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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…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Because of their excellent asymptotic and finite-length performance, spatially-coupled (SC) codes are a class of low-density parity-check codes that is gaining increasing attention. Multi-dimensional (MD) SC codes are constructed by…
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
In this paper, we present a sequential sampling-based algorithm for the two-stage distributionally robust linear programming (2-DRLP) models. The 2-DRLP models are defined over a general class of ambiguity sets with discrete or continuous…
Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as…
We present a robust and flexible optimization approach for dynamic mode decomposition analysis of data with complex dynamics and low signal-to-noise ratios. The approach borrows techniques and insights from the field of deep learning.…
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the…
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…
The efficient generation of meshes is an important component in the numerical solution of problems in physics and engineering. Of interest are situations where global mesh quality and a tight coupling to the solution of the physical partial…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…
This paper presents a method of data-driven parametric Dynamic Mode Decomposition (p-DMD) to derive a linear parameter-varying reduced-order model (LPV-ROM) for the nonlinear aeroelasticity of highly flexible aircraft. It directly uses the…
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…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…