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87 records · Page 5

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↗

Comparison of Quantum Mechanical and Empirical Potential Energy Surfaces and Computed Rate Coefficients for N2 Dissociation

Physics-based modeling of hypersonic flows is predicated on the availability of chemical reaction rate coefficients and cross sections for the collisional processes. This approach has been built around the use of quantum mechanical calculations to describe the interaction between the colliding particles. In this approach a potential energy surface (PES) is computed by solving the electronic Schrödinger equation and collision cross sections are determined for that PES using classical, semiclassical or quantum mechanical scattering methods. The rate coefficients are computed by integrating the thermally weighted cross sections. State-to-state rate coefficients are determined by only integrating over a thermal distribution of collisional energies. Finally, thermal rate coefficients are determined by summation of the state-to-state rate coefficients for reactions of molecules in all relevant ro-vibrational energy levels. If the flow is in thermal non-equilibrium, the translational, vibrational and rotational energy modes can be represented in different ways: three unique temperatures can be used to describe the distributions, the populations of individual ro-vibrational energy levels can be determined by solving the Master Equation, or through the use of direct simulation in particle-based Monte Carlo sampling. The PES-to-rate coefficient approach had been proposed and attempted in the early days of digital computing, but it is only in the last 15 years that computer hardware and software have been up to the task of calculating accurate interatomic and intermolecular potentials.

Jaffe, Richard L.↗

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↗

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↗

Shape optimization and CAD

Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are available for the solution of single problems. By implementing collections of the available techniques into general software systems, operational environments for structural optimization have been created. The forthcoming years must bring solutions to the problem of integrating such systems into more general design environments. The result of this work should be CAD systems for rational design in which structural optimization is one important design tool among many others.

Rasmussen, John↗

How Autonomous Intelligent Systems Can Facilitate Earth-independent Medical Care: Going Beyond Telepresence

During the last decade, teleoperated robotic systems have extended humans’ sensorimotor competence to digitally fly beyond the physical barrier of distance and scale and thus transmit sensorimotor skills of the human through direct communication. Telepresence capabilities have enabled tele-physical remote access at small scales thanks to telerobotic mediums. Although the concept was initially motivated by space applications, such technologies quickly have expanded into the medical domain and resulted in teleoperated medical robots, including telerobotic surgical systems (such as the da Vinci surgical system). Effective telepresence fundamentally depends on an agile, reliable, and secure communication medium that can transmit real-time information between the operator and a remote device. However, direct telepresence may not be achievable for long-duration exploration spaceflight missions. Thus, autonomous systems and local intelligence represent potential solutions to the aforementioned issues. One example solution employs demonstration systems which enable learning from the pre-captured inputs of a skilled human operator. These will be computationally modeled and later probabilistically replicated toward the completion of remote physical tasks when direct telepresence is not viable - such as under communication blackout conditions. In other words, trained autonomous systems (e.g., robots) can perform remote operations that mimic the physical performance of experts during remote operations/training. Beyond learning the physics of the task, autonomous agents can also be used to conduct algorithmic decision-making that mimics the higher-level cognition of the expert. Thus, using an autonomous system, pre-trained cognitive and manipulation-based skills can be leveraged (acquired during pre-mission events) to produce digital twins of an intelligent operator. Such systems can be used for the real-time conduction of intricate tasks in complex and unstructured environments. Such systems will operationalize “cognitive digital twins” and can expand the reach of human cognition and manipulation through the power of data-driven learning from demonstration algorithms. This system category will be discussed as a fully autonomous operation in this talk. In addition to the above, we will also propose and discuss the possibility of partial-automation using remote intelligence and remote sensing. In contrast to full automation, partial automation can close the loop through a local operator equipped with augmented sensory awareness through wearable systems. Such technologies will allow the local operator to conduct delicate tasks while being guided using sensory augmentation and being monitored to gauge her/his level of cognitive focus and performance. The difference with the previous category is that a remote human will conduct the task. Further, rather than making a digital twin of human cognition, we will augment the control inputs of the local human to match those of the skilled expert operator who is not accessible in real-time. Going beyond classic telepresence and thus approaching intelligent telepresence, our vision is that autonomous agents will eventually enable the safe, consistent and efficient delivery of complex, remote and smart medical care during space exploration across operators in an Earth-independent fashion. We will discuss our collective vision from NASA and MERIIT@NYU lab in this talk.

Telepresence↗

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↗

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↗

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↗

Test Cases for the Benchmark Active Controls: Spoiler and Control Surface Oscillations and Flutter

As a portion of the Benchmark Models Program at NASA Langley, a simple generic model was developed for active controls research and was called BACT for Benchmark Active Controls Technology model. This model was based on the previously-tested Benchmark Models rectangular wing with the NACA 0012 airfoil section that was mounted on the Pitch and Plunge Apparatus (PAPA) for flutter testing. The BACT model had an upper surface spoiler, a lower surface spoiler, and a trailing edge control surface for use in flutter suppression and dynamic response excitation. Previous experience with flutter suppression indicated a need for measured control surface aerodynamics for accurate control law design. Three different types of flutter instability boundaries had also been determined for the NACA 0012/PAPA model, a classical flutter boundary, a transonic stall flutter boundary at angle of attack, and a plunge instability near M = 0.9. Therefore an extensive set of steady and control surface oscillation data was generated spanning the range of the three types of instabilities. This information was subsequently used to design control laws to suppress each flutter instability. There have been three tests of the BACT model. The objective of the first test, TDT Test 485, was to generate a data set of steady and unsteady control surface effectiveness data, and to determine the open loop dynamic characteristics of the control systems including the actuators. Unsteady pressures, loads, and transfer functions were measured. The other two tests, TDT Test 502 and TDT Test 5 18, were primarily oriented towards active controls research, but some data supplementary to the first test were obtained. Dynamic response of the flexible system to control surface excitation and open loop flutter characteristics were determined during Test 502. Loads were not measured during the last two tests. During these tests, a database of over 3000 data sets was obtained. A reasonably extensive subset of the data sets from the first two tests have been chosen for Test Cases for computational comparisons concentrating on static conditions and cases with harmonically oscillating control surfaces. Several flutter Test Cases from both tests have also been included. Some aerodynamic comparisons with the BACT data have been made using computational fluid dynamics codes at the Navier-Stokes level (and in the accompanying chapter SC). Some mechanical and active control studies have been presented. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. Cases for static angles of attack, static trailing-edge and upper-surface spoiler deflections are included for a range of conditions near those for the oscillation cases. Cases for trailing-edge control and upper-surface spoiler oscillations for a range of Mach numbers, angle of attack, and static control deflections are included. Cases for all three types of flutter instability are selected. In addition some cases are included for dynamic response measurements during forced oscillations of the controls on the flexible mount. An overview of the model and tests is given, and the standard formulary for these data is listed. Some sample data and sample results of calculations are presented. Only the static pressures and the first harmonic real and imaginary parts of the pressures are included in the data for the Test Cases, but digitized time histories have been archived. The data for the Test Cases are also available as separate electronic files.

Bennett, Robert M.↗

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↗