Related papers: Multi-variable Integration with a Neural Network

Automatic cell image segmentation methods in connectomics produce merge and split errors, which require correction through proofreading. Previous research has identified the visual search for these errors as the bottleneck in interactive…

We present a new method for blind motion deblurring that uses a neural network trained to compute estimates of sharp image patches from observations that are blurred by an unknown motion kernel. Instead of regressing directly to patch…

In this paper, we study the efficient numerical integration of functions with sharp gradients and cusps. An adaptive integration algorithm is presented that systematically improves the accuracy of the integration of a set of functions. The…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

Hyperspectral unmixing remains one of the most challenging tasks in the analysis of such data. Deep learning has been blooming in the field and proved to outperform other classic unmixing techniques, and can be effectively deployed onboard…

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…

Neural networks are known to be vulnerable to adversarial attacks, which are small, imperceptible perturbations that can significantly alter the network's output. Conversely, there may exist large, meaningful perturbations that do not…

Aerodynamic analysis during aircraft design usually involves methods of varying accuracy and spatial resolution, which all have their advantages and disadvantages. It is therefore desirable to create data-driven models which effectively…

In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…

This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…

With the increasing adoption of metal additive manufacturing (AM), researchers and practitioners are turning to data-driven approaches to optimise printing conditions. Cross-sectional images of melt tracks provide valuable information for…

The present study aims to extend the novel physics-informed machine learning approach, specifically the neural-integrated meshfree (NIM) method, to model finite-strain problems characterized by nonlinear elasticity and large deformations.…

This paper presents a novel method for autonomously enhancing deep neural network training. My approach employs an Evaluation Neural Network (ENN) trained via deep reinforcement learning to predict the performance of the target network. The…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

We suggest a general approach to quantification of different forms of aleatoric uncertainty in regression tasks performed by artificial neural networks. It is based on the simultaneous training of two neural networks with a joint loss…

Depth-adaptive neural networks can dynamically adjust depths according to the hardness of input words, and thus improve efficiency. The main challenge is how to measure such hardness and decide the required depths (i.e., layers) to conduct.…

We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…

Hyperspectral image fusion (HIF) is critical to a wide range of applications in remote sensing and many computer vision applications. Most traditional HIF methods assume that the observation model is predefined or known. However, in real…