相关论文: Sensitivity Approximation by the Peano-Baker Serie…

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

Parameter estimation and associated uncertainty quantification is an important problem in dynamical systems characterized by ordinary differential equation (ODE) models that are often nonlinear. Typically, such models have analytically…

We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…

Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for…

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…

The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing…

Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…

Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…

Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation…

The quest for an algorithm that solves an $n\times n$ linear system in $O(n^2)$ time complexity, or $O(n^2 \text{poly}(1/\epsilon))$ when solving up to $\epsilon$ relative error, is a long-standing open problem in numerical linear algebra…

We consider the problem of estimating the spectral density of the normalized adjacency matrix of an $n$-node undirected graph. We provide a randomized algorithm that, with $O(n\epsilon^{-2})$ queries to a degree and neighbor oracle and in…

A method for approximating sixth-order ordinary differential equations is proposed, which utilizes a deep learning feedforward artificial neural network, referred to as a neural solver. The efficacy of this unsupervised machine learning…

Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address…

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

An \emph{$\alpha$-approximate vertex fault-tolerant distance sensitivity oracle} (\emph{$\alpha$-VSDO}) for a weighted input graph $G=(V, E, w)$ and a source vertex $s \in V$ is the data structure answering an $\alpha$-approximate distance…

We design the first efficient sensitivity oracles and dynamic algorithms for a variety of parameterized problems. Our main approach is to modify the algebraic coding technique from static parameterized algorithm design, which had not…

Inferring the parameters of ordinary differential equations (ODEs) from noisy observations is an important problem in many scientific fields. Currently, most parameter estimation methods that bypass numerical integration tend to rely on…

In this paper, we propose a general approach for approximate simulation and analysis of delay differential equations (DDEs) with distributed time delays based on methods for ordinary differential equations (ODEs). The key innovation is that…

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer…