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In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose…
Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…
We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical…
Bayesian Neural Networks (BNNs) that possess a property of uncertainty estimation have been increasingly adopted in a wide range of safety-critical AI applications which demand reliable and robust decision making, e.g., self-driving, rescue…
Deep neural networks (DNNs) have achieved state-of-the-art performances in many important domains, including medical diagnosis, security, and autonomous driving. In these domains where safety is highly critical, an erroneous decision can…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…
Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…
While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulation (DNS) create opportunities to leverage data-driven…
This work develops rigorous theoretical basis for the fact that deep Bayesian neural network (BNN) is an effective tool for high-dimensional variable selection with rigorous uncertainty quantification. We develop new Bayesian non-parametric…
The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…
Deep learning tools have gained tremendous attention in applied machine learning. However such tools for regression and classification do not capture model uncertainty. In comparison, Bayesian models offer a mathematically grounded…
Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions,…
This paper presents the concept of "model-based neural network"(MNN), which is inspired by the classic artificial neural network (ANN) but for different usages. Instead of being used as a data-driven classifier, a MNN serves as a modeling…
While Deep Neural Networks (DNNs) achieve state-of-the-art accuracy in various applications, they often fall short in accurately estimating their predictive uncertainty and, in turn, fail to recognize when these predictions may be wrong.…
We introduce a probabilistic robustness measure for Bayesian Neural Networks (BNNs), defined as the probability that, given a test point, there exists a point within a bounded set such that the BNN prediction differs between the two. Such a…
Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational…
Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…
Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns…