相关论文: Adaptive LOOCV-based kernel methods for solving ti…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…

With machine learning being a popular topic in current computational materials science literature, creating representations for compounds has become common place. These representations are rarely compared, as evaluating their performance -…

We consider the general problem of learning a predictor that satisfies multiple objectives of interest simultaneously, a broad framework that captures a range of specific learning goals including calibration, regret, and multiaccuracy. We…

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…

This paper is concerned with adaptive kernel estimation of the L\'evy density N(x) for bounded-variation pure-jump L\'evy processes. The sample path is observed at n discrete instants in the "high frequency" context (\Delta = \Delta(n)…

In this paper, an algorithm is developed to solve a multilevel mono-objective linear programming problem (ML(MO)LPP), where the constructive adaptive method of linear programming is nested. This procedure is the modified version of the SB.…

We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…

The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…

Cross validation is widely used for selecting tuning parameters in regularization methods, but it is computationally intensive in general. To lessen its computational burden, approximation schemes such as generalized approximate cross…

Complex computer codes or models can often be run in a hierarchy of different levels of complexity ranging from the very basic to the sophisticated. The top levels in this hierarchy are typically expensive to run, which limits the number of…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

Decoding from large language models (LLMs) typically relies on fixed sampling hyperparameters (e.g., temperature, top-p), despite substantial variation in task difficulty and uncertainty across prompts and individual decoding steps. We…

We present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to…

In this paper we propose a framework to analyze iterative first-order optimization algorithms for time-varying convex optimization. We assume that the temporal variability is caused by a time-varying parameter entering the objective, which…

Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated…

In this paper, we consider a boundary value problem (BVP) for a fourth order nonlinear functional integro-differential equation. We establish the existence and uniqueness of solution and construct a numerical method for solving it. We prove…

Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…

This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…