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The high accuracy of detector simulation is crucial for modern particle physics experiments. However, this accuracy comes with a high computational cost, which will be exacerbated by the large datasets and complex detector upgrades…

Low-precision formats have proven to be an efficient way to reduce not only the memory footprint but also the hardware resources and power consumption of deep learning computations. Under this premise, the posit numerical format appears to…

Computational complexity has been the bottleneck of applying physically-based simulations on large urban areas with high spatial resolution for efficient and systematic flooding analyses and risk assessments. To address this issue of long…

Enabling low precision implementations of deep learning models, without considerable performance degradation, is necessary in resource and latency constrained settings. Moreover, exploiting the differences in sensitivity to quantization…

Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…

As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large…

This paper develops a framework for the error analysis in nonparametric model fitting of fractional stochastic differential equations based on discrete observations. We identify and quantify the main error sources -- time discretization,…

Miscalibration - a mismatch between a model's confidence and its correctness - of Deep Neural Networks (DNNs) makes their predictions hard to rely on. Ideally, we want networks to be accurate, calibrated and confident. We show that, as…

Reliable prediction of turbulent flows is an important necessity across different fields of science and engineering. In Computational Fluid Dynamics (CFD) simulations, the most common type of models are eddy viscosity models that are…

Monte Carlo simulations of physics processes at particle colliders like the Large Hadron Collider at CERN take up a major fraction of the computational budget. For some simulations, a single data point takes seconds, minutes, or even hours…

Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking…

Learning the fine-scale details of a coastal ocean simulation from a coarse representation is a challenging task. For real-world applications, high-resolution simulations are necessary to advance understanding of many coastal processes,…

Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…

Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

Neural networks of simple structures are used to construct a turbulence model for large-eddy simulation (LES). Data obtained by direct numerical simulation (DNS) of homogeneous isotropic turbulence are used to train neural networks. It is…

This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight…

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…