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A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Numerical models of complex real-world phenomena often necessitate High Performance Computing (HPC). Uncertainties increase problem dimensionality further and pose even greater challenges. We present a parallelization strategy for…
Stress and material deformation field predictions are among the most important tasks in computational mechanics. These predictions are typically made by solving the governing equations of continuum mechanics using finite element analysis,…
This paper studies the utility of techniques within uncertainty quantification, namely spectral projection and polynomial chaos expansion, in reducing sampling needs for characterizing acoustic metamaterial dispersion band responses given…
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…
Ensuring structural reliability remains a core concern in civil engineering, yet the quantitative effects of quality control measures on material variability and safety margins are not fully understood, especially for materials other than…
The distribution of quantum coherence in multipartite systems is one of the basic problems in the resource theory of coherence. While the usual coherence measures are defined on a single system and cannot capture the nonlocal correlation…
We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models…
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…
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…
This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with…
One compelling vision of the future of materials discovery and design involves the use of machine learning (ML) models to predict materials properties and then rapidly find materials tailored for specific applications. However, realizing…
Computer-driven molecular design combines the principles of chemistry, physics, and artificial intelligence to identify novel chemical compounds and materials with desired properties for a specific application. In particular,…
Motivation: Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
It is necessary to estimate the expected energy usage of a building to determine how to reduce energy usage. The expected energy usage of a building can be reliably simulated using a Building Energy Model (BEM). Many of the numerous input…
The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive…