Related papers: Multi-variable Integration with a Neural Network

In this paper, we propose an unified hyperspectral image classification method which takes three-dimensional hyperspectral data cube as an input and produces a classification map. In the proposed method, a deep neural network which uses…

Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…

We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…

We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be…

Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…

A new initialization method for hidden parameters in a neural network is proposed. Derived from the integral representation of the neural network, a nonparametric probability distribution of hidden parameters is introduced. In this…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

We propose an approach to applying neural networks on linear parabolic variational inequalities. We use loss functions that directly incorporate the variational inequality on the whole domain to bypass the need to determine the stopping…

A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…

Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging…

Neural networks have shown great abilities in estimating depth from a single image. However, the inferred depth maps are well below one-megapixel resolution and often lack fine-grained details, which limits their practicality. Our method…

An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is…

Convolution-type integral equations arise from various fields, \textit{e.g.}, finite impulse response filters in signal processing and deblurring problems in image processing. When solving these equations, conventional numerical methods,…

We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…

We present multimodal neural posterior estimation (MultiNPE), a method to integrate heterogeneous data from different sources in simulation-based inference with neural networks. Inspired by advances in deep fusion, it allows researchers to…

We demonstrate that neural networks can be FLOP-efficient integrators of one-dimensional oscillatory integrands. We train a feed-forward neural network to compute integrals of highly oscillatory 1D functions. The training set is a…

In this paper, we present a novel data-free method for merging neural networks in weight space. Differently from most existing works, our method optimizes for the permutations of network neurons globally across all layers. This allows us to…

Deploying depth estimation networks in the real world requires high-level robustness against various adverse conditions to ensure safe and reliable autonomy. For this purpose, many autonomous vehicles employ multi-modal sensor systems,…

Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…

Multi-Focus Image Fusion seeks to improve the quality of an acquired burst of images with different focus planes. For solving the task, an activity level measurement and a fusion rule are typically established to select and fuse the most…