Related papers: Input-output reduced order modeling for public hea…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven…
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…
Explicit high-order feature interactions efficiently capture essential structural knowledge about the data of interest and have been used for constructing generative models. We present a supervised discriminative High-Order Parametric…
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
For a given statistical model, it often happens that it is necessary to intervene the model to reduce the variances of the output variables. In structural equation models, this can be done by changing the values of the path coefficients by…
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…
Dynamic models have been successfully used in producing estimates of HIV epidemics at the national level due to their epidemiological nature and their ability to estimate prevalence, incidence, and mortality rates simultaneously. Recently,…
In the wake of COVID-19, every government huddles to find the best interventions that will reduce the number of infection cases while minimizing the economic impact. However, with many intervention policies available, how should one decide…
The mathematical interpretation of interventions for the mitigation of epidemics and pandemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of infections to manage impact. Whilst these…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…
Dynamic models have been successfully used in producing estimates of HIV epidemics at national level, due to their epidemiological nature and their ability to simultaneously estimate prevalence, incidence, and mortality rates. Recently, HIV…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
Off-policy Evaluation (OPE) methods are crucial tools for evaluating policies in high-stakes domains such as healthcare, where direct deployment is often infeasible, unethical, or expensive. When deployment environments are expected to…
In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative…
In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints,…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
In this work, we aim to solve data-driven optimization problems, where the goal is to find an input that maximizes an unknown score function given access to a dataset of inputs with corresponding scores. When the inputs are high-dimensional…