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Tensor neural networks for high-dimensional Fokker-Planck equations

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arXiv 2024年

作者： Wang, Taorui Hu, Zheyuan Kawaguchi, Kenji Zhang, Zhongqiang Karniadakis, George Em Department of Mathematical Sciences Worcester Polytechnic Institute WorcesterMA United States Department of Computer Science National University of Singapore 119077 Singapore Division of Applied Mathematics Brown University ProvidenceRI02912 United States Advanced Computing Mathematics and Data Division Pacific Northwest National Laboratory RichlandWA United States

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear combination of several selected radial basis functions. The use of tensor feedforward networks allows us to efficiently exploit auto-differentiation (in physical variables) in major Python packages while using radial basis functions can fully avoid auto-differentiation, which is rather expensive in high dimensions. We then use the physics-informed neural networks and stochastic gradient descent methods to learn the tensor networks. One essential step is to determine a proper bounded domain or numerical support for the Fokker-Planck equation. To better train the tensor radial basis function networks, we impose some constraints on parameters, which lead to relatively high accuracy. We demonstrate numerically that the tensor neural networks in physics-informed machine learning are efficient for steady-state Fokker-Planck equations from two to ten dimensions. Copyright © 2024, The Authors. All rights reserved.

关键词： Radial basis function networks

AutoML for neuromorphic computing and application-driven co-design: asynchronous, massively parallel optimization of spiking architectures

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AutoML for neuromorphic computing and application-driven co-...

IEEE International Conference on Rebooting Computing (ICRC)

作者： Angel Yanguas-Gil Sandeep Madireddy Applied Materials Division Argonne National Laboratory Lemont IL USA Mathematics and Computer Science Division Argonne National Laboratory Lemont IL USA

In this work we have extended AutoML inspired approaches to the exploration and optimization of neuromorphic architectures. Through the integration of a parallel asynchronous model-based search approach with a simulation framework to simulate spiking architectures, we are able to efficiently explore the configuration space of neuromorphic architectures and identify the subset of conditions leading to the highest performance in a targeted application. We have demonstrated this approach on an exemplar case of real time, on-chip learning application. Our results indicate that we can effectively use optimization approaches to optimize complex architectures, therefore providing a viable pathway towards application-driven codesign.

关键词： Neuromorphics Computational modeling Supervised learning Stochastic processes computer architecture Signal processing Space exploration

Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods

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arXiv 2023年

作者： Moral, Pierre Del Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux FR Bordeaux33405 France School of Mathematics and Statistics Wenlan School of Business China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Zhongnan University of Economics and Law CN China

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE);see [12]. These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of O(ϵ2), for ϵ > 0 given, the associated work is O(ϵ−2). Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Diffusion

Forward Brillouin Point Sensor in a Multi-Core Fiber 27

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Forward Brillouin Point Sensor in a Multi-Core Fiber

27th International Conference on Optical Fiber Sensors, OFS 2022

作者： Shemer, Keren Bashan, Gil Zehavi, Elad Diamandi, Hilel Hagai Bernstein, Alon Sharma, Kavita London, Yosef Barrera, David Sales, Salvador Zadok, Avi Faculty of Engineering and Institute for Nano-Technology and Advanced Materials Bar-Ilan University Ramat-Gan5290002 Israel Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot7610001 Israel Currently with Applied Physics Division Soreq NRC Yavne81800 Israel Photonics Research Labs Universitat Politècnica de València Valencia46022 Spain

Forward Brillouin point sensing is demonstrated in a multi-core fiber. Acoustic waves are stimulated by light in one core and monitored using a grating in another. Measurements distinguish between ethanol and water ou... 详细信息

ISBN: (纸本)9781957171142

关键词： Effective refractive index Fiber optic sensors Forward scattering Multicore fibers Phase modulation Tunable diode lasers

EAIRA: Establishing a Methodology for Evaluating AI Models as Scientific Research Assistants

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arXiv 2025年

作者： Cappello, Franck Madireddy, Sandeep Underwood, Robert Getty, Neil Chia, Nicholas Lee-Ping Ramachandra, Nesar Nguyen, Josh Keçeli, Murat Mallick, Tanwi Li, Zilinghan Ngom, Marieme Zhang, Chenhui Yanguas-Gil, Angel Antoniuk, Evan Kailkhura, Bhavya Tian, Minyang Du, Yufeng Ting, Yuan-Sen Wells, Azton Nicolae, Bogdan Maurya, Avinash Mustafa Rafique, M. Huerta, Eliu Li, Bo Foster, Ian Stevens, Rick Mathematics and Computer Science Division Argonne National Laboratory United States Data Science and Learning Division Argonne National Laboratory United States Computational Science Division Argonne National Laboratory United States Applied Materials Division Argonne National Laboratory United States Department of Computer Science The University of Chicago United States University of Pennsylvania United States Lawrence Livermore National Laboratory United States The Ohio State University United States Rochester Institute of Technology United States Massachusetts Institute of Technology United States

Recent advancements have positioned AI, and particularly Large Language Models (LLMs) as transformative tools for scientific research, capable of addressing complex tasks that require reasoning, problem-solving, and decision-making. Their exceptional capabilities suggest their potential as scientific research assistants, but also highlight the need for holistic, rigorous, and domain-specific evaluation to assess effectiveness in real-world scientific applications. This paper describes a multifaceted methodology for Evaluating AI models as scientific Research Assistants (EAIRA) developed at Argonne National Laboratory. This methodology incorporates four primary classes of evaluations. 1) Multiple Choice Questions to assess factual recall;2) Open Response to evaluate advanced reasoning and problem-solving skills;3) Lab-Style Experiments involving detailed analysis of capabilities as research assistants in controlled environments;and 4) Field-Style Experiments to capture researcher-LLM interactions at scale in a wide range of scientific domains and applications. These complementary methods enable a comprehensive analysis of LLM strengths and weaknesses with respect to their scientific knowledge, reasoning abilities, and adaptability. Recognizing the rapid pace of LLM advancements, we designed the methodology to evolve and adapt so as to ensure its continued relevance and applicability. This paper describes the methodology’s state at the end of February 2025. Although developed within a subset of scientific domains, the methodology is designed to be generalizable to a wide range of scientific domains. Copyright © 2025, The Authors. All rights reserved.

关键词： Decision making

Leveraging Interpolation Models and Error Bounds for Verifiable Scientific Machine Learning

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arXiv 2024年

作者： Chang, Tyler Gillette, Andrew Maulik, Romit Mathematics and Computer Science Division Argonne National Laboratory United States Center for Applied Scientific Computing Lawrence Livermore National Laboratory United States Information Sciences and Technology Department The Pennsylvania State University United States

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. In this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently;(2) comparative performance among distinct interpolants can aid in validation goals;(3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository. © 2024, CC BY-NC-SA.

关键词： Interpolation

Diabetes Prediction Model for Better Clarification by using Machine Learning 6

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Diabetes Prediction Model for Better Clarification by using ...

6th International Conference on Inventive Computation Technologies, ICICT 2023

作者： Eben, J. Lysa Jayasudha, R. Ramya, S. Kaliappan, S. Aswal, Shobha Al-Salehi, Khalid Ali Salem Department of Computer Applications School of Computing Sciences Vels Institute of Science Technology and Advanced Studies Tamilnadu Chennai India Department of Mathematics Dr.N.G.P.Institute of Technology Coimbatore India Department of Computer Science and Engineering Kongu Engineering College Tamilnadu Erode India Division of Research and Development Lovely Professional University Punjab Phagwara144411 India School of Computing Graphic Era Hill University Dehradun India Biomedical Engineering Study Program Faculty of Science and Technology Airlangga University Surabaya Indonesia

ISBN: (纸本)9798350398496

Diabetes mellitus is one of the most pressing health concerns because so many people are afflicted by its disabling symptoms. Factors such as age, excess body fat, insufficient physical activity, a history of diabetes in one's family, a sedentary lifestyle, an unhealthy diet, hypertension, etc., all increase the likelihood of developing diabetes mellitus. Health complications are more common in people with diabetes, including cardiovascular disease, renal failure, stroke, blindness, and nerve injury. To validate a diagnosis of diabetes, hospitals typically perform a battery of procedures on the patient. Big data analytics has many vital applications in the healthcare sector. Numerous large computer systems are used in the healthcare sector. With the help of big data analytics, researchers can sift through mountains of data in search of previously unseen patterns and insights. Current techniques have a poor degree of precision in classification and forecast. While previous research has focused on factors such as glucose, body mass index, age, insulin, etc., the proposed model takes these into account and also the other factors that may be more relevant to the development of diabetes. The newer sample is superior to the older one based on categorization accuracy. A workflow algorithm for diabetes prognosis is also required to improve the accuracy. © 2023 IEEE.

关键词： Forecasting

On an initial value problem for time fractional pseudo-parabolic equation with Caputo derivative

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On an initial value problem for time fractional pseudo-parab...

作者： Luc, Nguyen Hoang Jafari, Hossein Kumam, Poom Tuan, Nguyen Huy Department of Mathematics and Computer Science University of Science Ho Chi Minh City Viet Nam Vietnam National University Ho Chi Minh City Viet Nam Division of Applied Mathematics Thu Dau Mot University Binh Duong Province Viet Nam Department of Mathematic University of Mazandaran Babolsar Iran Department of Mathematical Sciences University of South Africa UNISA 0003 South Africa Department of Medical Research China Medical University Hospital China Medical University Taichung110122 Taiwan 126 Pracha-Uthit Road Bang Mod Thrung Khru Bangkok10140 Thailand 126 Pracha-Uthit Road Bang Mo Thrung Khru Bangkok10140 Thailand Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam

In this paper, we consider a pseudo-parabolic equation with the Caputo fractional derivative. We study the existence and uniqueness of a class of mild solutions of these equations. For a nonlinear problem, we first investigate the global solution under the initial data u0 ∈ L2. In the case of initial data u0 ∈ Lq, q ≠ 2, we obtain the local existence result. Our main tool here is using fundamental tools, namely, Banach fixed point theorem and Sobolev embeddings. In addition, we give an example to illustrate the effectiveness of the method has been proposed. © 2021 John Wiley & Sons, Ltd.

关键词： Initial value problems

THE EFFECT OF LIMITED MOBILITY ON THE EXPERIENCED SEGREGATION OF FOREIGN-BORN MINORITIES

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arXiv 2024年

作者： Liao, Yuan Gil, Jorge Yeh, Sonia Pereira, Rafael H.M. Alessandretti, Laura Department of Space Earth and Environment Chalmers University of Technology Gothenburg Sweden Department of Architecture and Civil Engineering Chalmers University of Technology Gothenburg Sweden - Brazil Data Science Division Brazil Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby Denmark

Segregation is a key challenge in promoting more diverse and inclusive cities. Research based on large-scale mobility data indicates that segregation between majority and minority groups persists in daily activities beyond residential areas, like visiting shops and restaurants. Aspects including lifestyle differences, homophily, and mobility constraints have been proposed as drivers of this phenomenon, but their contributions remain poorly quantified. Here, we elucidate how different mechanisms influence segregation outside home, looking at the distinctive segregation experienced by native and foreign-born individuals. Our study is based on the movement of ∼320,000 individual smartphone devices collected in Sweden, where immigration creates profound divides. We find that while day-to-day activities lead to mixing for native-born individuals, foreign-born individuals remain segregated in their out-of-home activities. Using counterfactual simulations, we show that this heterogeneous effect of mobility on experienced segregation results mainly from two mechanisms: homophily and limited travel, i.e. foreign-born individuals (i) tend to visit destinations visited by similar individuals, and (ii) have limited mobility ranges. We show that homophily, as represented by destination preference, plays a minor role, while limited mobility, associated with reduced transport access, limits opportunities for foreign-born minorities to diversify their encounters. Our findings suggest that enhancing transport accessibility in foreign-born concentrated areas could reduce social segregation. © 2024, CC BY-SA.

关键词： Smartphones