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Generalized Additive Runge-Kutta schemes have shown to be a suitable tool for solving ordinary differential equations with additively partitioned right-hand sides. This work develops symplectic GARK schemes for additively partitioned…
In this paper, we present a heuristic adaptive fast gradient method. We show that in practice our method has a better convergence rate than popular today optimization methods. Moreover, we justify our method and point out some problems that…
Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually…
The choices of hyperparameters have critical effects on the performance of machine learning models. In this paper, we present a general framework that is able to construct an adaptive optimizer, which automatically adjust the appropriate…
The architectures of deep neural networks (DNN) rely heavily on the underlying grid structure of variables, for instance, the lattice of pixels in an image. For general high dimensional data with variables not associated with a grid, the…
Discriminantal arrangements are hyperplane arrangements, which are generalized braid ones. They are constructed from given hyperplane arrangements, but their combinatorics are not invariant under combinatorial equivalence. However, it is…
Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…
Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…
Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference…
Dyadic lattice graphs and their duals are commonly used as discrete approximations to the hyperbolic plane. We use them to give examples of random rooted graphs that are stationary for simple random walk, but whose duals have only a…
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
A novel finite element method for the approximation of Maxwell's equations over hybrid two-dimensional grids is studied. The choice of appropriate basis functions and numerical quadrature leads to diagonal mass matrices which allow for…
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
The difference variational bicomplex, which is the natural setting for systems of difference equations, is constructed and used to examine the geometric and algebraic properties of various systems. Exactness of the bicomplex gives a…
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in…