Related papers: High-Dimensional Stochastic Design Optimization by…
In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…
We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…
This technical note reviews sate-of-the-art algorithms for linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). While repeating several parts of our article "low-rank dynamic mode…
In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…
In this paper, we consider multi-stage stochastic optimization problems with convex objectives and conic constraints at each stage. We present a new stochastic first-order method, namely the dynamic stochastic approximation (DSA) algorithm,…
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…
Brain-inspired hyperdimensional computing (HDC) has been recently considered a promising learning approach for resource-constrained devices. However, existing approaches use static encoders that are never updated during the learning…
In this paper, we extend the adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse to the multistage stochastic programming setting. The proposed algorithms integrate the adaptive partition-based…
Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under…
We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…
Direct Statistical Simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by Direct Numerical Simulation (DNS). That low-order statistics usually…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first…
In this paper we introduce a class of novel distributed algorithms for solving stochastic big-data convex optimization problems over directed graphs. In the addressed set-up, the dimension of the decision variable can be extremely high and…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive…