相关论文: Mesh refinement for uncertainty quantification thr…

The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Despite apparent human-level performances of deep neural networks (DNN), they behave fundamentally differently from humans. They easily change predictions when small corruptions such as blur and noise are applied on the input (lack of…

Applying Bayesian optimization in problems wherein the search space is unknown is challenging. To address this problem, we propose a systematic volume expansion strategy for the Bayesian optimization. We devise a strategy to guarantee that…

The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…

Numerical simulation of the complex plasma dynamics associated with high power, high frequency microwave breakdown at high pressures, leading to the formation of filamentary plasma structures such as self-organized plasma arrays, is a…

Trimmed (multi-patch) geometries are the state-of-the-art technology in computer-aided design for industrial applications such as automobile crashworthiness. In this context, fast solution techniques extensively rely on explicit time…

Recurrent neural networks have proven effective in modeling sequential user feedbacks for recommender systems. However, they usually focus solely on item relevance and fail to effectively explore diverse items for users, therefore harming…

We show that the effectiveness of the well celebrated Mixup [Zhang et al., 2018] can be further improved if instead of using it as the sole learning objective, it is utilized as an additional regularizer to the standard cross-entropy loss.…

In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

In many applications (in particular information systems, such as pattern recognition, machine learning, cheminformatics, bioinformatics to name but a few) the assessment of uncertainty is essential - i.e., the estimation of the underlying…

The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…

We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing…

Bayesian inference in function space has gained attention due to its robustness against overparameterization in neural networks. However, approximating the infinite-dimensional function space introduces several challenges. In this work, we…

Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is that linear trends -- and in general polynomial trends -- in…

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the…