Related papers: A general framework for knowledge integration in m…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…

Nonlinear electromagnetic (EM) inverse scattering is a quantitative and super-resolution imaging technique, in which more realistic interactions between the internal structure of scene and EM wavefield are taken into account in the imaging…

Recent work showed that hybrid networks, which combine predefined and learnt filters within a single architecture, are more amenable to theoretical analysis and less prone to overfitting in data-limited scenarios. However, their performance…

We introduce a Bayesian protocol based on artificial neural networks that is suitable for modeling inclusive electron-nucleus scattering on a variety of nuclear targets with quantified uncertainties. Unlike previous applications in the…

Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized…

The rapid scaling of deep neural networks comes at the cost of unsustainable power consumption. While optical neural networks offer an alternative, their capabilities remain constrained by the lack of efficient optical nonlinearities. To…

The study of structure-spectrum relationships is essential for spectral interpretation, impacting structural elucidation and material design. Predicting spectra from molecular structures is challenging due to their complex relationships.…

This paper introduces an innovative physics-informed deep learning framework for metamodeling of nonlinear structural systems with scarce data. The basic concept is to incorporate physics knowledge (e.g., laws of physics, scientific…

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.…

Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…

Electromagnetic inverse scattering problems (ISPs) aim to retrieve permittivities of dielectric scatterers from the scattering measurement. It is often highly nonlinear, caus-ing the problem to be very difficult to solve. To alleviate the…

Due to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This so-called phase…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

Neural networks (NNs) lack measures of "reliability" estimation that would enable reasoning over their predictions. Despite the vital importance, especially in areas of human well-being and health, state-of-the-art uncertainty estimation…

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…