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arXiv 2025年

作者： Tang, Yingheng Xu, Wenbin Cao, Jie Ma, Jianzhu Gao, Weilu Farrell, Steve Erichson, Benjamin Mahoney, Michael W. Nonaka, Andy Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States NSF National AI Institute for Student-AI Teaming University of Colorado at Boulder Boulder United States Institute for AI Industry Research Tsinghua University Beijing China Department of Electrical and Computer Engineering The University of Utah Salt Lake CityUT United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States International Computer Science Institute BerkeleyCA United States Department of Statistics University of California at Berkeley BerkeleyCA United States

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material structure data with language-based information through multi-modal large language models (LLMs) offers great potential to support these efforts by enhancing human–AI interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multi-modal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat employs a bridging module to effectively align a pretrained machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat significantly improves performance in material property prediction and human-AI interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis. © 2025, CC BY.

关键词： Materials properties

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Semantic preserving bijective mappings of mathematical formulae between document preparation systems and computer algebra systems

arXiv

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arXiv 2021年

作者： Cohl, Howard S. Schubotz, Moritz Youssef, Abdou Greiner-Petter, André Gerhard, Jürgen Saunders, Bonita V. McClain, Marjorie A. Applied and Computational Mathematics Division NIST GaithersburgMD United States Dept. of Computer and Information Science University of Konstanz Konstanz Germany Dept. of Computer Science GWU WashingtonDC United States DSIMG Technische Universität Berlin Germany Maplesoft WaterlooON Canada

Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well. © 2021, CC BY.

关键词： Semantics

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A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

arXiv

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arXiv 2024年

作者： Hirsbrunner, Mark R. Mullinax, J. Wayne Shen, Yizhi Williams-Young, David B. Klymko, Katherine Van Beeumen, Roel Tubman, Norm M. Department of Physics University of Illinois at Urbana-Champaign UrbanaIL61801 United States USRA Research Institute for Advanced Computer Science Mountain ViewCA94043 United States KBR Inc. NASA Ames Research Center Moffett FieldCA94035 United States Intelligent Systems Division NASA Ames Research Center Moffett FieldCA94035 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States NERSC Lawrence Berkeley National Lab BerkeleyCA94720 United States

Recent research has shown that wavefunction evolution in real- and imaginary-time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at a local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima. © 2024, CC BY-NC-SA.

关键词： Ground state

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Neural FIM for learning Fisher information metrics from point cloud data

arXiv

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arXiv 2023年

作者： Fasina, Oluwadamilola Huguet, Guillaume Tong, Alexander Zhang, Yanlei Wolf, Guy Nickel, Maximilian Adelstein, Ian Krishnaswamy, Smita Applied Math Program Yale University New HavenCT United States Mila - Quebec AI Institute MontrealQC Canada Department of Mathematics and Statistics Université de Montréal MontrealQC Canada Department of Computer Science and Operations Research Université de Montréal MontrealQC Canada FAIR Meta AI United States Department of Math Yale University New HavenCT United States Department of Computer Science Yale University New HavenCT United States Department of Genetics Yale University New HavenCT United States

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells). Copyright © 2023, The Authors. All rights reserved.

关键词： Embeddings

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The Manifold Scattering Transform for High-Dimensional Point Cloud Data

arXiv

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arXiv 2022年

作者： Chew, Joyce Steach, Holly R. Viswanath, Siddharth Wu, Hau-Tieng Hirn, Matthew Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael UCLA Department of Mathematics Los AngelesCA United States Yale University Department of Genetics New HavenCT United States UC Irvine Department of Computer Science IrvineCA United States Duke University Department of Mathematics DurhamNC United States Duke University Department of Statistical Science DurhamNC United States Michigan State University Department of Mathematics East Lansing United States Michigan State University Department of CMSE East Lansing United States Yale University Department of Computer Science New HavenCT United States Yale University Applied Math Program New HavenCT United States

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification *** Codes 68T07 Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

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Direct Visualization of a Disorder Driven Electronic Smectic Phase in Dirac Nodal Line Semimetal GdSbTe

arXiv

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arXiv 2024年

作者： Venkatesan, Balaji Guan, Syu-You Chang, Jen-Te Chiu, Shiang-Bin Yang, Po-Yuan Su, Chih-Chuan Chang, Tay-Rong Raju, Kalaivanan Sankar, Raman Fongchaiya, Somboon Chu, Ming-Wen Chang, Chia-Seng Chang, Guoqing Lin, Hsin Del Maestro, Adrian Kao, Ying-Jer Chuang, Tien-Ming Department of Physics National Taiwan University Taipei10617 Taiwan Nano Science and Technology Program Taiwan International Graduate Program Academia Sinica National Taiwan University Taipei11529 Taiwan Institute of Physics Academia Sinica Taipei11529 Taiwan Department of Physics National Cheng-Kung University Tainan701 Taiwan Center for Condensed Matter Sciences National Taiwan University Taipei10617 Taiwan Molecular Science and Technology Program Taiwan International Graduate Program Academia Sinica Taipei11529 Taiwan Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link 637371 Singapore Department of Physics and Astronomy University of Tennessee KnoxvilleTN37996 United States Institute for Advanced Materials & Manufacturing University of Tennessee KnoxvilleTN37996 United States Min H. Kao Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN37996 United States Center for Quantum Science and Technology National Taiwan University Taipei10607 Taiwan

Electronic liquid crystal (ELC) phases are spontaneous symmetry breaking states believed to arise from strong electron correlation in quantum materials such as cuprates and iron pnictides. Here, we report a direct observation of a smectic phase in a weakly correlated Dirac nodal line (DNL) semimetal GdSbxTe2-x. Incommensurate smectic charge modulation and intense local unidirectional nanostructure are visualized by using spectroscopic imaging - scanning tunneling microscopy. As topological materials with symmetry protected Dirac or Weyl fermions are mostly weakly correlated, the discovery of such an ELC phase are anomalous and raise questions on the origin of their emergence. Specifically, we demonstrate how chemical substitution generates these symmetry breaking phases before the system undergoes a charge density wave (CDW) - orthorhombic structural transition. Our results highlight the importance of impurities in realizing ELC phases and present a new material platform for exploring the interplay among quenched disorder, topology and electron correlation. Copyright © 2024, The Authors. All rights reserved.

关键词： Charge density waves

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Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI

arXiv

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arXiv 2024年

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. © 2024, CC BY-NC-ND.

关键词： Large datasets

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Three-dimensional stagnation point motion of bioconvection nanofluid via moving stretching sheet with convective and anisotropic slip condition

引用

Partial Differential Equations in applied mathematics 2024年 12卷

作者： Pratyusha, Nune Tarakaramu, Nainaru R, Suresh Babu Somasekhar Srinivas, V.K. Ahmad, Furqan Waqas, M. Abdullaeva, Barno Gupta, Manish MLR Institute of Technology Dundigal Police Station road Telangana Hyderabad 500043 India Department of Mathematics School of Liberal Arts and Sciences Mohan Babu University Sree Sainath Nagar A.P Tirupati 517102 India Department of Mathematics M S Ramaiah Institute of Technology Karnataka Bangalore 560054 India Western Caspian University Baku Azerbaijan NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Department of Mathematics and Information Technologies Vice-Rector for Scientific Affairs Tashkent State Pedagogical University Tashkent Uzbekistan Division of Research and Development Lovely Professional University Phagwara India

The current article deals with the SM of a NFs on a 3D moving surface containing bioconvection, microorganisms, and convective conditions over anisotropic slip. This work reports describes the characteristics of bioconvection aspects of nanofluid containing microorganisms with anisotropic slip condition. The study may be important from the application point of view in microfluidic devices, antibiotics, enhanced oil recovery and many other areas. Applying the similarity variables, the basic gov. Eqs are translated to ordinary ones, and such Eqs are calculate by R-K-F fourth order programming with shooting scheme by MATLAB software. The physical parameters on the moving surface are explained in detail via graphs. We found that the temperature increases with a higher revolution and larger numerical numbers (convection parameter), while the HTR declined for various values of the SFP. The HTR enhances with surface convection, and therefore, the convection condition is helpful in reducing the viscous drag on the moving SS. © 2024 The Author(s)

关键词： Anisotropic slip Convective conditions Motile microorganisms Nanoparticles Stagnation point

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Two-step electronic response to magnetic ordering in a van der Waals ferromagnet

引用

Physical Review B 2024年第4期109卷 045416-045416页

作者： Han Wu Jian-Xin Zhu Lebing Chen Matthew W. Butcher Ziqin Yue Dongsheng Yuan Yu He Ji Seop Oh Bin Gao Jianwei Huang Shan Wu Cheng Gong Yucheng Guo Sung-Kwan Mo Jonathan Denlinger Donghui Lu Makoto Hashimoto Matthew B. Stone Alexander I. Kolesnikov Songxue Chi Junichiro Kono Andriy H. Nevidomskyy Robert J. Birgeneau Pengcheng Dai Ming Yi Department of Physics and Astronomy and Rice Center for Quantum Materials Rice University Houston Texas 77005 USA Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Center for Integrated Nanotechnologies Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Department of Physics University of California at Berkeley Berkeley California 94720 USA Applied Physics Graduate Program Smalley-Curl Institute Rice University Houston Texas 77005 USA Materials Sciences Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA National Institute for Materials Science 1-1 Namiki Tsukuba Ibaraki 305-0044 Japan Department of Applied Physics Yale University New Haven Connecticut 06511 USA Department of Electrical and Computer Engineering and Quantum Technology Center University of Maryland College Park Maryland 20742 USA Advanced Light Source Lawrence Berkeley National Laboratory Berkeley California 94720 USA Stanford Synchrotron Radiation Lightsource SLAC National Accelerator Laboratory Menlo Park California 94025 USA Neutron Scattering Division Oak Ridge National Laboratory Oak Ridge Tennessee 37831 USA Department of Electrical and Computer Engineering Rice University Houston Texas 77005 USA Smalley-Curl Institute Rice University Houston Texas 77005 USA Department of Material Science and Nanoengineering Rice University Houston Texas 77005 USA Department of Materials Science and Engineering University of California Berkeley California 94720 USA

The two-dimensional material Cr2Ge2Te6 is a member of the class of insulating van der Waals (vdW) magnets. Here, using high resolution angle-resolved photoemission spectroscopy in a detailed temperature dependence study, we identify a clear response of the electronic structure to a dimensional crossover in the form of two distinct temperature scales marking onsets of modifications in the electronic structure. Specifically, we observe Te p-orbital-dominated bands to undergo changes at the Curie transition temperature TC while the Cr d-orbital-dominated bands begin evolving at a higher temperature scale. Combined with neutron scattering, density functional theory calculations, and Monte Carlo simulations, we find that the electronic system can be consistently understood to respond sequentially to the distinct temperatures at which in-plane and out-of-plane spin correlations exceed a characteristic length scale. Our findings reveal the sensitivity of the orbital-selective electronic structure for probing the dynamical evolution of local moment correlations in vdW insulating magnets.

关键词： Electronic structure Magnetic order Magnetic phase transitions Van der Waals systems Angle-resolved photoemission spectroscopy

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Beyond trees: classification with sparse pairwise dependencies

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 7728-7760页

作者： Yaniv Tenzer Amit Moscovich Mary Frances Dorn Boaz Nadler Clifford Spiegelman Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ Los Alamos National Laboratory Los Alamos NM Department of Statistics Texas A&M University College Station TX

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attaining low classification errors. In this setting, the optimal classifier is linear in the log-transformed univariate and bivariate densities that correspond to the tree edges. In practice, observed data may not be well approximated by trees. Yet, motivated by the importance of pairwise dependencies for accurate classification, here we propose to approximate the optimal decision boundary by a sparse linear combination of the univariate and bivariate log-transformed densities. Our proposed approach is semi-parametric in nature: we non-parametrically estimate the univariate and bivariate densities, remove pairs of variables that are nearly independent using the Hilbert-Schmidt independence criterion, and finally construct a linear SVM using the retained log-transformed densities. We demonstrate on synthetic and real data sets, that our classifier, named SLB (sparse log-bivariate density), is competitive with other popular classification methods.

关键词： binary classification graphical model Bayesian network sparsity semi-parametric

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