Related papers: Learning Constitutive Relations from Indirect Obse…

Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we…

Existing procedures for model validation have been deemed inadequate for many engineering systems. The reason of this inadequacy is due to the high degree of complexity of the mechanisms that govern these systems. It is proposed in this…

Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems…

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…

The internal representations learned by deep networks are often sensitive to architecture-specific choices, raising questions about the stability, alignment, and transferability of learned structure across models. In this paper, we…

The mathematical formulation of constitutive models to describe the path-dependent, i.e., inelastic, behavior of materials is a challenging task and has been a focus in mechanics research for several decades. There have been increased…

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…

Constitutive relations close the balance laws of continuum mechanics and serves as the surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

This paper presents a deep learning based model predictive control algorithm for control affine nonlinear discrete time systems with matched and bounded state-dependent uncertainties of unknown structure. Since the structure of…

We leverage probabilistic models of neural representations to investigate how residual networks fit classes. To this end, we estimate class-conditional density models for representations learned by deep ResNets. We then use these models to…

Precise estimation of predictive uncertainty in deep neural networks is a critical requirement for reliable decision-making in machine learning and statistical modeling, particularly in the context of medical AI. Conformal Prediction (CP)…

Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…

Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images.…

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional…

Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…