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Coarse-scale PDEs from fine-scale observations via machine learning

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arXiv 2019年

作者： Lee, Seungjoon Kooshkbaghi, Mahdi Spiliotis, Konstantinos Siettos, Constantinos I. Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University Program in Applied and Computational Mathematics Princeton University Institute of Mathematics University of Rostock Dipartimento di Matematica e Applicazioni "Renato Caccioppoli" Universitá degli Studi di Napoli Federico II

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using e.g. partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g. concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. Recent developments in data science provide alternative ways to effectively extract/learn accurate macroscopic descriptions approximating the underlying microscopic observations. In this paper, we introduce a data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine learning algorithms. Specifically, using Gaussian Processes, Artificial Neural Networks, and/or Diffusion Maps, the proposed framework uncovers the relation between the relevant macroscopic space fields and their time evolution (the right-hand-side of the explicitly unavailable macroscopic PDE). Interestingly, several choices equally representative of the data can be discovered. The framework will be illustrated through the data-driven discovery of macroscopic, concentration-level PDEs resulting from a fine-scale, Lattice Boltzmann level model of a reaction/transport process. Once the coarse evolution law is identified, it can be simulated to produce long-term macroscopic predictions. Different features (pros as well as cons) of alternative machine learning algorithms for performing this task (Gaussian Processes and Artificial Neural Networks), are presented and discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Neural networks

14 Examples of How LLMs Can Transform Materials Science and Chemistry: A Reflection on a Large Language Model Hackathon

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arXiv 2023年

作者： Jablonka, Kevin Maik Ai, Qianxiang Al-Feghali, Alexander Badhwar, Shruti Bocarsly, Joshua D. Bran, Andres M. Bringuier, Stefan Brinson, L. Catherine Choudhary, Kamal Circi, Defne Cox, Sam de Jong, Wibe A. Evans, Matthew L. Gastellu, Nicolas Genzling, Jerome Gil, María Victoria Gupta, Ankur K. Hong, Zhi Imran, Alishba Kruschwitz, Sabine Labarre, Anne Lála, Jakub Liu, Tao Ma, Steven Majumdar, Sauradeep Merz, Garrett W. Moitessier, Nicolas Moubarak, Elias Mouriño, Beatriz Pelkie, Brenden Pieler, Michael Ramos, Mayk Caldas Ranković, Bojana Rodriques, Samuel G. Sanders, Jacob N. Schwaller, Philippe Schwarting, Marcus Shi, Jiale Smit, Berend Smith, Ben E. Van Herck, Joren Völker, Christoph Ward, Logan Warren, Sean Weiser, Benjamin Zhang, Sylvester Zhang, Xiaoqi Zia, Ghezal Ahmad Scourtas, Aristana Schmidt, K.J. Foster, Ian White, Andrew D. Blaiszik, Ben Sion Valais Switzerland Department of Chemical Engineering Massachusetts Institute of Technology CambridgeMA02139 United States Department of Chemistry McGill University MontrealQC Canada Reincarnate Inc. United States Yusuf Hamied Department of Chemistry University of Cambridge Lensfield Road CambridgeCB2 1EW United Kingdom Lausanne Switzerland Lausanne Switzerland San Diego CA United States Mechanical Engineering and Materials Science Duke University United States Material Measurement Laboratory National Institute of Standards and Technology MD20899 United States Department of Chemical Engineering University of Rochester United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States UCLouvain Chemin des Étoiles 8 Louvain-la-Neuve1348 Belgium Matgenix SRL 185 Rue Armand Bury Gozée 6534 Belgium CSIC Francisco Pintado Fe 26 Oviedo33011 Spain Department of Computer Science University of Chicago ChicagoIL60637 United States Computer Science University of California Berkeley BerkeleyCA94704 United States Bundesanstalt für Materialforschung und -Prüfung Unter den Eichen 87 Berlin12205 Germany Francis Crick Institute 1 Midland Rd LondonNW1 1AT United Kingdom American Family Insurance Data Science Institute University of Wisconsin-Madison MadisonWI53706 United States Department of Chemical Engineering University of Washington SeattleWA98105 United States *** Stability.AI United Kingdom Department of Chemistry and Biochemistry University of California Los AngelesCA90095 United States Department of Computer Science University of Chicago ChicagoIL60490 United States Data Science and Learning Division Argonne National Lab United States Globus University of Chicago Data Science and Learning Division Argonne National Lab United States Department of Computer Science University of Chicago Data Science and Learning Division Argonne National Lab United

Large-language models (LLMs) such as GPT-4 caught the interest of many scientists. Recent studies suggested that these models could be useful in chemistry and materials science. To explore these possibilities, we organized a hackathon. This article chronicles the projects built as part of this hackathon. Participants employed LLMs for various applications, including predicting properties of molecules and materials, designing novel interfaces for tools, extracting knowledge from unstructured data, and developing new educational applications. The diverse topics and the fact that working prototypes could be generated in less than two days highlight that LLMs will profoundly impact the future of our fields. The rich collection of ideas and projects also indicates that the applications of LLMs are not limited to materials science and chemistry but offer potential benefits to a wide range of scientific disciplines. © 2023, CC BY.

关键词： computational linguistics

Visualizing structure and transitions in high-dimensional biological data (vol 54, pg 781, 2019)

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NATURE BIOTECHNOLOGY 2020年第1期38卷 108-108页

作者： Moon, Kevin R. van Dijk, David Wang, Zheng Gigante, Scott Burkhardt, Daniel B. Chen, William S. Yim, Kristina van den Elzen, Antonia Hirn, Matthew J. Coifman, Ronald R. Ivanova, Natalia B. Wolf, Guy Krishnaswamy, Smita Department of Mathematics and Statistics Utah State University Logan USA Cardiovascular Research Center section Cardiology Department of Internal Medicine Yale University New Haven USA Department of Computer Science Yale University New Haven USA School of Basic Medicine Qingdao University Qingdao China Yale Stem Cell Center Department of Genetics Yale University New Haven USA Computational Biology and Bioinformatics Program Yale University New Haven USA Department of Genetics Yale University New Haven USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing USA Department of Mathematics Michigan State University East Lansing USA Applied Mathematics Program Yale University New Haven USA Department of Genetics Center for Molecular Medicine University of Georgia Athens USA Department of Mathematics and Statistics Université de Montréal Montréal Canada Mila—Quebec Artificial Intelligence Institute Montréal Canada

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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Image recovery from rotational and translational invariants

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arXiv 2019年

作者： Marshall, Nicholas F. Lan, Ti-Yen Bendory, Tamir Singer, Amit Department of Mathematics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotationally and translationally invariant features and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM. Copyright © 2019, The Authors. All rights reserved.

关键词： Electron microscopes

Corrigendum to "Synergetic effect of bismuth vanadate over copolymerized carbon nitride composites for highly efficient photocatalytic H2 and O2 generation" [J. Colloid Interface Sci. 627 (2022) 621-629]

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Journal of colloid and interface science 2022年第PT A期628卷 366-367页

作者： Asif Hayat Muhammad Sohail T A Taha Sunil Kumar Baburao Mane Abdullah G Al-Sehemi Ahmed A Al-Ghamdi W I Nawawi Arkom Palamanit Mohammed A Amin Ahmed M Fallatah Zeeshan Ajmal Hamid Ali Wasim Ullah Khan Muhammad Wajid Shah Javid Khan S Wageh State Key Laboratory of Photocatalysis on Energy and Environment College of Chemistry Fuzhou University Fuzhou 350116 China. Yangtze Delta Region Institute (Huzhou) University of Electronic Science and Technology of China Huzhou 313001 China. Physics Department College of Science Jouf University P.O. Box: 2014 Sakaka Saudi Arabia Physics and Engineering Mathematics Department Faculty of Electronic Engineering Menoufia University Menouf 32952 Egypt. Department of Chemistry Khaja Bandanawaz University Kalaburagi Karnataka 585104 India. Research Center for Advanced Materials Science (RCAMS) King Khalid University P.O. Box 9004 Abha 61413 Saudi Arabia Department of Chemistry College of Science King Khalid University P.O. Box 9004 Abha 61413 Saudi Arabia. Department of Physics Faculty of Science King Abdulaziz University Jeddah 21589 Saudi Arabia. Faculty of Applied Sciences Universiti Teknologi MARA Cawangan Perlis Arau Perlis 02600 Malaysia. Energy Technology Program Department of Specialized Engineering Faculty of Engineering Prince of Songkla University 15 Karnjanavanich Rd. Hat Yai Songkhla 90110 Thailand. Department of Chemistry College of Science Taif University P.O. Box 11099 Taif 21944 Saudi Arabia. School of Chemistry and Chemical Engineering Northwestern Polytechnical University Xian 710072 China. Multiscale Computational Materials Facility Key Laboratory of Eco-Materials Advanced Technology College of Materials Science and Engineering Fuzhou University Fuzhou 350100 China. State Key Laboratory of Optoelectronic Materials and Technologies School of Materials Science and Engineering Sun Yat-sen University Guangzhou 510275 China. Electronic address: wasimullah89@***. School Of Chemistry Sun Yat-sen University Guangzhou 510275 China. Electronic address: m.wajidshah@***. College of Materials Science and Engineering Hunan University Changsha Hunan 410082 China. Electronic address: javidchemist@yahoo.com.

Multiscale PHATE Exploration of SARS-CoV-2 Data Reveals Multimodal Signatures of Disease

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Research Square

Research Square 2021年

作者： Kuchroo, Manik Huang, Jessie Wong, Patrick Grenier, Jean-Christophe Shung, Dennis Tong, Alexander Lucas, Carolina Klein, Jon Burkhardt, Daniel B. Gigante, Scott Godavarthi, Abhinav Rieck, Bastian Israelow, Benjamin Simonov, Michael Mao, Tianyang Oh, Ji Eun Silva, Julio Takahashi, Takehiro Odio, Camila D. Casanovas-Massana, Arnau Fournier, John Farhadian, Shelli Dela Cruz, Charles S. Ko, Albert I. Hirn, Matthew J. Wilson, F. Perry Hussin, Julie Wolf, Guy Iwasaki, Akiko Krishnaswamy, Smita Department of Neuroscience Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Immunobiology Yale University New HavenCT United States Montreal Heart Institute MontréalQC Canada Department of Medicine Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States Computational Biology Bioinformatics Program Yale University New HavenCT United States Department of Applied Mathematics Yale University New HavenCT United States Department of Biosystems Science and Engineering ETH Zurich Switzerland Department of Epidemiology of Microbial Diseases Yale School of Public Health New HavenCT United States Department of Medicine Section of Infectious Diseases Yale University School of Medicine New HavenCT United States Department of Medicine Section of Pulmonary and Critical Care Medicine Yale University School of Medicine New HavenCT United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI United States Department of Mathematics Michigan State University East LansingMI United States Clinical and Translational Research Accelerator Department of Medicine Yale University New HavenCT United States Faculty of Medicine Université de Montréal Québec Canada Mila – Quebec AI institute MontréalQC Canada Department of Mathematics and Statistics Université de Montréal MontréalQC Canada Howard Hughes Medical Institute Chevy ChaseMD United States

The biomedical community is producing increasingly high dimensional datasets, integrated from hundreds of patient samples, which current computational techniques struggle to explore. To uncover biological meaning from these complex datasets, we present an approach called Multiscale PHATE, which learns abstracted biological features from data that can be directly predictive of disease. Built on a coarse graining process called diffusion condensation, Multiscale PHATE learns a data topology that can be analyzed at coarse levels for high level summarizations of data, as well as at fine levels for detailed representations on subsets. We apply Multiscale PHATE to study the immune response to COVID-19 in 54 million cells from 168 hospitalized patients. Through our analysis of patient samples, we identify CD16hiCD66blo neutrophil and IFNγ+GranzymeB+ Th17 cell responses enriched in patients who die. Furthermore, we show that population groupings Multiscale PHATE discovers can be directly fed into a classifier to predict disease outcome. We also use Multiscale PHATE-derived features to construct two different manifolds of patients, one from abstracted flow cytometry features and another directly on patient clinical features, both associating immune subsets and clinical markers with outcome. © 2021, CC BY.

关键词： Coronavirus

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

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arXiv 2022年

作者： Aubry, Jean-Francois Bates, Oscar Boehm, Christian Pauly, Kim Butts Christensen, Douglas Cueto, Carlos Gélat, Pierre Guasch, Lluis Jaros, Jiri Jing, Yun Jones, Rebecca Li, Ningrui Marty, Patrick Montanaro, Hazael Neufeld, Esra Pichardo, Samuel Pinton, Gianmarco Pulkkinen, Aki Stanziola, Antonio Thielscher, Axel Treeby, Bradley Van't Wout, Elwin Physics for Medicine Paris INSERM U1273 ESPCI Paris PSL University CNRS UMR 8063 France Department of Bioengineering Imperial College London Exhibition Road LondonSW7 2AZ United Kingdom Institute of Geophysics ETH Zürich Sonneggstrasse 5 Zürich8092 Switzerland Department of Radiology Stanford University StanfordCA United States Department of Biomedical Engineering Department of Electrical and Computer Engineering University of Utah United States Department of Surgical Biotechnology Division of Surgery and Interventional Science University College London LondonNW3 2PF United Kingdom Earth Science and Engineering Department Imperial College London London United Kingdom Centre of Excellence IT4Innovations Faculty of Information Technology Brno University of Technology Bozetechova 2 Brno612 00 Czech Republic Graduate Program in Acoustics The Pennsylvania State University University Park PA16802 United States Joint Department of Biomedical Engineering University of North Carolina at Chapel Hill North Carolina State University NC United States Department of Electrical Engineering Stanford University StanfordCA United States Zurich Switzerland Laboratory for Acoustics / Noise control Empa Swiss Federal Laboratories for Materials Science and Technology Dubendorf Switzerland Zurich Switzerland Radiology and Clinical Neurosciences Departments Cumming School of Medicine University of Calgary Canada Department of Applied Physics University of Eastern Finland Kuopio70211 Finland Department of Medical Physics and Biomedical Engineering University College London Gower Street LondonWC1E 6BT United Kingdom Technical University of Denmark Denmark Danish Research Center for Magnetic Resonance Copenhagen University Hospital Hvidovre Denmark Institute for Mathematical and Computational Engineering School of Engineering and Faculty of Mathematics Pontificia Universidad Catolica de Chile Santiago Chile

computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular-spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons. Copyright © 2022, The Authors. All rights reserved.

关键词： Bone

DPA-2: a large atomic model as a multi-task learner

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arXiv 2023年

作者： Zhang, Duo Liu, Xinzijian Zhang, Xiangyu Zhang, Chengqian Cai, Chun Bi, Hangrui Du, Yiming Qin, Xuejian Peng, Anyang Huang, Jiameng Li, Bowen Shan, Yifan Zeng, Jinzhe Zhang, Yuzhi Liu, Siyuan Li, Yifan Chang, Junhan Wang, Xinyan Zhou, Shuo Liu, Jianchuan Luo, Xiaoshan Wang, Zhenyu Jiang, Wanrun Wu, Jing Yang, Yudi Yang, Jiyuan Yang, Manyi Gong, Fu-Qiang Zhang, Linshuang Shi, Mengchao Dai, Fu-Zhi York, Darrin M. Liu, Shi Zhu, Tong Zhong, Zhicheng Lv, Jian Cheng, Jun Jia, Weile Chen, Mohan Ke, Guolin Weinan, E. Zhang, Linfeng Wang, Han AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Academy for Advanced Interdisciplinary Studies Peking University Beijing100871 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100871 China University of Chinese Academy of Sciences Beijing100871 China HEDPS CAPT College of Engineering Peking University Beijing100871 China Ningbo Institute of Materials Technology and Engineering Chinese Academy of Sciences Ningbo315201 China CAS Key Laboratory of Magnetic Materials and Devices Zhejiang Province Key Laboratory of Magnetic Materials and Application Technology Chinese Academy of Sciences Ningbo315201 China School of Electronics Engineering and Computer Science Peking University Beijing100871 China Shanghai Engineering Research Center of Molecular Therapeutics & New Drug Development School of Chemistry and Molecular Engineering East China Normal University Shanghai200062 China Laboratory for Biomolecular Simulation Research Institute for Quantitative Biomedicine Department of Chemistry and Chemical Biology Rutgers University PiscatawayNJ08854 United States Department of Chemistry Princeton University PrincetonNJ08540 United States College of Chemistry and Molecular Engineering Peking University Beijing100871 China Yuanpei College Peking University Beijing100871 China School of Electrical Engineering and Electronic Information Xihua University Chengdu610039 China State Key Laboratory of Superhard Materials College of Physics Jilin University Changchun130012 China Key Laboratory of Material Simulation Methods & Software of Ministry of Education College of Physics Jilin University Changchun130012 China International Center of Future Science Jilin University Changchun130012 China Key Laboratory for Quantum Materials of Zhejiang Province Department of Physics School of Science Westlake University Zhejiang Hangzhou310030 China Atomistic Simulations Italia

The rapid advancements in artificial intelligence (AI) are catalyzing transformative changes in atomic modeling, simulation, and design. AI-driven potential energy models have demonstrated the capability to conduct large-scale, long-duration simulations with the accuracy of ab initio electronic structure methods. However, the model generation process remains a bottleneck for large-scale applications. We propose a shift towards a model-centric ecosystem, wherein a large atomic model (LAM), pre-trained across multiple disciplines, can be efficiently fine-tuned and distilled for various downstream tasks, thereby establishing a new framework for molecular modeling. In this study, we introduce the DPA-2 architecture as a prototype for LAMs. Pre-trained on a diverse array of chemical and materials systems using a multi-task approach, DPA-2 demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning methodologies. Our approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research. Copyright © 2023, The Authors. All rights reserved.

关键词： Multi-task learning

On Phase Reduction and Time Period of Noisy Oscillators

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On Phase Reduction and Time Period of Noisy Oscillators

IEEE Annual Conference on Decision and Control

作者： Zahra Aminzare Philip Holmes Vaibhav Srivastava Department of Mathematics University of Iowa IA USA Program in Applied and Computational Mathematics Princeton Neuroscience Institute Princeton University Princeton NJ USA Electrical and Computer Engineering Michigan State University East Lansing MI USA

ISBN: (数字)9781728113982

ISBN: (纸本)9781728113999

We study phase reduction for noisy oscillator models by deriving a reduced order stochastic differential equation describing the phase evolution using the first and second order Phase Response Curves (PRCs). We discuss direct methods and ordinary differential equations for computing these PRCs, and derive approximate first and second moments of the time period of the oscillator models in terms of functions of the PRCs. We illustrate the theoretical results on a noisy Hopf bifurcation normal form, on a noisy Van der Pol oscillator, and on a noisy bursting neuron model.

关键词： Oscillators Limit-cycles Noise measurement Biological system modeling Perturbation methods Bifurcation Stochastic processes