Related papers: Numerical Algorithmic Science and Engineering with…
Neural Architecture Search (NAS) is a research field concerned with utilizing optimization algorithms to design optimal neural network architectures. There are many approaches concerning the architectural search spaces, optimization…
As a comprehensive indicator of mathematical thinking and intelligence, the number sense (Dehaene 2011) bridges the induction of symbolic concepts and the competence of problem-solving. To endow such a crucial cognitive ability to machine…
Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a…
Recent advances in artificial intelligence (AI) and quantum computing are accelerating automation in scientific and engineering processes, fundamentally reshaping research methodologies. This perspective highlights parallels between…
Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…
Binary Convolutional Neural Networks (CNNs) have significantly reduced the number of arithmetic operations and the size of memory storage needed for CNNs, which makes their deployment on mobile and embedded systems more feasible. However,…
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not…
Research and development in computer technology and computational methods have resulted in a wide variety of valuable tools for Computer-Aided Engineering (CAE) and Industrial Engineering. However, despite the exponential increase in…
Deep neural networks are increasingly utilized in various machine learning tasks. However, as these models grow in complexity, they often face calibration issues, despite enhanced prediction accuracy. Many studies have endeavored to improve…
The traditional foundation of science lies on the cornerstones of theory and experiment. Theory is used to explain experiment, which in turn guides the development of theory. Since the advent of computers and the development of…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…
The success of deep learning in recent years has lead to a rising demand for neural network architecture engineering. As a consequence, neural architecture search (NAS), which aims at automatically designing neural network architectures in…
Quantum computing is rapidly emerging as a new computing paradigm with the potential to improve decision-making, optimization, and simulation across industries. For industrial engineering (IE) and operations research (OR), this shift…
Neural Architecture Search (NAS) has emerged as a favoured method for unearthing effective neural architectures. Recent development of large models has intensified the demand for faster search speeds and more accurate search results.…
A large number of engineering, science and computational problems have yet to be solved in a computationally efficient way. One of the emerging challenges is how evolving technologies grow towards autonomy and intelligent decision making.…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Traditionally, numerical algorithms are seen as isolated pieces of code confined to an {\em in silico} existence. However, this perspective is not appropriate for many modern computational approaches in control, learning, or optimization,…