Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “classical digital computing model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

70 records · Page 4

General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Organismic materials for beyond von Neumann machines

The elementary basis of intelligence in organisms with a central nervous system includes neurons and synapses and their complex interconnections forming neural circuits. In non-neural organisms such as slime mold with gel-like media, viscosity modulation enables adaptation to changing environments. At a larger scale, collective intelligence emerges via social interactions and feedback in animal colonies. Learning and memory are therefore multi-scale features that evolve as a result of constant interactions with the environment. There is growing interest in emulating such features of intelligence in computing machines and autonomous systems. Materials that can respond to their environment in a manner similar to organisms (referred to as "organismic materials") therefore may be of interest as hardware components in artificial intelligence machines. In this brief review, we present a class of semiconductors called correlated oxides as candidates for learning machines. The term "correlated" refers to the fact that electrons in such lattices strongly interact and the ground state is not what is predicted by classical band theory. Such materials can undergo insulator-metal transitions at near ambient conditions under external stimuli such as thermal or electrical fields, strain, and chemical doping. Depending on the mechanism driving the transition, intermediate states can be metastable with different volatilities, and the time scales of phase change can be controlled over many orders of magnitude. The change in electronic properties can be sharp or gradual, leading to digital or analog behavior. These properties enable the realization of artificial neurons and synapses and emulate the associative and non-associative learning characteristics found in various organisms. We examine microscopic properties concerning electronic and structural transitions leading to collective behavior and theoretical treatments of the ground state and dynamical response, showcasing VO 2 as a model system. Next, we briefly review algorithms designed from the plasticity demonstrated by phase changing systems. Finally, we conclude the brief review with suggestions for future research toward realizing non-von Neumann machines.

42 ENGINEERING↗

Para-particle oscillator simulations on a trapped-ion quantum computer

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles remain hypothetical and unobserved in nature; yet, they can model physical phenomena, such as topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allows us to identify the para-particle oscillator Hamiltonian as an XY model and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Laser scanner data processing and 3D modeling using a free and open source software

The laser scanning is a technology that allows in a short time to run the relief geometric objects with a high level of detail and completeness, based on the signal emitted by the laser and the corresponding return signal. When the incident laser radiation hits the object to detect, then the radiation is reflected. The purpose is to build a three-dimensional digital model that allows to reconstruct the reality of the object and to conduct studies regarding the design, restoration and/or conservation. When the laser scanner is equipped with a digital camera, the result of the measurement process is a set of points in XYZ coordinates showing a high density and accuracy with radiometric and RGB tones. In this case, the set of measured points is called “point cloud” and allows the reconstruction of the Digital Surface Model. Even the post-processing is usually performed by closed source software, which is characterized by Copyright restricting the free use, free and open source software can increase the performance by far. Indeed, this latter can be freely used providing the possibility to display and even custom the source code. The experience started at the Faculty of Engineering in Catania is aimed at finding a valuable free and open source tool, MeshLab (Italian Software for data processing), to be compared with a reference closed source software for data processing, i.e. RapidForm. In this work, we compare the results obtained with MeshLab and Rapidform through the planning of the survey and the acquisition of the point cloud of a morphologically complex statue.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Markov chain Monte Carlo with digital dissipative dynamics on quantum computers

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To illustrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Unification of finite symmetries in the simulation of many-body systems on quantum computers

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can result in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed-matter physics and ab initio electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware and demonstrate the emulation of symmetry-adapted quantum phase estimation for preparing coherent superpositions of quantum states in various irreducible representations of a symmetry group. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries quantumly for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

quantum algorithms↗

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The research data alliance photon and neutron science interest group

Scientific research data provides unique challenges that are distinct from classic “Big Data” sources. One common element in research data is that the experiment, observations, or simulation were designed, and data were specifically acquired, to shed light on an open scientific question. The data and methods are usually “owned” by the researcher(s) and the data itself might not be viewed to have long-term scientific significance after the results have been published. Often, the data volume was relatively low, with data sometimes easier to reproduce than to catalog and store. Some data and meta-data were not collected in a digital form, or were stored on antiquated or obsolete media. Generally speaking, policies, tools, and management of digital research data have reflected an ad hoc approach that varies domain by domain and research group by research group. This model, which treats research data as disposable, is proving to be a serious limitation as the volume and complexity of research data explodes. Changes are required at every level of scientific research: within the individual groups, and across scientific domains and interdisciplinary collaborations. Enabling researchers to learn about available tools, processes, and procedures should encourage a spirit of cooperation and collaboration, allowing researchers to come together for the common good. In conclusion, these community-oriented efforts provide the potential for targeted projects with high impact.

97 MATHEMATICS AND COMPUTING↗

Characterization of drop aerodynamic fragmentation in the bag and sheet-thinning regimes by crossed-beam, two-view, digital in-line holography

When a spherical liquid drop is subjected to a step change in relative gas velocity, aerodynamic forces lead to drop deformation and possible breakup into a number of secondary fragments. In order to investigate this flow, a digital in-line holography (DIH) diagnostic is proposed which enables rapid quantification of spatial statistics with limited experimental repetition. To overcome the high uncertainty in the depth direction experienced in previous applications of DIH, a crossed-beam, two-view configuration is introduced. With appropriate calibration, this diagnostic is shown to provide accurate quantification of fragment sizes, three-dimensional positions and three-component velocities in a large measurement volume. We apply these capabilities in order to investigate the aerodynamic breakup of drops at two non-dimensional Weber numbers, We, corresponding to the bag (We = 14) and sheet-thinning (We = 55) regimes. Ensemble average results show the evolution of fragment size and velocity statistics during the course of breakup. Our results indicate that mean fragment sizes increase throughout the course of breakup. For the bag breakup case, the evolution of a multi-mode fragment size probability density is observed. This is attributed to separate fragmentation mechanisms for the bag and rim structures. In contrast, for the sheet-thinning case, the fragment size probability density shows only one distinct peak indicating a single fragmentation mechanism. Compared to previous related investigations of this flow, many orders of magnitude more fragments are measured per condition, resulting in a significant improvement in data fidelity. For this reason, this experimental dataset is likely to provide new opportunities for detailed validation of analytic and computational models of this flow.

42 ENGINEERING↗

Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation

Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion–laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac–Zoller or Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin–motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Towards intelligent diagnostic system employing integration of mathematical and engineering model

The development of medical diagnostic system has been one of the main research fields during years. The goal of the medical diagnostic system is to place a nosological system that could ease the diagnostic evaluation normally performed by scientists and doctors. Efficient diagnostic evaluation is essentials and requires broad knowledge in order to improve conventional diagnostic system. Several approaches on developing the medical diagnostic system have been designed and tested since the earliest 60s. Attempts on improving their performance have been made which utilizes the fields of artificial intelligence, statistical analyses, mathematical model and engineering theories. With the availability of the microcomputer and software development as well as the promising aforementioned fields, medical diagnostic prototypes could be developed. In general, the medical diagnostic system consists of several stages, namely the 1) data acquisition, 2) feature extraction, 3) feature selection, and 4) classifications stages. Data acquisition stage plays an important role in converting the inputs measured from the real world physical conditions to the digital numeric values that can be manipulated by the computer system. One of the common medical inputs could be medical microscopic images, radiographic images, magnetic resonance image (MRI) as well as medical signals such as electrocardiogram (ECG) and electroencephalogram (EEG). Normally, the scientist or doctors have to deal with myriad of data and redundant to be processed. In order to reduce the complexity of the diagnosis process, only the significant features of the raw data such as peak value of the ECG signal or size of lesion in the mammogram images will be extracted and considered in the subsequent stages. Mathematical models and statistical analyses will be performed to select the most significant features to be classified. The statistical analyses such as principal component analysis and discriminant analysis as well as mathematical model of clustering technique have been widely used in developing the medical diagnostic systems. The selected features will be classified using mathematical models that embedded engineering theory such as artificial intelligence, support vector machine, neural network and fuzzy-neuro system. These classifiers will provide the diagnostic results without human intervention. Among many publishable researches, several prototypes have been developed namely NeuralPap, Neural Mammo, and Cervix Kit. The former system (NeuralPap) is an automatic intelligent diagnostic system for classifying and distinguishing between the normal and cervical cancerous cells. Meanwhile, the Cervix Kit is a portable Field-programmable gate array (FPGA)-based cervical diagnostic kit that could automatically diagnose the cancerous cell based on the images obtained during sampling test. Besides the cervical diagnostic system, the Neural Mammo system is developed to specifically aid the diagnosis of breast cancer using a fine needle aspiration image.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Information for Fusion Energy Sciences (Final Technical Report)

The simulation of plasma dynamics is a critical area of Fusion Energy Sciences (FES) due to it’s usefulness in predicting, controlling, and confining plasmas in the context of potential fusion reactors. The simulation of plasmas is a computationally difficult problem in both classical and quantum physics, motivating investigation into the potential of quantum computers to simulate these systems. This project took several concrete steps towards this goal by developing tools for improving the control, characterization, and calibration of quantum gates on a superconducting quantum computer, developing error suppression and mitigation tools to reduce errors on the quantum computer, and utilizing these advancements to simulate reduced models of plasma dynamics on the quantum computer. In order to efficiently simulate plasma physics, an optimal control method which synthesizes, directly at the pulse level, any quantum gate on qubit and qutrit systems was developed. Using four superconducting transmon quantum processors at Rigetti and LLNL, it was demonstrated that any arbitrary quantum gate on qubits and qutrits could be implemented with high fidelity, leading to a significantly reduced length of a gate sequence. A problem of interest in FES is the nonlinear optical process of laser pulse compression within a plasma. Since quantum physics is linear, simulating nonlinear operations is not naturally feasible on a quantum computer, however it is possible to simulated a quantized version of the nonlinear process. A quantization approach to convert nonlinear wave-wave interaction problems to Hamiltonian simulation problems was developed and demonstrated using two qubits on a Rigetti device. In this experiment, a number of error suppression and mitigation techniques were investigated to determine how best to utilize the finite quantum resources. This study provides an example of how plasma problems may be solved on near-term, noisy quantum computing platforms and identified a promising set of techniques. Building on the insights of these experiments, the investigation turned to linear electron-plasma wave physics. A connection was identified between a local one-dimensional lattice spin model and linear wave phenomena, allowing a plasma physics problem to be efficiently mapped to the quantum computer. In this framework, reflection and transmission of plasma waves at a sharp boundary was studied, as well as the propagation of waves through an inhomogeneous plasma medium. In addition to the suite of error suppression and mitigation techniques developed, this experiment introduced the use of a digital-analog gate scheme designed to efficiently simulate the plasma Hamiltonian. With hardware available at the conclusion of the project, simulation at the scale of 9 qubits and 15 timesteps (60 entangling layers) was achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Projection Microstereolithography for Architected Materials

Stereolithography (SL) is a prominent paradigm in the realm of additive manufacturing (AM) technologies, which refers to fabrication approaches that build “bottom up” by adding material. Pioneered in 1984 by Chuck Hull, SL relies on light-activated solidification of a liquid photosensitive resin in a layer-by-layer fashion, with the geometry of each layer defined by sectioning a three-dimensional (3D) computer model by closely-spaced parallel planes. The maturation of the technology over nearly three subsequent decades has resulted in the wide availability of commercial SL products, such as the ProJet series from 3D Systems, Inc. (which uses the proprietary acronym SLA to refer to SL technology), which routinely produces parts with 50-100 µm resolution in all three axes, and overall dimensions of 0.25-0.5 m. In the most general terms, advancements in SL technology have generally been aimed at achieving four goals: decreasing (1) system cost and (2) minimum feature size (i.e. improving resolution), while (3) increasing overall part size and (4) build speed. SL systems can be broadly categorized into two classes, by the way in which they deliver illumination to produce the shape of each object layer to be fabricated: laser-scanning and mask projection approaches. Commercially-available SL systems incorporate the laser-scanning approach, following the original scheme described by Hull, since digital image projection technology has only emerged relatively recently as a viable alternative. A significant limitation of laser scanning is the relatively slow speed of rastering the laser to form each layer’s pattern, highlighting the need for a dynamic mask-based approach to polymerize larger areas in a single exposure. The recent proliferation of digital display technologies (referred to as spatial light modulators or SLMs) has enabled the implementation of such “dynamic masking,” increasing system throughput by allowing a complete image layer to be cross-linked simultaneously. These mask projection SL systems are gaining greater prominence, and the landscape of some of the parameters available for system design, as implemented in recent work by a variety of investigators, has been reviewed by Lambert et al.

36 MATERIALS SCIENCE↗

Blind identification of full-field vibration modes of output-only structures from uniformly-sampled, possibly temporally-aliased (sub-Nyquist), video measurements

Enhancing the spatial and temporal resolution of vibration measurements and modal analysis could significantly benefit dynamic modelling, analysis, and health monitoring of structures. For example, spatially high-density mode shapes are critical for accurate vibration-based damage localization. In experimental or operational modal analysis, higher (frequency) modes, which may be outside the frequency range of the measurement, contain local structural features that can improve damage localization as well as the construction and updating of the modal-based dynamic model of the structure. In general, the resolution of vibration measurements can be increased by enhanced hardware. Traditional vibration measurement sensors such as accelerometers have high-frequency sampling capacity; however, they are discrete point-wise sensors only providing sparse, low spatial sensing resolution measurements, while dense deployment to achieve high spatial resolution is expensive and results in the mass-loading effect and modification of structure's surface. Non-contact measurement methods such as scanning laser vibrometers provide high spatial and temporal resolution sensing capacity; however, they make measurements sequentially that requires considerable acquisition time. As an alternative non-contact method, digital video cameras are relatively low-cost, agile, and provide high spatial resolution, simultaneous, measurements. Combined with vision based algorithms (e.g., image correlation or template matching, optical flow, etc.), video camera based measurements have been successfully used for experimental and operational vibration measurement and subsequent modal analysis. However, the sampling frequency of most affordable digital cameras is limited to 30–60 Hz, while high-speed cameras for higher frequency vibration measurements are extremely costly. This work develops a computational algorithm capable of performing vibration measurement at a uniform sampling frequency lower than what is required by the Shannon-Nyquist sampling theorem for output-only modal analysis. In particular, the spatio-temporal uncoupling property of the modal expansion of structural vibration responses enables a direct modal decoupling of the temporally-aliased vibration measurements by existing output-only modal analysis methods, yielding (full-field) mode shapes estimation directly. Then the signal aliasing properties in modal analysis is exploited to estimate the modal frequencies and damping ratios. Furthermore, the proposed method is validated by laboratory experiments where output-only modal identification is conducted on temporally-aliased acceleration responses and particularly the temporally-aliased video measurements of bench-scale structures, including a three-story building structure and a cantilever beam.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Potential Applications of Quantum Computing at Los Alamos National Laboratory, v0.3.0

Since the scientific revolution in the 16th and 17th centuries, the process of scientific discovery has followed an iterative feedback process of observation, hypothesis development and testing with physical experiments, which is widely referred to as the scientific method. This process remained largely unchanged until the middle of the 20th century, when the emergence of digital computers empowered scientist to build and inspect detailed simulations of physical phenomena. Over the last century, computational tools have transformed modern approaches to scientific discovery by enabling fast and affordable hypothesis testing before physical experiments are conducted, shown in Figure 1-1. Some notable examples include: global climate forecasts to understand how the environment may change over decades [130]; modeling the behavior of plasma to design fusion reactors [59]; and understanding the behavior of molecules in biological processes [161, 223].

36 MATERIALS SCIENCE↗

MABAL: a Novel Deep-Learning Architecture for Machine-Assisted Bone Age Labeling

Bone age assessment (BAA) is a commonly performed diagnostic study in pediatric radiology to assess skeletal maturity. The most commonly utilized method for assessment of BAA is the Greulich and Pyle method (Pediatr Radiol 46.9:1269–1274, 2016; Arch Dis Child 81.2:172–173, 1999) atlas. The evaluation of BAA can be a tedious and time-consuming process for the radiologist. As such, several computer-assisted detection/diagnosis (CAD) methods have been proposed for automation of BAA. Classical CAD tools have traditionally relied on hard-coded algorithmic features for BAA which suffer from a variety of drawbacks. Recently, the advent and proliferation of convolutional neural networks (CNNs) has shown promise in a variety of medical imaging applications. There have been at least two published applications of using deep learning for evaluation of bone age (Med Image Anal 36:41–51, 2017; JDI 1–5, 2017). However, current implementations are limited by a combination of both architecture design and relatively small datasets. The purpose of this study is to demonstrate the benefits of a customized neural network algorithm carefully calibrated to the evaluation of bone age utilizing a relatively large institutional dataset. In doing so, this study will aim to show that advanced architectures can be successfully trained from scratch in the medical imaging domain and can generate results that outperform any existing proposed algorithm. The training data consisted of 10,289 images of different skeletal age examinations, 8909 from the hospital Picture Archiving and Communication System at our institution and 1383 from the public Digital Hand Atlas Database. The data was separated into four cohorts, one each for male and female children above the age of 8, and one each for male and female children below the age of 10. The testing set consisted of 20 radiographs of each 1-year-age cohort from 0 to 1 years to 14–15+ years, half male and half female. The testing set included left-hand radiographs done for bone age assessment, trauma evaluation without significant findings, and skeletal surveys. A 14 hidden layer-customized neural network was designed for this study. The network included several state of the art techniques including residual-style connections, inception layers, and spatial transformer layers. Data augmentation was applied to the network inputs to prevent overfitting. A linear regression output was utilized. Mean square error was used as the network loss function and mean absolute error (MAE) was utilized as the primary performance metric. MAE accuracies on the validation and test sets for young females were 0.654 and 0.561 respectively. For older females, validation and test accuracies were 0.662 and 0.497 respectively. For young males, validation and test accuracies were 0.649 and 0.585 respectively. Finally, for older males, validation and test set accuracies were 0.581 and 0.501 respectively. The female cohorts were trained for 900 epochs each and the male cohorts were trained for 600 epochs. An eightfold cross-validation set was employed for hyperparameter tuning. Test error was obtained after training on a full data set with the selected hyperparameters. Using our proposed customized neural network architecture on our large available data, we achieved an aggregate validation and test set mean absolute errors of 0.637 and 0.536 respectively. To date, this is the best published performance on utilizing deep learning for bone age assessment. Our results support our initial hypothesis that customized, purpose-built neural networks provide improved performance over networks derived from pre-trained imaging data sets. We build on that initial work by showing that the addition of state-of-the-art techniques such as residual connections and inception architecture further improves prediction accuracy. This is important because the current assumption for use of residual and/or inception architectures is that a large pre-trained network is required for successful implementation given the relatively small datasets in medical imaging. Instead we show that a small, customized architecture incorporating advanced CNN strategies can indeed be trained from scratch, yielding significant improvements in algorithm accuracy. It should be noted that for all four cohorts, testing error outperformed validation error. One reason for this is that our ground truth for our test set was obtained by averaging two pediatric radiologist reads compared to our training data for which only a single read was used. This suggests that despite relatively noisy training data, the algorithm could successfully model the variation between observers and generate estimates that are close to the expected ground truth.

62 RADIOLOGY AND NUCLEAR MEDICINE↗