Related papers: Data driven recovery of local volatility surfaces
This paper deals with the problem of reconstructing a band-limited signal when a finite subset of its samples and of its derivative are missing. The technique used, due to P.J.S.G. Ferreira, is based on the use of a particular frame for…
Inverse problems involving systems of partial differential equations (PDEs) with many measurements or experiments can be very expensive to solve numerically. In a recent paper we examined dimensionality reduction methods, both stochastic…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…
We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial…
We develop a trust-region method for efficiently minimizing the sum of a smooth function, a nonsmooth convex function, and the composition of a finite-valued support function with a smooth function. Optimization problems with this structure…
Federated learning (FL), aimed at leveraging vast distributed datasets, confronts a crucial challenge: the heterogeneity of data across different silos. While previous studies have explored discrete representations to enhance model…
Partially-Observable Markov Decision Processes (POMDPs) are typically solved by finding an approximate global solution to a corresponding belief-MDP. In this paper, we offer a new planning algorithm for POMDPs with continuous state, action…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
Simulation-based Dynamic Traffic Assignment models have important applications in real-time traffic management and control. The efficacy of these systems rests on the ability to generate accurate estimates and predictions of traffic states,…
This work investigates the impact of data augmentation on confidence calibration and uncertainty estimation in Named Entity Recognition (NER) tasks. For the future advance of NER in safety-critical fields like healthcare and finance, it is…
Both the current trends in technology such as smartphones, general mobile devices, stationary sensors, and satellites as well as a new user mentality of using this technology to voluntarily share enriched location information produces a…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…
We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated…
Artificial neural networks (ANNs) are highly flexible predictive models. However, reliably quantifying uncertainty for their predictions is a continuing challenge. There has been much recent work on "recalibration" of predictive…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
Inverse design is a central goal in much of science and engineering, including frequency-selective surfaces (FSS) that are critical to microelectronics for telecommunications and optical metamaterials. Traditional surrogate-assisted…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…