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Xie H, Li ZH, Wang H, Zhang L, Wang L. Deep Variational Free Energy Approach to Dense Hydrogen. Phys Rev Lett 2023; 131:126501. [PMID: 37802941 DOI: 10.1103/physrevlett.131.126501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Revised: 08/01/2023] [Accepted: 08/14/2023] [Indexed: 10/08/2023]
Abstract
We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wave function at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. The predicted equation of state of dense hydrogen under planetary conditions is denser than the findings of ab initio molecular dynamics calculation and empirical chemical model. Moreover, direct access to the entropy and free energy of dense hydrogen opens new opportunities in planetary modeling and high-pressure physics research.
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Affiliation(s)
- Hao Xie
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zi-Hang Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Han Wang
- Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, China
| | - Linfeng Zhang
- DP Technology, Beijing 100080, China
- AI for Science Institute, Beijing 100080, China
| | - Lei Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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3
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Martyn JM, Najafi K, Luo D. Variational Neural-Network Ansatz for Continuum Quantum Field Theory. Phys Rev Lett 2023; 131:081601. [PMID: 37683171 DOI: 10.1103/physrevlett.131.081601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 07/21/2023] [Accepted: 07/25/2023] [Indexed: 09/10/2023]
Abstract
Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state's Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.
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Affiliation(s)
- John M Martyn
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
| | - Khadijeh Najafi
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
- MIT-IBM Watson AI Lab, Cambridge, Massachusetts 02142, USA
| | - Di Luo
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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4
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Wang H, Fu T, Du Y, Gao W, Huang K, Liu Z, Chandak P, Liu S, Van Katwyk P, Deac A, Anandkumar A, Bergen K, Gomes CP, Ho S, Kohli P, Lasenby J, Leskovec J, Liu TY, Manrai A, Marks D, Ramsundar B, Song L, Sun J, Tang J, Veličković P, Welling M, Zhang L, Coley CW, Bengio Y, Zitnik M. Scientific discovery in the age of artificial intelligence. Nature 2023; 620:47-60. [PMID: 37532811 DOI: 10.1038/s41586-023-06221-2] [Citation(s) in RCA: 44] [Impact Index Per Article: 44.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 05/16/2023] [Indexed: 08/04/2023]
Abstract
Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment and accelerate research, helping scientists to generate hypotheses, design experiments, collect and interpret large datasets, and gain insights that might not have been possible using traditional scientific methods alone. Here we examine breakthroughs over the past decade that include self-supervised learning, which allows models to be trained on vast amounts of unlabelled data, and geometric deep learning, which leverages knowledge about the structure of scientific data to enhance model accuracy and efficiency. Generative AI methods can create designs, such as small-molecule drugs and proteins, by analysing diverse data modalities, including images and sequences. We discuss how these methods can help scientists throughout the scientific process and the central issues that remain despite such advances. Both developers and users of AI toolsneed a better understanding of when such approaches need improvement, and challenges posed by poor data quality and stewardship remain. These issues cut across scientific disciplines and require developing foundational algorithmic approaches that can contribute to scientific understanding or acquire it autonomously, making them critical areas of focus for AI innovation.
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Affiliation(s)
- Hanchen Wang
- Department of Engineering, University of Cambridge, Cambridge, UK
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA
- Department of Research and Early Development, Genentech Inc, South San Francisco, CA, USA
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | - Tianfan Fu
- Department of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - Yuanqi Du
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Wenhao Gao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kexin Huang
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | - Ziming Liu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Payal Chandak
- Harvard-MIT Program in Health Sciences and Technology, Cambridge, MA, USA
| | - Shengchao Liu
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Peter Van Katwyk
- Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA
- Data Science Institute, Brown University, Providence, RI, USA
| | - Andreea Deac
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Anima Anandkumar
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA
- NVIDIA, Santa Clara, CA, USA
| | - Karianne Bergen
- Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA
- Data Science Institute, Brown University, Providence, RI, USA
| | - Carla P Gomes
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Shirley Ho
- Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA
- Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA
- Department of Physics and Center for Data Science, New York University, New York, NY, USA
| | | | - Joan Lasenby
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Jure Leskovec
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | | | - Arjun Manrai
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA
| | - Debora Marks
- Department of Systems Biology, Harvard Medical School, Boston, MA, USA
- Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | | | - Le Song
- BioMap, Beijing, China
- Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates
| | - Jimeng Sun
- University of Illinois at Urbana-Champaign, Champaign, IL, USA
| | - Jian Tang
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- HEC Montréal, Montreal, Quebec, Canada
- CIFAR AI Chair, Toronto, Ontario, Canada
| | - Petar Veličković
- Google DeepMind, London, UK
- Department of Computer Science and Technology, University of Cambridge, Cambridge, UK
| | - Max Welling
- University of Amsterdam, Amsterdam, Netherlands
- Microsoft Research Amsterdam, Amsterdam, Netherlands
| | - Linfeng Zhang
- DP Technology, Beijing, China
- AI for Science Institute, Beijing, China
| | - Connor W Coley
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yoshua Bengio
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Marinka Zitnik
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA.
- Broad Institute of MIT and Harvard, Cambridge, MA, USA.
- Harvard Data Science Initiative, Cambridge, MA, USA.
- Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA, USA.
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6
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Schmitz N, Müller KR, Chmiela S. Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields. J Phys Chem Lett 2022; 13:10183-10189. [PMID: 36279418 PMCID: PMC9639201 DOI: 10.1021/acs.jpclett.2c02632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process, effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems─all of high value to the FF community─but also the simple inclusion of further physical knowledge, such as higher-order information (e.g., Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.
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Affiliation(s)
| | - Klaus-Robert Müller
- Machine
Learning Group, Technische Universität
Berlin, 10587Berlin, Germany
- BIFOLD
- Berlin Institute for the Foundations of Learning and Data, 10587Berlin, Germany
- Department
of Artificial Intelligence, Korea University, Seongbuk-gu, Seoul02841, Korea
- Max
Planck Institute for Informatics, Stuhlsatzenhausweg, 66123Saarbrücken, Germany
- Google
Research, Brain Team, 10117Berlin, Germany
| | - Stefan Chmiela
- Machine
Learning Group, Technische Universität
Berlin, 10587Berlin, Germany
- BIFOLD
- Berlin Institute for the Foundations of Learning and Data, 10587Berlin, Germany
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8
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Rosenberger D, Barros K, Germann TC, Lubbers N. Machine learning of consistent thermodynamic models using automatic differentiation. Phys Rev E 2022; 105:045301. [PMID: 35590626 DOI: 10.1103/physreve.105.045301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 03/09/2022] [Indexed: 06/15/2023]
Abstract
We propose a data-driven method to describe consistent equations of state (EOS) for arbitrary systems. Complex EOS are traditionally obtained by fitting suitable analytical expressions to thermophysical data. A key aspect of EOS is that the relationships between state variables are given by derivatives of the system free energy. In this work, we model the free energy with an artificial neural network and utilize automatic differentiation to directly learn the derivatives of the free energy. We demonstrate this approach on two different systems, the analytic van der Waals EOS and published data for the Lennard-Jones fluid, and we show that it is advantageous over direct learning of thermodynamic properties (i.e., not as derivatives of the free energy but as independent properties), in terms of both accuracy and the exact preservation of the Maxwell relations. Furthermore, the method implicitly provides the free energy of a system without explicit integration.
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Affiliation(s)
- David Rosenberger
- Los Alamos National Laboratory, Theoretical Division, Physics and Chemistry of Materials Group, Los Alamos, New Mexico 87545, USA
| | - Kipton Barros
- Los Alamos National Laboratory, Theoretical Division, Physics and Chemistry of Materials Group, Los Alamos, New Mexico 87545, USA
| | - Timothy C Germann
- Los Alamos National Laboratory, Theoretical Division, Physics and Chemistry of Materials Group, Los Alamos, New Mexico 87545, USA
| | - Nicholas Lubbers
- Los Alamos National Laboratory, Computer, Computational & Statistical Sciences Division, Information Sciences Group, Los Alamos, New Mexico 87545, USA
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