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Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an…

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…

This work studies Semantic Scene Completion which aims to predict a 3D semantic segmentation of our surroundings, even though some areas are occluded. For this we construct a Bayesian Convolutional Neural Network (BCNN), which is not only…

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in…

In this paper, we introduce BNN-DP, an efficient algorithmic framework for analysis of adversarial robustness of Bayesian Neural Networks (BNNs). Given a compact set of input points $T\subset \mathbb{R}^n$, BNN-DP computes lower and upper…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

Despite the remarkable performance, Deep Neural Networks (DNNs) behave as black-boxes hindering user trust in Artificial Intelligence (AI) systems. Research on opening black-box DNN can be broadly categorized into post-hoc methods and…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We study probabilistic safety for Bayesian Neural Networks (BNNs) under adversarial input perturbations. Given a compact set of input points, $T \subseteq \mathbb{R}^m$, we study the probability w.r.t. the BNN posterior that all the points…

Although deep neural networks have demonstrated significant success due to their powerful expressiveness, most models struggle to meet practical requirements for uncertainty estimation. Concurrently, the entangled nature of deep neural…

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data…

Bayesian Optimization (BO) is an effective approach for global optimization of black-box functions when function evaluations are expensive. Most prior works use Gaussian processes to model the black-box function, however, the use of kernels…

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…

Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…

Accurately detecting crack boundaries is crucial for reliability assessment and risk management of structures and materials, such as structural health monitoring, diagnostics, prognostics, and maintenance scheduling. Uncertainty…

While there has been progress in developing non-vacuous generalization bounds for deep neural networks, these bounds tend to be uninformative about why deep learning works. In this paper, we develop a compression approach based on…

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions.…

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often…