Related papers: Efficient Distribution Estimation and Uncertainty …
Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…
Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…
While recent computer vision algorithms achieve impressive performance on many benchmarks, they lack robustness - presented with an image from a different distribution, (e.g. weather or lighting conditions not considered during training),…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
Scientific machine learning has become an increasingly important tool in materials science and engineering. It is particularly well suited to tackle material problems involving many variables or to allow rapid construction of surrogates of…
We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
This paper is concerned with the derivation of computable and guaranteed upper bounds of the difference between the exact and the approximate solution of an exterior domain boundary value problem for a linear elliptic equation. Our analysis…
We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters.…
We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…
Estimators of parameters of truncated distributions, namely the truncated normal distribution, have been widely studied for a known truncation region. There is also literature for estimating the unknown bounds for known parent…
We investigate the realization of a myriad of general local and nonlocal inhomogeneous elliptic and parabolic boundary value problems over classes of irregular regions. We present a unified approach in which either local or nonlocal…
We consider an elliptic partial differential equation in non-divergence form with a random diffusion matrix and random forcing term. To address this, we propose a mixed-type continuous finite element discretization in the physical domain,…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…
Quantifying aleatoric uncertainty in medical image segmentation is critical since it is a reflection of the natural variability observed among expert annotators. A conventional approach is to model the segmentation distribution using the…