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Skip connection, is a widely-used technique to improve the performance and the convergence of deep neural networks, which is believed to relieve the difficulty in optimization due to non-linearity by propagating a linear component through…
With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying…
Steerable convolutional neural networks (SCNNs) enhance task performance by modelling geometric symmetries through equivariance constraints on weights. Yet, unknown or varying symmetries can lead to overconstrained weights and decreased…
Operator learning is a recently developed generalization of regression to mappings between functions. It promises to drastically reduce expensive numerical integration of PDEs to fast evaluations of mappings between functional states of a…
Quantifying uncertainty is crucial for robust and reliable predictions. However, existing spatiotemporal deep learning mostly focuses on deterministic prediction, overlooking the inherent uncertainty in such prediction. Particularly,…
Treating uncertainties in models is essential in many fields of science and engineering. Uncertainty quantification (UQ) on complex and computationally costly numerical models necessitates a combination of efficient model solvers, advanced…
Unsupervised anomaly detection is often framed around two widely studied paradigms. Deep one-class classification, exemplified by Deep SVDD, learns compact latent representations of normality, while density estimators realized by…
We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call \emph{Optimal Uncertainty Quantification} (OUQ),…
Training deep Convolutional Neural Networks (CNNs) presents unique challenges, including the pervasive issue of elimination singularities, consistent deactivation of nodes leading to degenerate manifolds within the loss landscape. These…
Robustness studies of black-box models is recognized as a necessary task for numerical models based on structural equations and predictive models learned from data. These studies must assess the model's robustness to possible…
Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…
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)…
Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An…
Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…
As neural networks have begun performing increasingly critical tasks for society, ranging from driving cars to identifying candidates for drug development, the value of their ability to perform uncertainty quantification (UQ) in their…
In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes…
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…
Conformal prediction (CP), a distribution-free uncertainty quantification (UQ) framework, reliably provides valid predictive inference for black-box models. CP constructs prediction sets that contain the true output with a specified…
For regression tasks, standard Gaussian processes (GPs) provide natural uncertainty quantification (UQ), while deep neural networks (DNNs) excel at representation learning. Deterministic UQ methods for neural networks have successfully…
Stochasticity plays a significant role in the low-power operation of a biological neural network. In an artificial neural network (ANN), stochasticity also contributes to critical functions such as the uncertainty quantification (UQ) for…