent steps, for…
Algorithmic regularization uses a transformation of the equations of motion such that the leapfrog algorithm produces exact trajectories for two-body motion as well as regular results in numerical integration of the motion of strongly…
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix,…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…