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In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…

Machine Learning · Computer Science 2021-07-08 Shengli Jiang , Victor M. Zavala

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PES) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set…

This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The…

Machine Learning · Computer Science 2018-01-31 Vikram Mullachery , Aniruddh Khera , Amir Husain

Neural networks (NNs) are employed to predict equations of state from a given isotropic pair potential using the virial expansion of the pressure. The NNs are trained with data from molecular dynamics simulations of monoatomic gases and…

Soft Condensed Matter · Physics 2024-06-19 Fabian Berressem , Arash Nikoubashman

Interatomic potentials learned using machine learning methods have been successfully applied to atomistic simulations. However, accurate models require large training datasets, while generating reference calculations is computationally…

Machine Learning · Computer Science 2024-01-23 John Falk , Luigi Bonati , Pietro Novelli , Michele Parrinello , Massimiliano Pontil

The development of artificial intelligence (AI) techniques has brought revolutionary changes across various realms. In particular, the use of AI-assisted methods to accelerate chemical research has become a popular and rapidly growing…

Chemical Physics · Physics 2025-08-05 Hu Ding , Pengxiang Hua , Zhen Huang

Context: Across different domains, Artificial Neural Networks (ANNs) are used more and more in safety-critical applications in which erroneous outputs of such ANN can have catastrophic consequences. However, the development of such neural…

We propose a simple scheme to estimate potential energy surface (PES) with which the accuracy can be easily controlled and improved up to the level of the density functional theory (DFT) calculations. It is based on a model selection within…

Materials Science · Physics 2014-07-11 Atsuto Seko , Akira Takahashi , Isao Tanaka

In recent years, several studies have provided insight on the functioning of the brain which consists of neurons and form networks via interconnection among them by synapses. Neural networks are formed by interconnected systems of neurons,…

Neurons and Cognition · Quantitative Biology 2021-01-22 Martin C. Nwadiugwu

We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an…

Numerical Analysis · Mathematics 2020-04-16 Zheyan Zhang , Yongxing Wang , Peter K. Jimack , He Wang

Active learning, an iterative process of selecting the most informative data points for exploration, is crucial for efficient characterization of materials and chemicals property space. Neural networks excel at predicting these properties…

Disordered Systems and Neural Networks · Physics 2025-06-02 Sarah I. Allec , Maxim Ziatdinov

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Numerical Analysis · Mathematics 2022-08-29 Antonio Tadeu Azevedo Gomes , Larissa Miguez da Silva , Frederic Valentin

We propose a methodology for designing dependable Artificial Neural Networks (ANN) by extending the concepts of understandability, correctness, and validity that are crucial ingredients in existing certification standards. We apply the…

In chemical engineering, process data are expensive to acquire, and complex phenomena are difficult to fully model. We explore the use of physics-informed neural networks (PINNs) for modeling dynamic processes with incomplete mechanistic…

Machine Learning · Computer Science 2024-10-01 Mehmet Velioglu , Song Zhai , Sophia Rupprecht , Alexander Mitsos , Andreas Jupke , Manuel Dahmen

Convolutional neural networks (CNNs) are widely used for image recognition and text analysis, and have been suggested for application on one-dimensional data as a way to reduce the need for pre-processing steps. Pre-processing is an…

Machine Learning · Computer Science 2020-05-18 Ine L. Jernelv , Dag Roar Hjelme , Yuji Matsuura , Astrid Aksnes

A nuclear reactor based on MIT BEAVRS benchmark was used as a typical power generating Pressurized Water Reactor (PWR). The PARCS v3.2 nodal-diffusion core simulator was used as a full-core reactor physics solver to emulate the operation of…

Machine Learning · Computer Science 2023-12-15 Krzysztof Palmi , Wojciech Kubinski , Piotr Darnowski

Financing high-tech projects always entails a great deal of risk. The lack of a systematic method to pinpoint the risk of such projects has been recognized as one of the most salient barriers for evaluating them. So, in order to develop a…

Neural and Evolutionary Computing · Computer Science 2018-09-17 Hossein Sabzian , Ehsan Kamrani , Seyyed Mostafa Seyyed Hashemi

Oxide-water interfaces govern a wide range of physical and chemical processes fundamental to many fields like catalysis, geochemistry, corrosion, electrochemistry, and sensor technology. Near solid oxide surfaces, water behaves differently…

Chemical Physics · Physics 2025-10-31 Jan Elsner , K Nikolas Lausch , Jörg Behler

Dynamics of flexible molecules are often determined by an interplay between local chemical bond fluctuations and conformational changes driven by long-range electrostatics and van der Waals interactions. This interplay between interactions…

Chemical Physics · Physics 2021-03-05 Valentin Vassilev-Galindo , Gregory Fonseca , Igor Poltavsky , Alexandre Tkatchenko

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

Computational Physics · Physics 2023-07-24 Luis Medrano Navarro , Luis Martín Moreno , Sergio G Rodrigo