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DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Satisfiability of logic programming based on radial basis function neural networks

In this paper, we propose a new technique to test the Satisfiability of propositional logic programming and quantified Boolean formula problem in radial basis function neural networks. For this purpose, we built radial basis function neural networks to represent the proportional logic which has exactly three variables in each clause. We used the Prey-predator algorithm to calculate the output weights of the neural networks, while the K-means clustering algorithm is used to determine the hidden parameters (the centers and the widths). Mean of the sum squared error function is used to measure the activity of the two algorithms. We applied the developed technique with the recurrent radial basis function neural networks to represent the quantified Boolean formulas. The new technique can be applied to solve many applications such as electronic circuits and NP-complete problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

A Comprehensive Comparative Study of Active Learning Schemes for Nanophotonics Design

We present a benchmarking study of active learning (AL) schemes for designing planar multilayer nanophotonic metamaterials, where the design tasks are formulated as binary optimization problems. Different surrogate models, including factorization machine (FM), Gaussian process regression (GPR), and convolutional neural network (CNN), combined with different optimization methods, including exhaustive enumeration, discrete particle swarm optimization (DPSO), quantum annealing (QA), hybrid QA, and simulated annealing are studied. The benchmark cases investigated range from small problems with short binary lengths (N = 25) to large problems with N up to 100, focusing on the design of two classes of photonic structures, including antireflective coatings for the long-wavelength infrared region and transparent radiative coolers. For small problems, CNN coupled with DPSO in AL achieves the best performance. As N increases, FM with QA outperforms GPR and CNN. For FM-based AL, hybrid QA yields the best optimization results, particularly in high-dimensional cases (N = 100). These results demonstrate that the optimization method can significantly affect in AL performance as N increases, and that QA-based optimization can provide practical routes for mitigating the optimization bottleneck in high-dimensional problems.

Jung, Serang [Kyung Hee University, Korea]↗

DOE OSTI2022

Crossing Versus Locking: Bit Threads and Continuum Multiflows

Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu–Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. Here, we investigate for which choices of bound a given set of boundary regions can be “locked”, in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings

This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory

It is explained why the set of the fundamental empirical features of traffic breakdown (a transition from free flow to congested traffic) should be the empirical basis for any traffic and transportation theory that can be reliable used for control and optimization in traffic networks. It is shown that generally accepted fundamentals and methodologies of traffic and transportation theory are not consistent with the set of the fundamental empirical features of traffic breakdown at a highway bottleneck. To these fundamentals and methodologies of traffic and transportation theory belong (i) Lighthill-Whitham-Richards (LWR) theory, (ii) the General Motors (GM) model class (for example, Herman, Gazis et al. GM model, Gipps’s model, Payne’s model, Newell’s optimal velocity (OV) model, Wiedemann’s model, Bando et al. OV model, Treiber’s IDM, Krauß’s model), (iii) the understanding of highway capacity as a particular stochastic value, and (iv) principles for traffic and transportation network optimization and control (for example, Wardrop’s user equilibrium (UE) and system optimum (SO) principles). Alternatively to these generally accepted fundamentals and methodologies of traffic and transportation theory, we discuss three-phase traffic theory as the basis for traffic flow modeling as well as briefly consider the network breakdown minimization (BM) principle for the optimization of traffic and transportation networks with road bottlenecks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Persistent topological features of dynamical systems

Inspired by an early work of Muldoon et al., Physica D 65, 1–16 (1993), we present a general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure. The obtained simplicial complex preserves all pertinent topological features of the reconstructed phase space, and it may be analyzed from topological, combinatorial, and algebraic aspects. In focus of this study is the computation of homology of the invariant set of some well known dynamical systems that display chaotic behavior. Persistent homology of simplicial complex and its relationship with the embedding dimensions are examined by studying the lifetime of topological features and topological noise. The consistency of topological properties for different dynamic regimes and embedding dimensions is examined. The obtained results shed new light on the topological properties of the reconstructed phase space and open up new possibilities for application of advanced topological methods. The method presented here may be used as a generic method for constructing simplicial complex from a scalar time series that has a number of advantages compared to the mapping of the same time series to a complex network.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity

Here, we investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). Furthermore, we suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Computational Workflow for Accelerated Molecular Design Using Quantum Chemical Simulations and Deep Learning Models

Efficient methods for searching the chemical space of molecular compounds are needed to automate and accelerate the design of new functional molecules such as pharmaceuticals. Given the high cost in both resources and time for experimental efforts, computational approaches play a key role in guiding the selection of promising molecules for further investigation. Here, we construct a workflow to accelerate design by combining approximate quantum chemical methods [i.e. density-functional tight-binding (DFTB)], a graph convolutional neural network (GCNN) surrogate model for chemical property prediction, and a masked language model (MLM) for molecule generation. Property data from the DFTB calculations are used to train the surrogate model; the surrogate model is used to score candidates generated by the MLM. The surrogate reduces computation time by orders of magnitude compared to the DFTB calculations, enabling an increased search of chemical space. Furthermore, the MLM generates a diverse set of chemical modifications based on pre-training from a large compound library. We utilize the workflow to search for near-infrared photoactive molecules by minimizing the predicted HOMO-LUMO gap as the target property. Our results show that the workflow can generate optimized molecules outside of the original training set, which suggests that iterations of the workflow could be useful for searching vast chemical spaces in a wide range of design problems.

Blanchard, Andrew↗

DOE OSTI2021

Potential energy surfaces for high-energy N + O 2 collisions

Potential energy surfaces for high-energy collisions between an oxygen molecule and a nitrogen atom are useful for modeling chemical dynamics in shock waves. In the present work, we present doublet, quartet, and sextet potential energy surfaces that are suitable for studying collisions of O 2 ( 3 Σ$^{–}_{g}$) with N( 4 S) in the electronically adiabatic approximation. Two sets of surfaces are developed, one using neural networks (NNs) with permutationally invariant polynomials (PIPs) and one with the least-squares many-body (MB) method, where a two-body part is an accurate diatomic potential and the three-body part is expressed with connected PIPs in mixed-exponential-Gaussian bond order variables (MEGs). We find, using the same dataset for both fits, that the fitting performance of the PIP-NN method is significantly better than that of the MB-PIP-MEG method, even though the MB-PIP-MEG fit uses a higher-order PIP than those used in previous MB-PIP-MEG fits of related systems (such as N 4 and N 2 O 2 ). However, the evaluation of the PIP-NN fit in trajectory calculations requires about 5 times more computer time than is required for the MB-PIP-MEG fit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Quantum paramagnetism in a non-Kramers rare-earth oxide: Monoclinic Pr 2 Ti 2 O 7

Little is so far known about the magnetism of the A 2 B 2 O 7 monoclinic layered perovskites that replace the spin-ice supporting pyrochlore structure for r A /r B > 1.78. We show that high quality monoclinic Pr 2 Ti 2 O 7 single crystals with a three-dimensional network of non-Kramers Pr 3+ ions that interact through edge-sharing superexchange interactions, form a singlet ground-state quantum paramagnet that does not undergo any magnetic phase transitions down to, at least, 1.8 K. The chemical phase stability, structure, and magnetic properties of the layered perovskite Pr 2 Ti 2 O 7 were investigated using x-ray diffraction, transmission electron microscopy, and magnetization measurements. Synthesis of polycrystalline samples with the nominal compositions of Pr 2 Ti 2+x O 7 (–0.16 ≤ x ≤ 0.16 ) showed that deviations from the Pr 2 Ti 2 O 7 stoichiometry lead to secondary phases of related structures including the perovskite phase Pr 2/3 TiO 3 and the orthorhombic phases Pr 4 Ti 9 O 24 and Pr 2 TiO 5 . No indications of site disordering (stuffing and antistuffing) or vacancy defects were observed in the Pr 2 Ti 2 O 7 majority phase. A procedure for growth of high-structural-quality stoichiometric single crystals of Pr 2 Ti 2 O 7 by the traveling solvent floating zone method is reported. Thermomagnetic measurements of single-crystalline Pr 2 Ti 2 O 7 reveal an isolated singlet ground state that we associate with the low-symmetry crystal electric-field environments that split the (2J + 1 = 9)-fold degenerate spin-orbital multiplets of the four differently coordinated Pr 3+ ions into 36 isolated singlets resulting in an anisotropic temperature-independent van Vleck susceptibility at low T. Here, a small isotropic Curie term is associated with 0.96(2)% noninteracting Pr 4+ impurities.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Catalysis of Ground State cis → trans Isomerization of Bacteriorhodopsin’s Retinal Chromophore by a Hydrogen-Bond Network

For the photocycle of the membrane protein bacteriorhodopsin to proceed efficiently, the thermal 13-cis to all-trans back-isomerization of the retinal chromophore must return the protein to its resting state on a time-scale of milliseconds. Here, we report on quantum mechanical/molecular mechanical energy calculations examining the structural and energetic determinants of the retinal cis–trans isomerization in the protein environment. The results suggest that a hydrogen-bonded network consisting of the retinal Schiff base, active site amino acid residues, and water molecules can stabilize the twisted retinal, thus reducing the intrinsic energy cost of the cis–trans thermal isomerization barrier.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2014

Pulsed Laser Deposition of Photoresponsive Two-Dimensional GaSe Nanosheet Networks

Here we explore pulsed laser deposition (PLD), a well known and versatile synthesis method principally used for epitaxial oxide thin film growth, for the synthesis of functional metal chalcogenide (GaSe) nanosheet networks by stoichiometric transfer of laser vaporized material from bulk GaSe targets in Ar background gas. Uniform coverage of interconnected, crystalline, few-layer, photoresponsive GaSe nanosheets in both in-plane and out-of-plane orientations were achieved under different ablation plume conditions over ~1.5 cm2 areas. Plume propagation was characterized by in situ ICCD-imaging. High (1 Torr) Ar background gas pressures were found to be crucial for the stoichiometric growth of GaSe nanosheet networks. Individual 1-3 layer GaSe triangular nanosheets of ~ 200 nm domain size were formed within 30 laser pulses, coalescing to form nanosheet networks in as few as 100 laser pulses. The thickness of the deposited networks increased linearly with pulse number, adding layers in a two-dimensional (2D) growth mode while maintaining a surface roughness of 2 GaSe layers for increasing overall thickness. Field effect transistors using these interconnected crystalline GaSe networks showed p-type semiconducting characteristics with mobilities reaching as high as 0.1 cm2V-1s-1. Spectrally-resolved photoresponsivities and external quantum efficiencies ranged from 0.4 AW-1 and 100% at 700 nm, to 1.4 AW-1 and 600 % at 240 nm, respectively. Pulsed laser deposition under these conditions appears to provide a versatile and rapid approach to stoichiometrically transfer and deposit photoresponsive networks of 2D nanosheets with digital thickness control and substrate-scale uniformity for a variety of applications.

GaSe↗

DOE OSTI2026

Shuttling Majorana zero modes in disordered and noisy topological superconductors

The braiding of Majorana zero modes (MZMs) forms the fundamental building block for topological quantum computation. Braiding protocols which involve the physical exchange of MZMs are typically envisioned on a network of topological superconducting wires. An important component of these protocols is the transport of MZMs, which can be performed by using electric gates to locally tune sections of the wire between topologically trivial and nontrivial phases. In this work, we numerically simulate this transport by tuning a single section of a superconducting wire which contains either disorder (uncorrelated and correlated) or noise. We focus on the impact of these additional effects on the diabatic error, which describes unwanted transitions between the ground state and excited states. We show that the behavior of the average diabatic error is predominantly controlled by the statistics of the minimum bulk energy gap which is suppressed in the presence of disorder. The increase in diabatic error can be several orders of magnitude and is most deleterious when the disorder correlation length is a finite fraction of the transport distance and negligible when these lengths are far apart. In the presence of noise, the diabatic error is significantly enhanced due to optical transitions which depend on the minimum bulk energy gap as well as the frequency modes present in the noise. The results presented here serve to further characterize the diabatic error in disordered and noisy settings, which are important considerations in practical implementations of physical braiding schemes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Investigating the Chinese postman problem on a quantum annealer

The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and simulated annealing, and using a D-Wave device. The efficiency of quantum annealing with respect to the simulated annealing has been demonstrated using the optimal time to solution metric. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution

36 MATERIALS SCIENCE↗

DOE OSTI2022

Two-dimensional materials for bio-realistic neuronal computing networks

Two-dimensional (2D) van der Waals materials have found broad utility in a diverse range of applications including electronics, optoelectronics, renewable energy, and quantum information technologies. Meanwhile, exponentially growing digital data coupled with the ubiquity of artificial intelligence algorithms have generated significant interest in edge neuromorphic computing as an alternative to centralized cloud computing. The drive to incorporate neuroscience principles into computing hardware is motivated by the low power consumption, parallel processing, and reconfigurability of the human brain. The diverse library of 2D materials with atomic-level thicknesses, exceptional electrostatic tunability, and integration versatility is particularly well-suited for realizing bio-realistic synaptic and neuronal functionality. Here, we summarize past and present work in this field and outline the frontier challenges that have not yet been overcome. Here we also delineate potential solutions and suggest that the neuroscience principles of criticality and synchrony have the potential to inspire breakthrough applications of 2D materials in neuronal computing networks.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Quantum computing based hybrid deep learning for fault diagnosis in electrical power systems

Quantum computing (QC) and deep learning have shown promise of supporting transformative advances and have recently gained popularity in a wide range of areas. Here, this paper proposes a hybrid QC-based deep learning framework for fault diagnosis of electrical power systems that combine the feature extraction capabilities of conditional restricted Boltzmann machine with an efficient classification of deep networks. Computational challenges stemming from the complexities of such deep learning models are overcome by QC-based training methodologies that effectively leverage the complementary strengths of quantum assisted learning and classical training techniques. The proposed hybrid QC-based deep learning framework is tested on a simulated electrical power system with 30 buses and wide variations of substation and transmission line faults, to demonstrate the framework’s applicability, efficiency, and generalization capabilities. High computational efficiency is enjoyed by the proposed hybrid approach in terms of computational effort required and quality of diagnosis performance over classical training methods. In addition, superior and reliable fault diagnosis performance with faster response time is achieved over state-of-the-art pattern recognition methods based on artificial neural networks (ANN) and decision trees (DT).

42 ENGINEERING↗

DOE OSTI2021

TensorBNN: Bayesian inference for neural networks using TensorFlow

We report that TensorBNN is a new package based on TensorFlow that implements Bayesian inference for modern neural network models. The posterior density of neural network model parameters is represented as a point cloud sampled using Hamiltonian Monte Carlo. The TensorBNN package leverages TensorFlow's architecture and its ability to use modern graphics processing units in both the training and prediction stages.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗