Related papers: Acceleration of Source Iteration using the Dynamic…
In this study, an efficient reanalysis strategy for dynamic topology optimization is proposed. Compared with other related studies, an online successive dynamic reanalysis method and POD-based approximate dynamic displacement strategy are…
Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration,…
An accelerated block coordinate descent (ABCD) method in Hilbert space is analyzed to solve the sparse optimal control problem via its dual. The finite element approximation of this method is investigated and convergence results are…
This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…
We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree--Fock equations for atoms interacting both with each other and with an external potential. Our development…
Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with…
In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology…
A standard approach to solving the S$_N$ transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues…
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The…
The decomposition method which makes the parallel solution of the block-tridiagonal matrix systems possible is presented. The performance of the method is analytically estimated based on the number of elementary multiplicative operations…
One of the most widely used methods for solving average cost MDP problems is the value iteration method. This method, however, is often computationally impractical and restricted in size of solvable MDP problems. We propose acceleration…
This paper presents a machine-learning-enhanced longitudinal scanline method to extract vehicle trajectories from high-angle traffic cameras. The Dynamic Mode Decomposition (DMD) method is applied to extract vehicle strands by decomposing…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…