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Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…

This paper studies the numerical analysis of a parameter identification problem governed by elliptic equations with power-type nonlinearity. We propose a numerical reconstruction via a suitable least-squares minimization problem based on…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…

Heterogeneity is an unwanted variation when analyzing aggregated datasets from multiple sources. Though different methods have been proposed for heterogeneity adjustment, no systematic theory exists to justify these methods. In this work,…

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Accurately calibrating light field camera is essential to its applications. Rapid progress has been made in this area in the past decades. In this paper, detailed analysis was first performed towards the state of the art projection models…

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…

In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…

We introduce a reinforcement learning (RL) based adaptive optimization algorithm for aerodynamic shape optimization focused on dimensionality reduction. The form in which RL is applied here is that of a surrogate-based, actor-critic policy…

The core challenge in applying abstract interpretation lies in the configuration of abstraction and analysis strategies encoded by a large number of external parameters of static analysis tools. To attain low false-positive rates (i.e.,…

Currently, machine learning (ML) methods are widely used to process the results of physical experiments. In some cases, due to the limited amount of experimental data, ML-models can be pre-trained on synthetic data simulated based on the…

Standard methods of data assimilation assume prior knowledge of a model that describes the system dynamics and an observation function that maps the model state to a predicted output. An accurate mapping from model state to observation…

Machine learning models commonly exhibit unexpected failures post-deployment due to either data shifts or uncommon situations in the training environment. Domain experts typically go through the tedious process of inspecting the failure…

State estimates from weak constraint 4D-Var data assimilation can vary significantly depending on the data and model error covariances. As a result, the accuracy of these estimates heavily depends on the correct specification of both model…

Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…

We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many…

A goodness-of-fit test for the fitting of a parametric model to data obtained from a detector with finite resolution and limited acceptance is proposed. The parameters of the model are found by minimization of a statistic that is used for…

We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…