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arXiv 2023年

作者： Sharma, Aniket Medeiros, Lia Chan, Chi-Kwan Halevi, Goni Mullen, Patrick D. Stone, James M. Wong, George N. Indian Institute of Science Education and Research Mohali Sector 81 SAS Nagar PO Manauli Punjab Mohali140306 India School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Ave. TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 N. Santa Rita TucsonAZ85721 United States Department of Astrophysical Sciences Princeton University 4 Ivy Lane PrincetonNJ08544 United States CCS-2 Los Alamos National Laboratory Los AlamosNM United States Center for Theoretical Astrophysics Los Alamos National Laboratory Los AlamosNM United States Princeton Gravity Initiative Princeton University PrincetonNJ08544 United States

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved space-times. We employ Google’s JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr metrics. JAX also enables Mahakala to run in parallel on both CPUs and GPUs and achieve speeds comparable to C-based codes. Mahakala natively uses the Cartesian Kerr-Schild coordinate system, which avoids numerical issues caused by the "pole" of spherical coordinates. We demonstrate Mahakala’s capabilities by simulating the 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to easily quantify the relative contribution of different regions of the flow to image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole. We also quantify the relative contribution of the disk, forward jet, and counter jet to 1.3 mm images. Copyright © 2023, The Authors. All rights reserved.

关键词： Python

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End-To-End Quantum Machine Learning Implemented with Controlled Quantum Dynamics

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Physical Review applied 2020年第6期14卷 064020-064020页

作者： Re-Bing Wu Xi Cao Pinchen Xie Yu-xi Liu Department of Automation Tsinghua University Beijing 100084 China Beijing National Research Center for Information Science and Technology Beijing 100084 China Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Institute of Microelectronics Tsinghua University Beijing 100084 China

To achieve quantum machine learning on imperfect noisy intermediate-scale quantum (NISQ) processors, the entire physical implementation should include as few as possible hand-designed modules with only a few ad hoc parameters to be determined. This work presents such a hardware-friendly end-to-end quantum-machine-learning scheme that can be implemented with imperfect NISQ processors. The proposal transforms the machine-learning task to the optimization of controlled quantum dynamics, in which the learning model is parameterized by experimentally tunable control variables. Our design also enables automated feature selection by encoding the raw input to quantum states through agent control variables. Comparing with the gate-based parameterized quantum circuits, the proposed end-to-end quantum-learning model is easy to implement as there are only a few ad hoc parameters to be determined. Numerical simulations on the benchmarking MNIST (Mixed National Institute of Standards and Technology) dataset of handwritten digits demonstrate that the model can achieve high performance using only 3–5 qubits without downsizing the dataset, which shows great potential for accomplishing large-scale real-world learning tasks on NISQ processors.

关键词： Machine learning Noise Quantum control Quantum information architectures & platforms Artificial neural networks

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A machine learning-based high-precision density functional method for drug-like molecules

Artificial Intelligence Chemistry

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Artificial Intelligence Chemistry 2024年第1期2卷

作者： Jin Xiao YiXiao Chen LinFeng Zhang Han Wang Tong Zhu Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development Shanghai Frontiers Science Center of Molecule Intelligent Syntheses School of Chemistry and Molecular Engineering East China Normal University Shanghai 200062 P.R. China Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA AI for Science Institute Beijing 100080 P.R. China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 P.R. China NYU-ECNU Center for Computational Chemistry at NYU Shanghai Shanghai 200062 P.R. China Shenzhen Institute of Advanced Technology Chinese Academy of Sciences Shenzhen 518005 P.R. China

In computer-aided drug discovery, accurately determining the structure and properties of drug-like molecules is of utmost importance. This necessitates the use of precise and efficient electronic structure methods. Here, we developed two deep learning-based density functional methods, namely DeePHF and DeePKS, specifically tailored for drug-like molecules. Notably, DeePKS incorporates self-consistency into its framework. With a limited dataset labelled at the CCSD(T)/def2-TZVP level, both models have been able to achieve chemical accuracy in calculating molecular energies and have demonstrated excellent transferability. We anticipate that further advancements in this field will lead to the development of high-quality density functional methods designed specifically for drug discovery purposes. This research showcases the capabilities of deep learning approaches in simplifying the construction complexity associated with traditional DFT methods.

关键词： Machine Learning Density Functional Theory DeePHF DeePKS

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Modeling liquid water by climbing up Jacob’s ladder in density functional theory facilitated by using deep neural network potentials

arXiv

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arXiv 2021年

作者： Zhang, Chunyi Tang, Fujie Chen, Mohan Zhang, Linfeng Qiu, Diana Y. Perdew, John P. Klein, Michael L. Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Chemistry Temple University PhiladelphiaPA19122 United States Institute for Computational Molecular Science Temple University PhiladelphiaPA19122 United States

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. In order to generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water towards the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. © 2021, CC BY.

关键词： Deep neural networks

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Critical pore radius and transport properties of disordered hard- And overlapping-sphere models

arXiv

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arXiv 2021年

作者： Klatt, Michael A. Ziff, Robert M. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Center for the Study of Complex Systems Department of Chemical Engineering University of Michigan Ann ArborMI48109 United States Department of Physics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, "quantizer" sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato. Adv. Wat. Resour. 140,103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size hδ2i, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size hδ2i, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to hδ2i. However, unlike hδ2i, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm hδ2i to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via target

关键词： Porous materials

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Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

arXiv

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arXiv 2024年

作者： Barton, Brandon Sagal, Jacob Feeney, Sean Grattan, George Patnaik, Pratik Oganesyan, Vadim Carr, Lincoln D. Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Department of Physics and Astronomy College of Staten Island City University of New York Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center City University of New York New YorkNY10016 United States

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over trotterized adiabatic quantum computation (TAQC) and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critial Hamming radius(CHR), or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. By combining IST-SAT with future classical or quantum approximation algorithms, larger gains may be achieved. The mechanism we present in this work thus presents a new path toward achieving quantum advantage in optimization. © 2024, CC BY.

关键词： Combinatorial optimization

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Accelerating Giant Impact Simulations with Machine Learning

arXiv

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arXiv 2024年

作者： Lammers, Caleb Cranmer, Miles Hadden, Sam Ho, Shirley Murray, Norman Tamayo, Daniel Department of Astrophysical Sciences Princeton University 4 Ivy Lane PrincetonNJ08544 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge Wilberforce Road CambridgeCB3 0WA United Kingdom Institute of Astronomy University of Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Kavli Institute for Cosmology University of Cambridge Madingley Road CambridgeCB3 0HA United Kingdom Canadian Institute for Theoretical Astrophysics University of Toronto 60 St. George Street TorontoONM5S 3H8 Canada Center for Computational Astrophysics Flatiron Institute New YorkNY10010 United States Department of Physics Center for Data Science New York University 726 Broadway New YorkNY10003 United States Department of Physics University of Toronto 60 St. George Street TorontoONM5S 1A7 Canada Department of Physics Harvey Mudd College ClaremontCA91711 United States

Constraining planet formation models based on the observed exoplanet population requires generating large samples of synthetic planetary systems, which can be computationally prohibitive. A significant bottleneck is simulating the giant impact phase, during which planetary embryos evolve gravitationally and combine to form planets, which may themselves experience later collisions. To accelerate giant impact simulations, we present a machine learning (ML) approach to predicting collisional outcomes in multiplanet systems. Trained on more than 500,000 N-body simulations of three-planet systems, we develop an ML model that can accurately predict which two planets will experience a collision, along with the state of the post-collision planets, from a short integration of the system's initial conditions. Our model greatly improves on non-ML baselines that rely on metrics from dynamics theory, which struggle to accurately predict which pair of planets will experience a collision. By combining with a model for predicting long-term stability, we create an ML-based giant impact emulator, which can predict the outcomes of giant impact simulations with reasonable accuracy and a speedup of up to four orders of magnitude. We expect our model to enable analyses that would not otherwise be computationally feasible. As such, we release our training code, along with an easy-to-use API for our collision outcome model and giant impact emulator. Copyright © 2024, The Authors. All rights reserved.

关键词： Exoplanets

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DeePN2: A deep learning-based non-Newtonian hydrodynamic model

arXiv

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arXiv 2021年

作者： Fang, Lidong Ge, Pei Zhang, Lei Weinan, E. Lei, Huan Department of Computational Mathematics Science and Engineering Michigan State University MI48824 United States School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC Shanghai Jiao Tong University 800 Dongchuan Road Shanghai200240 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100871 China AI for Science Institute Beijing100080 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Statistics and Probability Michigan State University MI48824 United States

A long standing problem in the modeling of non-Newtonian hydrodynamics of polymeric flows is the availability of reliable and interpretable hydrodynamic models that faithfully encode the underlying micro-scale polymer dynamics. The main complication arises from the long polymer relaxation time, the complex molecular structure and heterogeneous interaction. DeePN2, a deep learning-based non-Newtonian hydrodynamic model, has been proposed and has shown some success in systematically passing the micro-scale structural mechanics information to the macro-scale hydrodynamics for suspensions with simple polymer conformation and bond potential. The model retains a multi-scaled nature by mapping the polymer configurations into a set of symmetry-preserving macro-scale features. The extended constitutive laws for these macro-scale features can be directly learned from the kinetics of their micro-scale counterparts. In this paper, we develop DeePN2 using more complex micro-structural models. We show that DeePN2 can faithfully capture the broadly overlooked viscoelastic differences arising from the specific molecular structural mechanics without human intervention. © 2021, CC BY.

关键词： Non Newtonian flow

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Localization transition in three-dimensional stealthy hyperuniform disordered systems

arXiv

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arXiv 2021年

作者： Sgrignuoli, F. Torquato, S. Dal Negro, L. Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary’s Street BostonMA02215 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Division of Material Science and Engineering Boston University 15 Saint Mary’s Street BrooklineMA02446 United States Department of Physics Boston University 590 Commonwealth Avenue BostonMA02215 United States

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems (3D-SHDS) are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green’s matrix spectral method, we establish a transport phase diagram that demonstrates a clear delocalization-localization transition beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed sub-radiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and localization properties of light in stealthy hyperuniform structures and motivates the engineering of novel photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices. Copyright © 2021, The Authors. All rights reserved.

关键词： Phase diagrams

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A spacetime finite elements method to solve the dirac equation

arXiv

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arXiv 2021年

作者： Sundermann, Rylee Lim, Hyun Waybright, Jace Kimn, Jung-Han Department of Mathematics and Statistics South Dakota State University BrookingsSD57007 United States Computational Physics and Methods Group Los Alamos National Laboratory Los AlamosNM87545 United States Center for Theoretical Astrophysics Los Alamos National Laboratory Los AlamosNM87545 United States Applied Computer Science Group Los Alamos National Laboratory Los AlamosNM87545 United States Princeton Plasma Physics Laboratory Princeton University PrincetonNJ08543 United States

In this work, a fully implicit numerical approach based on space-time finite element method is presented to solve the Dirac equation in 1 (space) + 1 (time), 2 + 1, and 3 + 1 dimensions. We utilize PETSc/Tao library to implement our linear system and for using Krylov subspace based solvers such as GMRES. We demonstrate our method by analyzing several different cases including plane wave solution, Zitterbewegung, and Klein paradox. Parallel performance of this implementation is also presented. © 2021, CC BY.

关键词： Finite element method

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