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Design decisions for integrating Prescriptive Analytics Use Cases into Smart Factories

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Procedia CIRP 2024年 128卷 424-429页

作者： Julian Weller Nico Migenda Sebastian von Enzberg Martin Kohlhase Wolfram Schenck Roman Dumitrescu Fraunhofer Institute for Mechatronic Systems Design Zukunftsmeile 1 33102 Paderborn Germany Center for Applied Data Science Gütersloh Faculty of Engineering and Mathematics Bielefeld University of Applied Sciences and Arts Schulstraße 10 33330 Gütersloh Germany Chair for Advanced Systems Engineering Heinz Nixdorf Institute Fürstenallee 11 33102 Paderborn Germany

The emerging trend of Prescriptive Analytics tries to prescribe actionable decisions. The goal is to help production experts in automating their decisions in the factory. Decision making processes in factories mostly rely on experts inside the company. Current trends such as demographic shifts and shortages of skilled personnel are challenging organizations to find ways to become less dependent on the ad hoc availability of expert knowledge through digitalization and data analytics. Existing data analytics approaches for smart factories usually focus on description, diagnosis, and prediction. An approach to differentiate between different application areas of Prescriptive Analytics in a smart factory is presented. Focus areas for a useful application and integration of Prescriptive Analytics are derived. Based on these applications, design principles are constructed. They help decision makers to select future lighthouse use cases for development and help smart factory advocates to strategically decide which prescriptive analytics approaches to highlight. The resulting design principles are based on a literature review and validated in a workshop with experts from research. Approaches are differentiated and key characteristics for future Use Case design decisions are derived.

关键词： Prescriptive Analytics Smart Factory Design methodology tools technologies

Enhancing the Swanepoel method: precise envelope detection of thin-film transmission spectra

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Optics Express 2025年第6期33卷 13376-13400页

作者： Ballester, Manuel Marquez, Almudena P. Lopez-Tapia, Santiago Fernandez, Susana Bass, John Minkov, Dorian Wuersch, Christoph Willomitzer, Florian Marquez, Emilio Katsaggelos, Aggelos K. Computer Science Department Northwestern University EvanstonIL60208 United States Department of Mathematics Faculty of Science University of Cadiz Puerto Real11510 Spain Department of Electrical and Computer Engineering Northwestern University EvanstonIL60208 United States CIEMAT Avenida Complutense 40 Madrid28040 Spain Wyant College of Optical Sciences University of Arizona TucsonAZ85721 United States Sofia1000 Bulgaria Institute for Computational Engineering ICE OST Eastern Switzerland University of Applied Sciences Switzerland Department of Condensed-matter Physics Faculty of Science University of Cadiz Puerto Real11510 Spain

The Swanepoel method is a widely used optical technique for characterizing thin films through normal-incidence transmission measurements. A critical step in this approach involves extracting the upper and lower envelopes of the measured oscillatory spectrum. By analyzing the transmission spectrum and its corresponding envelopes, the Swanepoel procedure enables precise determination of the film refractive index and extinction coefficient. However, even minor inaccuracies in envelope construction can propagate significant errors into the final characterization results. To address this challenge, we present what we believe to be a novel physics-informed optimization algorithm for envelope detection. Our mathematical model reformulates the envelope detection problem as a global optimization task that enforces the physical properties of the Swanepoel envelopes. Extensive validation on fifty randomly generated transmission spectra demonstrates unprecedented accuracy: the method achieves root-mean-square errors (RMSE) below 0.10% for the upper envelope and 0.06% for the lower envelope (more than doubling the accuracy of current state-of-the-art approaches). Furthermore, the proposed model has been assessed with two experimental transmission spectra, demonstrating its robustness and accuracy with real noisy data. We have developed an open-source Python software package (see text below). This software includes not only our innovative envelope construction algorithm but also additional envelope drawing algorithms for comparison and an efficient implementation of the Swanepoel method, enabling complete optical characterization of thin films. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

关键词： Mean square error

Novel Analysis of Two Kinds Hybrid Models in Ferro Martial Inserting Variable Lorentz Force Past a Heated Disk:An Implementation of Finite Element Method

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Computer Modeling in Engineering & sciences 2023年第5期135卷 1393-1411页

作者： Enran Hou Umar Nazir Samaira Naz Muhammad Sohail Muhammad Nadeem Jung Rye Lee Choonkil Park Ahmed MGalal College of Mathematics Huaibei Normal UniversityHuaibei235000China Department of Applied Mathematics and Statistics Institute of Space TechnologyP.O.Box 2750Islamabad44000Pakistan Department of Mathematics Government College University FaisalabadFaisalabad38000Pakistan Department of Mathematics Khwaja Fareed University of Engineering&Information TechnologyRahim Yar Khan64200Pakistan School of Mathematics and Statistics Qujing Normal UniersityQujing655011China Department of Data Science Daejin UniversityKyunggi11159Korea Research Institute for Natural Sciences Hanyang UniversitySeoul04763Korea Mechanical Engineering Department College of EngineeringPrince Sattam Bin Abdulaziz UniversityWadi Addawaser11991Saudi Arabia Production Engineering and Mechanical Design Department Faculty of EngineeringMansoura UniversityMansouraP.O 35516Egypt

In this article,the rheology of Ferro-fluid over an axisymmetric heated disc with a variable magnetic field by considering the dispersion of hybrid nanoparticles is *** flow is assumed to be produced by the stretching of a rotating heated *** contribution of variable thermophysical properties is taken to explore themomentum,mass and thermal *** concept of boundary layermechanismis engaged to reduce the complex problem into a simpler one in the form of coupled partial differential equations *** complex coupled PDEs are converted into highly nonlinear coupled ordinary differential equations system(ODEs)and the resulting nonlinear flow problem is handled *** solution is obtained via finite element procedure(FEP)and convergence is established by conducting the grid-independent *** solution of converted dimensionless problem containing fluid velocity,temperature and concentration field is plotted against numerous involved emerging parameters and their impact is *** the obtained solution,it is monitored that higher values of magnetic parameter retard the fluid flow and escalating values of Eckert number results in to enhance temperature ***-fluid flow and heat energy for the case of the Yamada Ota hybrid model are higher than for the case of the Hamilton Crosser hybrid *** a model is applicable to the printing process,electronic devices,temperature measurements,engineering process and food-making *** amount of mass species is reduced *** impacts of chemical reaction and Schmidt parameter.

关键词： Ferro-fluid non-constant magnetic field heated disc thermal properties of nanoparticles hybrid correlations among nanoparticles

Optimal testing using combined test statistics across independent studies

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arXiv 2023年

作者： Szabó, Botond van der Vaart, Aad Vuursteen, Lasse van Zanten, Harry Delft Institute of Applied Mathematics Delft University of Technology Netherlands Department of Decision Sciences Institute for Data Science and Analytics Bocconi University Italy Mathematics Department Vrije Universiteit Amsterdam Netherlands

Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the combined test, especially in high-dimensional models considering composite hypotheses tests. We derive a mathematical framework to study standard meta-analysis testing approaches in the context of the many normal means model, which serves as the platform to investigate more complex models. We introduce a natural and mild restriction on the meta-level combination functions of the local trials. This allows us to mathematically quantify the cost of compressing m trials into real-valued test statistics and combining these. We then derive minimax lower and matching upper bounds for the separation rates of standard combination methods for e.g. p-values and e-values, quantifying the loss relative to using the full, pooled data. We observe an elbow effect, revealing that in certain cases combining the locally optimal tests in each trial results in a sub-optimal meta-analysis method and develop approaches to achieve the global optima. We also explore the possible gains of allowing limited coordination between the trial designs. Our results connect meta-analysis with bandwidth constraint distributed inference and build on recent information theoretic developments in the latter *** Codes 62B10, 62C20, 62F30, 62F03 © 2023, CC BY.

关键词： Statistics

Spatial Second-Order Positive and Asymptotic Preserving Filtered Pn Schemes for Nonlinear Radiative Transfer Equations

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SSRN

SSRN 2023年

作者： Xu, Xiaojing Jiang, Song Sun, Wenjun School of Mathematics and Physics Southwest University of Science and Technology Sichuan Mianyang621010 China Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China

A spatial second-order scheme for the nonlinear radiative transfer equations is in-troduced in this paper. The discretization scheme is based on the filtered sphericalharmonics (FPN ) method for the angular variable and the unified gas kinetic scheme(UGKS) framework for the spatial and temporal variables respectively. In order tokeep the scheme positive and second-order accuracy, firstly, we use the implicit MonteCarlo (IMC) linearization method [6] in the construction of the UGKS numericalboundary fluxes. This is an essential point in the construction. Then, by carefullyanalyzing the constructed second-order fluxes involved in the macro-micro decomposition, which is induced by the FPN angular discretization, we establish the sufficient conditions that guarantee the positivity of the radiative energy density and material temperature. Finally, we employ linear scaling limiters for the angular variable in the PN reconstruction and for the spatial variable in the piecewise linear slopes re-construction respectively, which are shown to be realizable and reasonable to enforcethe sufficient conditions holding. Thus, the desired scheme, called the PPFPN-basedUGKS, is obtained. Furthermore, we can show that in the regime Ε«1 and theregime Ε=O(1), the second-order fluxes can be simplified. And, a simplified spatial second-order scheme, called the PPFPN-based SUGKS, is thus presented, whichpossesses all the properties of the non-simplified one. Inheriting the merit of UGKS,the proposed schemes are asymptotic preserving. By employing the FP N method forthe angular variable, the proposed schemes are almost free of ray effects. Moreover,the above-mentioned way of imposing the positivity would not destroy both AP andsecond-order accuracy properties. To our best knowledge, this is the first time thatspatial second-order, positive, asymptotic preserving and almost free of ray effectsschemes are constructed for the nonlinear radiative transfer equations without oper-ator splitting.

关键词： Radiative transfer

Hardware Acceleration for HPS Algorithms in Two and Three Dimensions

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arXiv 2025年

作者： Melia, Owen Fortunato, Daniel Hoskins, Jeremy Willett, Rebecca Department of Computer Science University of Chicago United States Center for Computational Mathematics Flatiron Institute United States Center for Computational Biology Flatiron Institute United States Data Science Institute University of Chicago United States Computational and Applied Mathematics Department of Statistics University of Chicago United States

We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré–Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU;in three dimensions, we modify and extend the adaptive discretization technique of Geldermans and Gillman [2019] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems. © 2025, CC BY.

关键词： Graphics processing unit

Convergence rates for the Adam optimizer

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arXiv 2024年

作者： Dereich, Steffen Jentzen, Arnulf Institute for Mathematical Stochastics University of Münster Germany School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen [CUHK-Shenzhen China Applied Mathematics: Institute for Analysis and Numerics University of Münster Germany

Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain vanilla standard SGD method is the employed optimization scheme but instead suitably accelerated and adaptive SGD optimization methods are applied. As of today, maybe the most popular variant of such accelerated and adaptive SGD optimization methods is the famous Adam optimizer proposed by Kingma & Ba in 2014. Despite the popularity of the Adam optimizer in implementations, it remained an open problem of research to provide a convergence analysis for the Adam optimizer even in the situation of simple quadratic stochastic optimization problems where the objective function (the function one intends to minimize) is strongly convex. In this work we solve this problem by establishing optimal convergence rates for the Adam optimizer for a large class of stochastic optimization problems, in particular, covering simple quadratic stochastic optimization problems. The key ingredient of our convergence analysis is a new vector field function which we propose to refer to as the Adam vector field. This Adam vector field accurately describes the macroscopic behaviour of the Adam optimization process but differs from the negative gradient of the objective function (the function we intend to minimize) of the considered stochastic optimization problem. In particular, our convergence analysis reveals that the Adam optimizer does typically not converge to critical points of the objective function (zeros of the gradient of the objective function) of the considered optimization problem but converges with rates to zeros of this Adam vector field. Even though our convergence results are only formulated for the Adam optimizer, the arguments in our convergence analysis can also be applied to other related SGD optimization methods and open the door for a sys

关键词： Vectors

Learning rate adaptive stochastic gradient descent optimization methods: numerical simulations for deep learning methods for partial differential equations and convergence analyses

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arXiv 2024年

作者： Dereich, Steffen Jentzen, Arnulf Riekert, Adrian Institute for Mathematical Stochastics University of Münster Germany School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong CUHK-Shenzhen Shenzhen China Applied Mathematics Institute for Analysis and Numerics University of Münster Germany

It is known that the plain vanilla standard stochastic gradient descent (SGD) optimization method, accelerated SGD methods such as the momentum SGD optimization method, adaptive SGD methods such the Adagrad and the RMSprop optimization methods, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as, for example, in the situation of constant learning rates). In numerical simulations SGD optimization methods are sometimes applied with learning rate schedules that are determined through human based tuning procedures and are also sometimes applied with small but constant learning rates. In standard machine learning implementation frameworks such as TensorFlow and Pytorch the default learning rate schedules for SGD optimization methods are constant learning rates. In this work we propose and study a learning-rate-adaptive approach for SGD optimization methods in which the learning rate is adjusted based on empirical estimates for the values of the objective function of the optimization problem (the function that one intends to minimize in the considered optimization problem). In particular, we propose a learning-rate-adaptive variant of the Adam optimizer and implement it in Pytorch in case of several neural network learning problems, particularly, in the context of deep learning approximation methods for partial differential equations (PDEs) such as deep Kolmogorov methods (DKMs), physics-informed neural networks (PINNs), and deep Ritz methods (DRMs). In each of the presented learning problems the proposed learning-rate-adaptive variant of the Adam optimizer faster reduces the value of the objective function than the Adam optimizer with the default learning rate. For a simple class of quadratic minimization problems we also rigorously prove that a learning-rate-adaptive variant of the SGD optimization method converges to the minimizer of the considered minimization proble

关键词： Partial differential equations

Unlocking Historical Clinical Trial data with ALIGN: A Compositional Large Language Model System for Medical Coding

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arXiv 2024年

作者： Seedat, Nabeel Tozzi, Caterina Ardiaca, Andrea Hita van der Schaar, Mihaela Weatherall, James Taylor, Adam Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Data Science & Artificial Intelligence BioPharmaceuticals R&D AstraZeneca Barcelona Spain Data Science & Artificial Intelligence BioPharmaceuticals R&D AstraZeneca Cambridge United Kingdom

Background: The reuse of historical clinical trial data has significant potential to accelerate medical research and drug development. However, interoperability challenges, particularly with missing medical codes, hinder effective data integration across studies. While Large Language Models (LLMs) offer a promising solution for automated coding without labeled data, current approaches face challenges on complex coding tasks. Methods: We introduce ALIGN, a novel compositional LLM-based system (i.e. compound AI system) for automated, zero-shot medical coding. ALIGN follows a three-step process: (1) diverse candidate code generation;(2) self-evaluation of codes and (3) confidence scoring and uncertainty estimation enabling human deferral to ensure reliability. We evaluate ALIGN on harmonizing medication terms into Anatomical Therapeutic Chemical (ATC) and medical history terms into Medical Dictionary for Regulatory Activities (MedDRA) codes extracted from 22 immunology trials (10 rheumatoid arthritis, 12 systemic lupus erythematosus) and compare to LLM baselines, including prompting and Retrieval Augmented Generation (RAG). Results: ALIGN outperformed the LLM baselines, while also providing capabilities for trustworthy deployment. For MedDRA coding, ALIGN achieved high accuracy across all levels, matching RAG and excelling at the most specific levels (87-90% for HLGT). For ATC coding, ALIGN demonstrated superior performance, particularly at lower hierarchy levels (ATC Level 4), with 72-73% overall accuracy and 86-89% accuracy for common medications, outperforming baselines by 7-22%. ALIGN's uncertainty-based deferral improved accuracy by 17% to ±90% accuracy with 30% deferral, notably enhancing performance on uncommon medications. ALIGN achieves this cost-efficiently at $0.0007 and $0.02 per code for GPT-4omini and GPT-4o, reducing barriers to clinical adoption. Conclusion: ALIGN advances automated medical coding for clinical trial data, contributing to enhanced data i

关键词： Clinical research