相关论文: A new embedded variable stepsize, variable order f…

A Variable Parameter (VP) analysis, that we introduce here, aims to give a precise algorithm time complexity expression in which an exponent appears solely in terms of a variable parameter. A variable parameter is the number of objects with…

Approximate Bayesian inference for models with computationally expensive, black-box likelihoods poses a significant challenge, especially when the posterior distribution is complex. Many inference methods struggle to explore the parameter…

We give an algorithm for efficient step size control in numerical integration of non-stiff initial value problems, based on a formula tailormade to methods where the numerical solution is compared with a solution of lower order.

A body of recent work has focused on constructing a variational family of filtered distributions using Sequential Monte Carlo (SMC). Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward…

In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…

Training and inference efficiency of deep neural networks highly rely on the performance of tensor operators on hardware platforms. Manually optimizing tensor operators has limitations in terms of supporting new operators or hardware…

The latest video coding standard, Versatile Video Coding (VVC), achieves almost twice coding efficiency compared to its predecessor, the High Efficiency Video Coding (HEVC). However, achieving this efficiency (for intra coding) requires 31x…

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the flux splitting of the compressible Navier-Stokes…

Diffusion models deliver high-fidelity generation but remain slow at inference time due to many sequential network evaluations. We find that standard timestep conditioning becomes a key bottleneck for few-step sampling. Motivated by…

This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs. The systematic design of these methods mixes the Runge-Kutta collocation formalism with…

Continuous-time models such as Neural ODEs and Neural Flows have shown promising results in analyzing irregularly sampled time series frequently encountered in electronic health records. Based on these models, time series are typically…

In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using the scalar auxiliary variable…

Node embedding methods find latent lower-dimensional representations which are used as features in machine learning models. In the last few years, these methods have become extremely popular as a replacement for manual feature engineering.…

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…

We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…

Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs).…

Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. However, practitioners are faced with a fragmented literature that offers a bewildering array of algorithmic options. First, the…

We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i)…

This paper presents an efficient algorithm, naming Centralized Searching and Decentralized Optimization (CSDO), to find feasible solution for large-scale Multi-Vehicle Trajectory Planning (MVTP) problem. Due to the intractable growth of…