Related papers: A probabilistic reduced basis method for parameter…
We present a generative reduced basis (RB) approach to construct reduced order models for parametrized partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent…
While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…
Bayesian inference for exponential family random graph models (ERGMs) is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…
We consider the Heston model as an example of a parameterized parabolic partial differential equation. A space-time variational formulation is derived that allows for parameters in the coefficients (for calibration) as well as choosing the…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
We address the design of a model predictive control (MPC) scheme for large-scale linear systems using reduced-order models (ROMs). Our approach uses a ROM, leverages tools from robust control, and integrates them into an MPC framework to…
A ubiquitous challenge in design space exploration or uncertainty quantification of complex engineering problems is the minimization of computational cost. A useful tool to ease the burden of solving such systems is model reduction. This…
This work considers the low-rank approximation of a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$. Application areas that give rise to such problems include computational statistics and dynamical…
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
This work considers a weighted POD-greedy method to estimate statistical outputs parabolic PDE problems with parametrized random data. The key idea of weighted reduced basis methods is to weight the parameter-dependent error estimate…
We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes…
This study focuses on solving group zero-norm regularized robust loss minimization problems. We propose a proximal Majorization-Minimization (PMM) algorithm to address a class of equivalent Difference-of-Convex (DC) surrogate optimization…
Although risk awareness is fundamental to an online operating agent, it has received less attention in the challenging continuous domain and under partial observability. This paper presents a novel formulation and solution for risk-averse…
We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a…
This paper describes a revision of the classic Lazy Probabilistic Roadmaps algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut (BC) algorithm. Cuts are dynamically generated constraints that are imposed on minimum…
In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…