Physics-Informed Neural Networks for Cardiac Activation Mapping
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs–Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗
Quantum-Based Molecular Dynamics Simulations Using Tensor Cores
Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix–matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born–Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born–Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Neural Network Molecular Dynamics at Scale
Neural network molecular dynamics (NNMD) simulations could revolutionize atomistic modeling of materials with quantum-mechanical accuracy at a fraction of computational cost. However, popular NNMD frameworks are generally implemented for a single computing node, and conventional energy-based NN models still suffer from large time-to-solution (T2S), prohibiting the application of NNMD to challenging materials simulations encompassing large spatiotemporal scales. Consequently, no leadership-scale NNMD simulation has thus far been reported. Here, we present a scalable parallel NNMD software (RXMD-NN) based on our scalable reactive molecular dynamics simulation engine named RXMD. RXMD-NN has achieved high scalability up to 786,432 IBM BlueGene/Q cores involving 1.7 billion atoms. Furthermore, we have achieved 4.6-fold reduction of T2S by using a novel network that directly predicts atomic forces from feature vectors. Reduced T2S has for the first time allowed the study of large-scale off-stoichiometry effect in a widely used phase change material, Ge 2 Se 2 Te 5 , thereby resolving its "firstsharp diffraction peak mystery".
fist sharp diffraction peak↗
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↗
Unsupervised quantum circuit learning in high energy physics
Unsupervised training of generative models is a machine learning task that has many applications in scientific computing. Here, in this work, we evaluate the efficacy of using quantum circuit-based generative models to generate synthetic data of high energy physics processes. We use nonadversarial, gradient-based training of quantum circuit Born machines to generate joint distributions over two and three variables.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗
Predicting impurity spectral functions using machine learning
The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410 000 and 600 000 spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with pointwise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of 10 5 over traditional AIM solvers. Finally, the required size of the training set of our model can be significantly reduced using farthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multichannel impurity problems of relevance to predicting the properties of real materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Identifying environmentally induced calibration changes in cryogenic RF axion detector systems using deep neural networks
The axion is a compelling hypothetical particle that could account for the dark matter in our universe while simultaneously solving the strong CP problem in quantum chromodynamics. The most sensitive axion detection technique demonstrated so far makes use of a high Q cavity immersed in a strong magnetic field, where axions are converted to microwave photons. This is called an axion haloscope and has primarily targeted the 1–10 GHz range. As searches scan up in axion mass, toward the parameter space favored by theoretical predictions, individual cavity sizes decrease in order to achieve higher frequencies. This shrinking cavity volume translates directly to a loss in signal-to-noise, motivating the plan to replace individual cavity detectors with arrays of cavities. When the transition from one to (N) multiple cavities occurs, haloscope searches are anticipated to become much more complicated to operate, requiring N times as many measurements but also the new requirement that N detectors operate in unison, which can be achieved by locking them to a common frequency. To offset this anticipated increase in detector complexity, we aim to develop new tools for diagnosing experiments using neural networks. Current experiments monitor scattering parameters of their receiver for periodically measuring cavity quality factor and coupling. However, off-resonant data remain relatively useless. In this paper, we ask if it is possible that off-resonant information contained in vector network analyzer scans could be used to diagnose equipment failures/anomalies and measure physical conditions (e.g., temperatures and ambient magnetic field). We demonstrate a proof-of-concept that AI techniques can help manage the complexity of an axion haloscope search for operators.
Engel, Andrew W. [Pacific Northwest National Labor↗
Identification of Non-Fermi Liquid Physics in a Quantum Critical Metal via Quantum Loop Topography
Non-Fermi liquid physics is ubiquitous in strongly correlated metals, manifesting itself in anomalous transport properties, such as a $\textit{T}$-linear resistivity in experiments. However, its theoretical understanding in terms of microscopic models is lacking, despite decades of conceptual work and attempted numerical simulations. In this work, we demonstrate that a combination of sign-problem-free quantum Monte Carlo sampling and quantum loop topography, a physics-inspired machine-learning approach, can map out the emergence of non-Fermi liquid physics in the vicinity of a quantum critical point (QCP) with little prior knowledge. Using only three parameter points for training the underlying neural network, we are able to robustly identify a stable non-Fermi liquid regime tracing the fans of metallic QCPs at the onset of both spin-density wave and nematic order. In particular, we establish for the first time that a spin-density wave QCP commands a wide fan of non-Fermi liquid region that funnels into the quantum critical point. Our study thereby provides an important proof-of-principle example that new physics can be detected via unbiased machine-learning approaches.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantum optimal control of superconducting qubits based on machine-learning characterization
Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations in detailed numerical simulations of a superconducting transmon qubit. Furthermore, we demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of ∼99.99%.
Artificial neural networks↗
Learning to identify electrons
In this report we investigate whether state-of-the-art classification features commonly used to distinguish electrons from jet backgrounds in collider experiments are overlooking valuable information. A deep convolutional neural network analysis of electromagnetic and hadronic calorimeter deposits is compared to the performance of typical features, revealing a ≈ 5% gap which indicates that these lower-level data do contain untapped classification power. To reveal the nature of this unused information, we use a recently developed technique to map the deep network into a space of physically interpretable observables. We identify two simple calorimeter observables which are not typically used for electron identification, but which mimic the decisions of the convolutional network and nearly close the performance gap.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
Model fusion with physics-guided machine learning: Projection-based reduced-order modeling
The unprecedented amount of data generated from experiments, field observations, and large-scale numerical simulations at a wide range of spatiotemporal scales has enabled the rapid advancement of data-driven and especially deep learning models in the field of fluid mechanics. Although these methods are proven successful for many applications, there is a grand challenge of improving their generalizability. This is particularly essential when data-driven models are employed within outer-loop applications like optimization. In this work, we put forth a physics-guided machine learning (PGML) framework that leverages the interpretable physics-based model with a deep learning model. Leveraging a concatenated neural network design from multi-modal data sources, the PGML framework is capable of enhancing the generalizability of data-driven models and effectively protects against or inform about the inaccurate predictions resulting from extrapolation. We apply the PGML framework as a novel model fusion approach combining the physics-based Galerkin projection model and long- to short-term memory (LSTM) network for parametric model order reduction of fluid flows. We demonstrate the improved generalizability of the PGML framework against a purely data-driven approach through the injection of physics features into intermediate LSTM layers. Our quantitative analysis shows that the overall model uncertainty can be reduced through the PGML approach, especially for test data coming from a distribution different than the training data. Moreover, we demonstrate that our approach can be used as an inverse diagnostic tool providing a confidence score associated with models and observations. The proposed framework also allows for multi-fidelity computing by making use of low-fidelity models in the online deployment of quantified data-driven models.
42 ENGINEERING↗
Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces
Here, this paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C 5 H 5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree–Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Spatial Mode Correction of Single Photons Using Machine Learning
Abstract Spatial modes of light constitute valuable resources for a variety of quantum technologies ranging from quantum communication and quantum imaging to remote sensing. Nevertheless, their vulnerabilities to phase distortions, induced by random media, impose significant limitations on the realistic implementation of numerous quantum‐photonic technologies. Unfortunately, this problem is exacerbated at the single‐photon level. Over the last two decades, this challenging problem has been tackled through conventional schemes that utilize optical nonlinearities, quantum correlations, and adaptive optics. In this article, the self‐learning and self‐evolving features of artificial neural networks are exploited to correct the complex spatial profile of distorted Laguerre–Gaussian modes at the single‐photon level. Furthermore, the potential of this technique is used to improve the channel capacity of an optical communication protocol that relies on structured single photons. The results have important implications for real‐time turbulence correction of structured photons and single‐photon images.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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]↗