Related papers: Time-adaptive optimization in a parameter identifi…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
In this paper, we construct a model to describe the transmission of HIV in a homogeneous host population. By considering the specific mechanism of HIV, we derive a model structured in three successive stages: (i) primary infection, (ii)…
For time-to-event data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the cause-specific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541--554]. This article studies…
Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…
Strategic test allocation plays a major role in the control of both emerging and existing pandemics (e.g., COVID-19, HIV). Widespread testing supports effective epidemic control by (1) reducing transmission via identifying cases, and (2)…
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference…
This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…
For complex, high-dimensional Markov Decision Processes (MDPs), it may be necessary to represent the policy with function approximation. A problem is misspecified whenever, the representation cannot express any policy with acceptable…
Identification of biomarkers is an emerging area in Oncology. In this article, we develop an efficient statistical procedure for classification of protein markers according to their effect on cancer progression. A high-dimensional…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
HIV/AIDs Regimen specification one of many problems for which bioinformaticians have implemented and trained machine learning methods such as neural networks. Predicting HIV resistance would be much easier, but unfortunately we rarely have…
In this letter, we propose a model parameter identification method via a hyperparameter optimization scheme (MI-HPO). Our method adopts an efficient explore-exploit strategy to identify the parameters of dynamic models in a data-driven…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
Over the last ten years, Patient-Derived Organoids (PDOs) emerged as the most reliable technology to generate ex-vivo tumor avatars. PDOs retain the main characteristics of their original tumor, making them a system of choice for…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
This paper addresses the properties of Continuous Interior Penalty (CIP) finite element solutions for the Helmholtz equation. The $h$-version of the CIP finite element method with piecewise linear approximation is applied to a…
In vaccine development, the temporal profiles of relative abundance of subtypes of immune cells (T-cells) is key to understanding vaccine efficacy. Complex and expensive experimental studies generate very sparse time series data on this…
Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment…
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic…
We consider an adaptive finite element method with arbitrary but fixed polynomial degree $p \ge 1$, where adaptivity is driven by an edge-based residual error estimator. Based on the modified maximum criterion from [Diening et al, Found.…