Related papers: A Time-parallel Approach to Strong-constraint Four…
In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve the targeted {\bf QP} problems to a desired…
Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
We present an efficient computational framework to quantify the impact of individual observations in four dimensional variational data assimilation. The proposed methodology uses first and second order adjoint sensitivity analysis, together…
A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in Wibisono et al. (2016) and Duruisseaux and Leok (2021). It was observed that a careful combination of…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
We identify a strong equivalence between neural network based machine learning (ML) methods and the formulation of statistical data assimilation (DA), known to be a problem in statistical physics. DA, as used widely in physical and…
The integration of observational data into numerical models, known as data assimilation (DA), is fundamental for making Numerical Weather Prediction (NWP) possible, with breathtaking success over the past 60 years (Bauer et al. 2015).…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
Recent studies have demonstrated that it is possible to combine machine learning with data assimilation to reconstruct the dynamics of a physical model partially and imperfectly observed. Data assimilation is used to estimate the system…
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…
Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional…
Constrained blackbox optimization is a difficult problem, with most approaches coming from the mathematical programming literature. The statistical literature is sparse, especially in addressing problems with nontrivial constraints. This…
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refinement and synchronization techniques and is motivated by…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
This paper focuses on integrating the networks and adversarial training into constrained optimization problems to develop a framework algorithm for constrained optimization problems. For such problems, we first transform them into minimax…
This paper considers large scale constrained convex (possibly composite and non-separable) programs, which are usually difficult to solve by interior point methods or other Newton-type methods due to the non-smoothness or the prohibitive…
In this paper, we design, analyze and implement efficient time parallel method for a class of fourth order time-dependent partial differential equations (PDEs), namely biharmonic heat equation, linearized Cahn-Hilliard (CH) equation and the…