Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session F62: Machine Learning for Quantum Matter IIFocus
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Sponsoring Units: DCOMP Chair: Iris Mowgood, Chapman University Room: Room 417 |
Tuesday, March 7, 2023 8:00AM - 8:36AM |
F62.00001: A Bayesian machine-learning approach to the quantum many-body problemInvited Talk: George Booth, King's College London Invited Speaker: George Booth The quantum many-body problem is a keystone challenge, with developments impacting a huge diversity of fields. At its heart is an exponentially complex space, which naturally lends itself to synergistic developments with the machine learning community. In this presentation, we will consider the problem from a Bayesian perspective, whereby the many-body wavefunction is rigorously and statistically inferred from a set of support states, in a novel form we have denoted the Gaussian Process State. We find that connections from this viewpoint naturally emerge with both tensor networks and neural quantum states. We will show that as well as providing a compact, expressive and systematically improvable approximation, we can also lean more heavily on machine learning ideas of generalization errors and regularization which can be efficiently formulated in this framework, to extend the toolset at hand to treat the challenge of quantum many-body problems. |
Tuesday, March 7, 2023 8:36AM - 8:48AM |
F62.00002: Electronic excited states in deep variational Monte Carlo Mike Entwistle, Zeno Schätzle, Paolo Erdman, Jan Hermann, Frank Noe Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. Here, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods. |
Tuesday, March 7, 2023 8:48AM - 9:00AM |
F62.00003: Improving Machine Learning Modelling of Physical Properties with Isometry Invariants Alya Alqaydi, Bartomeu Monserrat Machine learning techniques are increasingly capable of improving the accuracy of atomistic simulations. However, many challenges remain before we can build practical, robust, and fully transferable models. One of these challenges is the problem of quantifying the similarity between any two given structures. A promising route to addressing this problem are the recently developed isometry invariants for (periodic) point clouds, which are complete and Lipschitz continuous. We show that the efficient calculation of structural and compositional invariants across large inorganic materials datasets can improve data handling and model training in machine learning tasks, specifically to better understand, quantify, and impute the data. We also discuss how invariants-based distances can be used to optimize the selection of representative structures and perform a quantifiable exploration of phase transitions and predicted properties in terms of perturbations such as adding strain or changing the amount of disorder. |
Tuesday, March 7, 2023 9:00AM - 9:12AM |
F62.00004: Machine Learning Model of Generalized Force Field in Condensed Matter Systems Gia-Wei Chern, Puhan Zhang, Sheng Zhang We outline the general framework of machine learning (ML) methods for multi-scale dynamical modeling of condensed matter systems, and in particular of strongly correlated electron models. Complex spatial temporal behaviors in these systems often arise from the interplay between quasi-particles and the emergent dynamical classical degrees of freedom, such as local lattice distortions, spins, and order-parameters. Central to the proposed framework is the ML energy model that, by successfully emulating the time-consuming electronic structure calculation, can accurately predict a local energy based on the classical field in the intermediate neighborhood. In order to properly include the symmetry of the electron Hamiltonian, a crucial component of the ML energy model is the descriptor that transforms the neighborhood configuration into invariant feature variables. A general theory of the descriptor for the classical fields is formulated, and several specific implementations are also discussed. Our focus is on the group-theoretical method that offers a systematic and rigorous approach to compute invariants based on the bispectrum coefficients. We propose an efficient implementation of the bispectrum method based on the concept of reference irreducible representations. |
Tuesday, March 7, 2023 9:12AM - 9:24AM |
F62.00005: Improvements to Neural Network Backflow Wavefunctions Zejun Liu, Bryan K Clark The Neural Network backflow (NNBF) is a highly accurate variational wave-function ansatz for fermionic Hamiltonians. In this work, we consider a number of methodological developments to improve upon NNBF including looking at multideterminant expansions. We also compare the NNBF both empirically and analytically to other variational architectures understanding where it fits into the hiearchy of variational ansatz. We benchmark these new improvements on various model systems comparing the energetics and observables with other high-accuracy simulations. |
Tuesday, March 7, 2023 9:24AM - 9:36AM |
F62.00006: Similarities and differences in flat-band models with randomness detected by machine learning Takumi Kuroda, Tomonari Mizoguchi, Yasuhiro Hatsugai Since Anderson localization was proposed, disordered electron systems have been studied extensively. As a recent development, systems that have characteristic electronic structures in the clean limit have been actively studied. For example, the flat-band (FB) systems have attracted attention because of their characteristic behavior to disorder [1,2]. Besides, it has also been shown, from the technical point of view, that machine learning (ML) is a useful method for identifying characteristic real-space distributions of wavefunctions. In our previous work, we studied the phase classification of FB states of molecular orbital (MO) models by ML [3]. A MO model is a model constructed on the basis of a linear combination of atomic orbitals, and it is known that macroscopic degeneracy remains even in the presence of randomness [4,5,6]. |
Tuesday, March 7, 2023 9:36AM - 9:48AM |
F62.00007: Studying the Superfluid Ground-State of the Unitary Fermi Gas with Fermionic Neural Networks. Wan Tong Lou, Gino W Cassella, Halvard Sutterud, W Matthew C Foulkes, Johannes Knolle, David Pfau, James Spencer Understanding the properties of superfluidity has been a major challenge in condensed matter physics. Here we propose to tackle this challenge utilizing the recently developed Fermionic neural network Ansatz (FermiNet) for variational Monte Carlo (VMC) calculations, which has been proven successful in molecular systems as well as periodic homogeneous electron gas, often outperforming state-of-the-art methods. |
Tuesday, March 7, 2023 9:48AM - 10:00AM |
F62.00008: Machine learning quantum Monte Carlo: application to water clusters Matteo Peria, Michele Casula, A. Marco Saitta A complete understanding of the hydrogen bond and proton transfer mechanism in water is still lacking, since it requires an accurate potential energy surface (PES) and very expensive quantum mechanical simulations of the nuclear part. Reproducing this high-dimensional surface with current high-level computational chemistry methods is infeasible for the largest clusters. We test the gradient-based kernel ridge regression methods to reproduce the PES starting from a dataset of energies and forces of the protonated water hexamer obtained via simulations combining classical molecular dynamics (MD) for the nuclei and quantum Monte Carlo (QMC) for the electrons. The QMC+MD approach yields very accurate results for classical dynamics, which are however affected by the intrinsic noise inherent in the stochastic sampling of both nuclear and electronic phase space. Despite the intrinsic noise, QMC energies and forces can be successfully machine learned using less than 1000 samples and the derived force field can be used to run long and reliable MD simulations. |
Tuesday, March 7, 2023 10:00AM - 10:12AM |
F62.00009: Inverse Hamiltonian design by automatic differentiation Koji Inui, Yukitoshi Motome
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Tuesday, March 7, 2023 10:12AM - 10:24AM |
F62.00010: Variational simulations of fermionic matter with neural-network quantum states Jannes Nys, Giuseppe Carleo Neural networks have proven to form a powerful variational representation for the quantum states of quantum many-body systems, especially in >1d. While most research has focused on studying quantum spin systems, extending Neural-network Quantum states (NQS) to fermionic degrees of freedom remains underexplored. The main reason is the additional challenges introduced by fermionic anti-commutation relations. A first design choice in variational simulations of fermionic systems is to represent the state in first or second quantization. While the first requires explicit anti-symmetrization of the wave function through the use of determinants, the second can introduce non-local interactions in >1d after Jordan-Wigner transformations. In this work, we discuss our recent progress on how to obtain the low-energy spectrum of fermionic Hamiltonians (on a lattice), by mapping local fermionic Hamiltonians onto local spin Hamiltonians, as well as embedding symmetries in fermionic NQS. We will demonstrate how this allows us to use the power of NQS (originally designed for quantum spin systems) to study fermionic matter with Variational Monte Carlo. |
Tuesday, March 7, 2023 10:24AM - 10:36AM |
F62.00011: Langevin Dynamics/Monte Carlo Simulations of Nanoscale Dielectric Function Modulations of Moire Materials Steven B Hancock We have developed a fast and flexible computational scheme to calculate the complex valued, frequency dependent dielectric function of correlated materials. The premise of such a methodology is to use the atomistic crystal structure of materials and designate relatively simple bond length and bond-angle interactions, as well as internal field couplings to accommodate correlation. Once these interactions are appropriated, we simulate systems thin films with periodic boundary conditions via Langevin dynamics under an oscillating external electric field. We validate our method by recreating high-resoltuion infrared near-field experimental results of the dielectric function of perovskite oxide SmNiO3 . We show quantitative agreement with experimental data concerning the modulation of the nanoscale dielectric changes as a function of hydrogen doping and the prevalence of oxygen vacancies within the sample. We also show representative example of how our methodology can gain us nanoscale insight into the dielectric behavior of Moire patterned two-dimensional transition metal dichalcogenides and compare our results with high-resolution near-field measurements. |
Tuesday, March 7, 2023 10:36AM - 10:48AM |
F62.00012: Machine learning universal empirical pseudopotentials for density functional theory calculations Rokyeon Kim, Young-Woo Son Traditional empirical pseudopotentials allow for efficient calculations of electronic band structures. Such potentials, however, are not so versatile enough to reproduce wave functions and related quantities, and their transferability to different environments is limited. Here, we introduce a method to generate universal empirical pseudopotentials for density functional theory calculations with machine learning. The transferability of empirical pseudopotentials could be achieved by using both atom-density representations and machine-learning procedures. We demonstrate that these empirical pseudopotentials produce not only band structures, but also wave functions, total energies, forces, and other physical quantities without the self-consistent conditions. We apply the method to a few examples such as Si, Ge, and SiO2, finding excellent agreements with density functional theory results. |
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