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In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
This paper introduces time-continuous numerical schemes to simulate stochastic differential equations (SDEs) arising in mathematical finance, population dynamics, chemical kinetics, epidemiology, biophysics, and polymeric fluids. These…
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
We show that it is possible to obtain a linear computational cost FEM-based solver for non-stationary Stokes and Navier-Stokes equations. Our method employs a technique developed by Guermond and Minev, which consists of singular…
For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…
Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…
This paper considers a fractional programming problem (P) which minimizes a ratio of quadratic functions subject to a two-sided quadratic constraint. As is well-known, the fractional objective function can be replaced by a parametric family…
Low-rank approximation using time-dependent bases (TDBs) has proven effective for reduced-order modeling of stochastic partial differential equations (SPDEs). In these techniques, the random field is decomposed to a set of deterministic…
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equations (PDEs). Particularly, the PDE models in the group could…
We introduce a method which provides accurate numerical solutions to fractional-in-time partial differential equations posed on $[0,T] \times \Omega$ with $\Omega \subset \mathbb{R}^d$ without the excessive memory requirements associated…
In this work, the phase function method (PFM) is employed for the first time to explicitly construct scattering wavefunctions for the $\alpha\alpha$ system using a single-term Morse potential. Unlike earlier PFM-based studies that primarily…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
This paper is about learning the parameter-to-solution map for systems of partial differential equations (PDEs) that depend on a potentially large number of parameters covering all PDE types for which a stable variational formulation (SVF)…
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…