Related papers: Neural Network Parametrization of Deep-Inelastic S…
Structures are abundant in both natural and human-made environments and usually studied in the form of images or scattering patterns. To characterize structures a huge variety of descriptors is available spanning from porosity to radial and…
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our…
Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nevertheless, the majority of these studies examine how well deep…
Recently developed deep learning techniques have significantly improved the accuracy of various speech and image recognition systems. In this paper we adapt some of these techniques for protein secondary structure prediction. We first train…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
We introduce the neural network approach to global fits of parton distrubution functions. First we review previous work on unbiased parametrizations of deep-inelastic structure functions with faithful estimation of their uncertainties, and…
We study the power corrections (infrared renormalon contributions) to the coefficient functions for non-singlet deep inelastic structure functions due to gluon vacuum polarization insertions in one-loop graphs. Remarkably, for all the…
A new method of calculating deep inelastic structure functions for the nucleon in independent particle models is presented. The method is applied to the bag-like model and its predictions are compared with the parametrisation of Gluck, Reya…
The primary motive of parity violating deep inelastic scattering experiments has been to test the standard model, particularly the axial couplings to the quarks, in the scaling region. The measurements can also test for the validity of…
Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…
The inference structures and computational complexity of existing deep neural networks, once trained, are fixed and remain the same for all test images. However, in practice, it is highly desirable to establish a progressive structure for…
We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when…
We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…
We discuss a hybrid model of the proton and neutron inelastic structure functions which incorporates both the partonic and the nucleon resonance structures and applicable in a wide region of the invariant mass $W$ of produced hadronic…
Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…
Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between…
For safety and robustness of AI systems, we introduce topological parallax as a theoretical and computational tool that compares a trained model to a reference dataset to determine whether they have similar multiscale geometric structure.…
We study nonparametric covariance function estimation for functional data observed with noise at discrete locations on a $d$-dimensional domain. Estimating the covariance function from discretely observed data is a challenging nonparametric…
The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary…