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Learning solutions of parametric Navier-Stokes with physics-informed neural networks

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arXiv 2024年

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs’ limitations in converging to solutions of highly nonlinear parametric-PDEs like NSE. We consider the parameter(s) of interest as inputs of PINNs along with spatio-temporal coordinates, and train PINNs on generated numerical solutions of parametric-PDES for instances of the parameters. We perform experiments on the classical 2D flow past cylinder problem aiming to learn velocities and pressure functions over a range of Reynolds numbers as parameter of interest. Provision of training data from generated numerical simulations allows for interpolation of the solution functions for a range of parameters. Therefore, we compare PINNs with unconstrained conventional Neural Networks (NN) on this problem setup to investigate the effectiveness of considering the PDEs regularization in the loss function. We show that our proposed approach results in optimizing PINN models that learn the solution functions while making sure that flow predictions are in line with conservational laws of mass and momentum. Our results show that PINN results in accurate prediction of gradients compared to NN model, this is clearly visible in predicted vorticity fields given that none of these models were trained on vorticity labels. © 2024, CC BY.

关键词： Navier Stokes equations

iPINNs: Incremental learning for Physics-informed neural networks

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arXiv 2023年

作者： Dekhovich, Aleksandr Sluiter, Marcel H.F. Tax, David M.J. Bessa, Miguel A. Department of Materials Science and Engineering Delft University of Technology Mekelweg 2 Delft2628 CD Netherlands Pattern Recognition and Bioinformatics Laboratory Delft University of Technology Van Mourik Broekmanweg 6 Delft2628 XE Netherlands School of Engineering Brown University 184 Hope St. ProvidenceRI02912 United States

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, there is no incremental training procedure for PINNs that can effectively mitigate such training challenges. We propose incremental PINNs (iPINNs) that can learn multiple tasks (equations) sequentially without additional parameters for new tasks and improve performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE);and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction-diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field. © 2023, CC BY.

关键词： Complex networks

Inductive Conformal Prediction under Data Scarcity: Exploring the Impacts of Nonconformity Measures

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arXiv 2024年

作者： Kato, Yuko Tax, David M.J. Loog, Marco Pattern Recognition and Bio-informatics Group Delft University of Technology Van Mourik Broekmanweg 6 Delft2628 XE Netherlands Institute for Computing and Information Sciences Radboud University Toernooiveld 212 Nijmegen6525 EC Netherlands

Conformal prediction, which makes no distributional assumptions about the data, has emerged as a powerful and reliable approach to uncertainty quantification in practical applications. The nonconformity measure used in conformal prediction quantifies how a test sample differs from the training data and the effectiveness of a conformal prediction interval may depend heavily on the precise measure employed. The impact of this choice has, however, not been widely explored, especially when dealing with limited amounts of data. The primary objective of this study is to evaluate the performance of various nonconformity measures (absolute error-based, normalized absolute error-based, and quantile-based measures) in terms of validity and efficiency when used in inductive conformal prediction. The focus is on small datasets, which is still a common setting in many real-world applications. Using synthetic and real-world data, we assess how different characteristics—such as dataset size, noise, and dimensionality—can affect the efficiency of conformal prediction intervals. Our results show that although there are differences, no single nonconformity measure consistently outperforms the others, as the effectiveness of each nonconformity measure is heavily influenced by the specific nature of the data. Additionally, we found that increasing dataset size does not always improve efficiency, suggesting the importance of fine-tuning models and, again, the need to carefully select the nonconformity measure for different applications. © 2024, CC BY.

关键词： Prediction models

POS0750 WHO PARTICIPATES IN AN ONLINE SYMPTOM CHECKER? CHARACTERISTICS, ATTRITION AND REPRESENTATIVENESS IN THE RHEUMATIC? STUDY

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Annals of the Rheumatic Diseases 2024年 83卷 1128-1129页

作者： F. Zegers L. Qin D. Selani G. Gomon T.D. Maarseveen H.K. Glas A. Van Tubergen Y. Goekoop-Ruiterman M.J.T. Reinders E.B. Van den Akker C. Baatenburg de Jong L. Klareskog B. Axnäs E. Steyerberg R. Bos S. Le Cessie R. Knevel Leiden University Medical Center Department of Biomedical Data Sciences Leiden Netherlands Leiden University Medical Center Department of Rheumatology Leiden Netherlands Delft University of Technology Department of Intelligent Systems Pattern Recognition and Bioinformatics Delft Netherlands Reumazorg Zuid West Neder；anmd Goes Netherlands Maastricht University Medical Center Department of Internal Medicine Division of Rheumatology Maastricht Netherlands Maastricht University Care and Public Health Research Institute (CAPHRI) Maastricht Netherlands Haga Hospital Department of Rheumatology Den Haag Netherlands Delft Technical University Delft Bioinformatics Lab Delft Netherlands Leiden University Medical Center Leiden Computational Biology Department of Biomedical Data Sciences Leiden Netherlands Delft University of Technology The Delft Bioinformatics Lab Pattern Recognition and Bioinformatics Delft Netherlands ReumaNederland Amsterdam Netherlands (Solna) Karolinska Institutet Division for Rheumatology Department of Medicine Stockholm Sweden Elsa Science Stockholm Sweden University Medical Center Rotterdam Department of Public Health Erasmus MC Rotterdam Netherlands Medical Center Leeuwarden Department of Rheumatology Leeuwarden Netherlands Nij Smellinghe Hospital Department of Rheumatology Drachten Netherlands Leiden University Medical Center Department of Clinical Epidemiology Leiden Netherlands Newcastle University Translational and Clinical Research Institute Rheumatology Newcastle upon Tyne United Kingdom

Background: Online symptom checkers (OSCs) could provide guidance in the diagnostic process. The number of OSCs are expanding yet often lack rigorous validation. Rheumatic? is an online questionnaire designed to provide a fast and reliable risk assessment of possible rheumatic diagnoses for individuals with musculoskeletal complaints (MSCs). We set out to validate this tool by following individuals with MSCs. A key question is representativity of the participants as attrition bias can complicate the construction of a precise prediction model. Objectives: This project aims to assess aspects of attrition and selection bias in Rheumatic? by comparing participants who did and did not respond to the first follow-up survey, by comparing participants versus patients from general practitioners (GP) and rheumatology clinics, and by exploring variations in characteristics across different recruitment policies. Methods: Rheumatic? includes a baseline questionnaire about current symptoms and past diagnoses. Participants were recruited online, at primary care or at rheumatology outpatient clinics. Four surveys followed after 0, 3, 6 and 12 months, about source of recruitment, medication, further diagnoses etc. We considered data of July 2021 to July 2023. We compared participants who solely answered the questionnaire to those who also answered the first follow up survey. Secondly, we compared characteristics of participants across different sources of recruitment (i.e. at primary or secondary care clinics or online (Instagram, Facebook, Google, the Dutch Arthritis Association)). For this, we calculated differences in percentages with confidence intervals and applied chi squared tests. We assessed representability of the cohort with the expected target population by comparing age, sex and BMI of the participants with information on new patients with MSC from the same period at primary care (GP), Rheumatology clinics in the South West of the Netherlands (RZWN), and the Rheumatolog

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On the reusability of samples in active learning

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arXiv 2022年

作者： van Tulder, Gijs Loog, Marco Data Science Group Faculty of Science Radboud University Nijmegen Netherlands Pattern Recognition Laboratory Delft University of Technology Delft Netherlands

An interesting but not extensively studied question in active learning is that of sample reusability: to what extent can samples selected for one learner be reused by another? This paper explains why sample reusability is of practical interest, why reusability can be a problem, how reusability could be improved by importance-weighted active learning, and which obstacles to universal reusability remain. With theoretical arguments and practical demonstrations, this paper argues that universal reusability is impossible. Because every active learning strategy must undersample some areas of the sample space, learners that depend on the samples in those areas will learn more from a random sample selection. This paper describes several experiments with importance-weighted active learning that show the impact of the reusability problem in practice. The experiments confirmed that universal reusability does not exist, although in some cases - on some datasets and with some pairs of classifiers - there is sample reusability. Finally, this paper explores the conditions that could guarantee the reusability between two classifiers. © 2022, CC BY-SA.

关键词： Reusability

Cooperative data-driven modeling

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arXiv 2022年

作者： Dekhovich, Aleksandr Turan, O. Taylan Yi, Jiaxiang Bessa, Miguel A. Department of Material Science and Engineering Delft University of Technology Mekelweg 2 Delft2628 CD Netherlands Pattern Recognition and Bioinformatics Laboratory Delft University of Technology Van Mourik Broekmanweg 6 Delft2628 XE Netherlands School of Engineering Brown University 184 Hope St. ProvidenceRI02912 United States

Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening possibilities for cooperative modeling. However, artificial neural networks suffer from catastrophic forgetting, i.e. they forget how to perform an old task when trained on a new one. This hinders cooperation because adapting an existing model for a new task affects the performance on a previous task trained by someone else. The authors developed a continual learning method1 that addresses this issue, applying it here for the first time to solid mechanics. In particular, the method is applied to recurrent neural networks to predict history-dependent plasticity behavior, although it can be used on any other architecture (feedforward, convolutional, etc.) and to predict other phenomena. This work intends to spawn future developments on continual learning that will foster cooperative strategies among the mechanics community to solve increasingly challenging problems. We show that the chosen continual learning strategy can sequentially learn several constitutive laws without forgetting them, using less data to achieve the same error as standard (non-cooperative) training of one law per model. © 2022, CC BY.

关键词： Recurrent neural networks

Multi-Unit Floor Plan recognition and Reconstruction Using Improved Semantic Segmentation of Raster-Wise Floor Plans

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arXiv 2024年

作者： Kratochvila, Lukas de Jong, Gijs Arkesteijn, Monique Bilík, Šimon Zemčík, Tomáš Horak, Karel Rellermeyer, Jan S. Department of Control and Instrumentation Faculty of Electrical Engineering and Communication Brno University of Technology Brno Czech Republic Department of Software Technology Faculty of Electrical Engineering Mathematics and Computer Science TU Delft Delft Netherlands Department of Management in the Built Environment Faculty of Architecture and the Built Environment TU Delft Delft Netherlands Computer Vision and Pattern Recognition Laboratory Department of Computational Engineering Lappeenranta-Lahti University of Technology LUT Lappeenranta Finland Dependable and Scalable Software Systems Institute of Systems Engineering Faculty of Electrical Engineering and Computer Science Leibniz University Hannover Hannover Germany

Digital twins have a major potential to form a significant part of urban management in emergency planning, as they allow more efficient designing of the escape routes, better orientation in exceptional situations, and faster rescue intervention. Nevertheless, creating the twins still remains a largely manual effort, due to a lack of 3D-representations, which are available only in limited amounts for some new buildings. Thus, in this paper we aim to synthesize 3D information from commonly available 2D architectural floor plans. We propose two novel pixel-wise segmentation methods based on the MDA-Unet and MACU-Net architectures with improved skip connections, an attention mechanism, and a training objective together with a reconstruction part of the pipeline, which vectorizes the segmented plans to create a 3D model. The proposed methods are compared with two other state-of-the-art techniques and several benchmark datasets. On the commonly used CubiCasa benchmark dataset, our methods have achieved the mean F1 score of 0.86 over five examined classes, outperforming the other pixel-wise approaches tested. We have also made our code publicly available to support research in the field. © 2024, CC BY.

关键词： Semantic Segmentation

AB1448 DIFFERENTIATION OF IMMUNE MEDIATED VERSUS NON IMMUNE MEDIATED RHEUMATIC DISEASES BY ONLINE SYMPTOM CHECKER IN REAL-WORLD PATIENTS – MULTIPLE DIAGNOSES AND PARTICULARLY FIBROMYALGIA IS A STUMBLING BLOCK

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Annals of the Rheumatic Diseases 2024年 83卷 2082-2083页

作者： L. Qin F. Zegers D. Selani E.B. Van den Akker R. Bos S. Le Cessie I. Gehring H.K. Glas M. Johannesson J. Knitza L. Mathsson-Alm M.J.T. Reinders E. Steyerberg A. Van Tubergen L.M. Verhoef B. Axnäs L. Klareskog R. Knevel Leiden University Medical Center Department of Rheumatology Leiden Netherlands Leiden University Medical Center Department of Biomedical Data Sciences Leiden Netherlands Delft University of Technology Department of Intelligent Systems Pattern Recognition and Bioinformatics Delft Netherlands Leiden University Medical Center Leiden Computational Biology Department of Biomedical Data Sciences Leiden Netherlands Delft University of Technology The Delft Bioinformatics Lab Pattern Recognition and Bioinformatics Delft Netherlands Medical Center Leeuwarden Department of Rheumatology Leeuwarden Netherlands Nij Smellinghe Hospital Department of Rheumatology Drachten Netherlands Leiden University Medical Center Department of Clinical Epidemiology Leiden Netherlands Thermo Fisher Scientific Freiburg Germany Reumazorg Zuid West Nederland Goes Netherlands Karolinska Institutet and Karolinska University Hospital Department of Medicine Solna Solna Sweden University Hospital of Giessen and Marburg Philipps-University Marburg Institute for Digital Medicine Marburg Germany Uppsala University Department of Immunology Genetics and Pathology Uppsala Sweden Thermo Fisher Scientific Uppsala Sweden University Medical Center Rotterdam Department of Public Health Rotterdam Netherlands Maastricht University Medical Center Department of Internal Medicine Division of Rheumatology Maastricht Netherlands Maastricht University Care and Public Health Research Institute (CAPHRI) Maastricht Netherlands Sint Maartenskliniek Research Department Ubbergen Netherlands Elsa Science Stockholm Sweden Karolinska Institutet and Karolinska University hospital Department of Medicine Solna Solna Sweden Newcastle University Translational and Clinical Research Institute Rheumatology Newcastle upon Tyne United Kingdom

Background: Rheumatic? is an online symptom checker developed collaboratively by designers, engineers, clinical experts and patients. It is designed to identify individuals at high risk of developing rheumatic diseases and patients with immune-mediated rheumatic diseases (IRD). After completion of the questionnaire, Rheumatic? gives a weighted score based on expert assessments of the clinical significance of the answers [1] . A previous retrospective study has demonstrated the potential to distinguish IRD from osteoarthritis(OA) and gout, where clinicians filled out the questionnaire based on the medical notes [2] . In order to use a questionnaire in real life, it should be tested on real life participants, as they may describe their symptoms differently than experts. In order to evaluate the performance of the current Rheumatic? score, to differentiate between IRDs and non-IRDs we conducted a prospective real-world study in the Netherlands and assessed the differences in Rheumatic? total scores between individuals diagnosed with IRD and non-IRD. Objectives: Examine the difference in scores of Rheumatic? between IRD (Rheumatoid arthritis, Psoriatic arthritis, Myositis, Sjogren’s syndrome, SLE, Spondyloarthritis and Polymyalgia rheumatica) and non-IRD(OA, Gout, Fibromyalgia and other) diagnoses. Methods: We analyzed data submitted by Dutch participants recruited via multiple channels between July 2021 and July 2022. After completing the online questionnaire Rheumatic? participants received four follow-up surveys at 1 week, 3, 6 and 12 months asking, among other things, for previous and novel diagnoses. The theoretical total score for the participant was determined using the current, expert developed, risk assessment model post collection of all data [1,2] . We used t-test and analysis of variance (ANOVA) to compared the observed differences in mean and median of total scores among these groups. Results: 8,727 participants were included, of which 6861(79%) were female

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Bayesian Active Learning for Maximal Information Gain on Model Parameters

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Bayesian Active Learning for Maximal Information Gain on Mod...

International Conference on pattern recognition

作者： Kasra Arnavaz Aasa Feragen Oswin Krause Marco Loog DanStem University of Copenhagen DTU Compute Technical University of Denmark University of Copenhagen Pattern Recognition Laboratory Delft University of Technology

The fact that machine learning models, despite their advancements, are still trained on randomly gathered data is proof that a lasting solution to the problem of optimal data gathering has not yet been found. In this paper, we investigate whether a Bayesian approach to the classification problem can provide assumptions under which one is guaranteed to perform at least as good as random sampling. For a logistic regression model, we show that maximal expected information gain on model parameters is a promising criterion for selecting samples, assuming that our classification model is well-matched to the data. Our derived criterion is closely related to the maximum model change. We experiment with data sets which satisfy this assumption to varying degrees to see how sensitive our performance is to the violation of our assumption in practice.

关键词： Machine learning Data models Bayes methods pattern recognition Logistics