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Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high…

Recent innovations in x-ray technology (namely phase-based and energy-resolved imaging) offer unprecedented opportunities for material discrimination, however they are often used in isolation or in limited combinations. Here we show that…

Transfer learning has become an essential technique for utilizing information from source datasets to improve the performance of the target task. However, in the context of high-dimensional data, heterogeneity arises due to heteroscedastic…

A fundamental issue in multiscale materials modeling and design is the consideration of traction-separation behavior at the interface. By enriching the deep material network (DMN) with cohesive layers, the paper presents a novel data-driven…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

In this paper, we investigate data-driven parameterized modeling of insertion loss for transmission lines with respect to design parameters. We first show that direct application of neural networks can lead to non-physics models with…

Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…

We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…

Deep learning (DL) has shown great potential in medical image enhancement problems, such as super-resolution or image synthesis. However, to date, little consideration has been given to uncertainty quantification over the output image. Here…

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the…

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…

The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound…

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…

In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…

We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…