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NASA NTRS2001

Method and Apparatus for High Data Rate Demodulation

A method to demodulate BPSK or QPSK data using clock rates for the receiver demodulator of one-fourth the data rate is presented. This is accomplished through multirate digital signal processing techniques. The data is sampled with an analog-to-digital converter and then converted from a serial data stream to a parallel data stream. This signal processing requires a clock cycle four times the data rate. Once converted into a parallel data stream, the demodulation operations including complex baseband mixing, lowpass filtering, detection filtering, symbol-timing recovery, and carrier recovery are all accomplished at a rate one-fourth the data rate. The clock cycle required is one-sixteenth that required by a traditional serial receiver based on straight convolution. The high rate data demodulator will demodulate BPSK, QPSK, UQPSK, and DQPSK with data rates ranging from 10 Mega-symbols to more than 300 Mega-symbols per second. This method requires less clock cycles per symbol tan traditional serial convolution techniques.

Gerald J Grebowsky↗

NASA NTRS2000

Digital Channel Simulator Developed and Tested

The Digital Channel Simulator (DCS) is a real-time test set developed in-house by the NASA Glenn Research Center at Lewis Field that simulates the characteristics of the modulator, demodulator, and transmission medium in a typical communications system to enable controlled laboratory testing of codec pairs. The DCS can support data rates up to 100 megasymbols per second (Msymbols/sec) with symbol sizes up to 10 bits and is compatible with both TTL (transistor transistor logic) and ECL (emitter coupled logic) interfaces. Because of its use of digital integrated circuits (IC's), the DCS offers the user accurate and repeatable testing while maintaining a simple reconfiguration of the modulation scheme and noise characteristics. The PC-based graphical user interface (GUI) assures user friendly operation for configuring, controlling, and monitoring the DCS and system during tests. In a typical communications system, the modulator places a symbol in constellation space and puts it on a carrier to be sent to the demodulator. Because of noise on the channel, the I and Q position in constellation space cannot be recovered exactly, and the received coordinates shift. To mimic this process in the laboratory, the DCS uses a mapper to place the symbol in constellation space. It simulates the shift in coordinates by digitally adding "noise" to the I and Q values. The mapper and noise source are implemented in lookup tables. Modulation schemes and noise characteristics are set by the values loaded in these tables. The mapper also has a pass-through mode to facilitate modulator testing, allowing noise to be added to 8-bit I and Q values of modulated data without a second mapping. To achieve high symbol rates, eight processing circuits are placed in parallel between an ECL demultiplexer and multiplexer. A graphical user interface was developed to calculate, load, and verify the values for the lookup tables. This interface can also be used to debug and verify proper operation of the channel simulator or to control an experiment. Operation of the DCS has been verified through three tests: a low-speed comprehensive system test, a high-speed (20 Msymbols/sec) test of the TTL interface, and a high-speed (100 Msymbols/sec) test of the ECL interface. The DCS is now ready for use by NASA and external customers.

Bizon, Thomas P.↗

NASA NTRS2007

Distributed Saturation

The Saturation algorithm for symbolic state-space generation, has been a recent break-through in the exhaustive veri cation of complex systems, in particular globally-asyn- chronous/locally-synchronous systems. The algorithm uses a very compact Multiway Decision Diagram (MDD) encoding for states and the fastest symbolic exploration algo- rithm to date. The distributed version of Saturation uses the overall memory available on a network of workstations (NOW) to efficiently spread the memory load during the highly irregular exploration. A crucial factor in limiting the memory consumption during the symbolic state-space generation is the ability to perform garbage collection to free up the memory occupied by dead nodes. However, garbage collection over a NOW requires a nontrivial communication overhead. In addition, operation cache policies become critical while analyzing large-scale systems using the symbolic approach. In this technical report, we develop a garbage collection scheme and several operation cache policies to help on solving extremely complex systems. Experiments show that our schemes improve the performance of the original distributed implementation, SmArTNow, in terms of time and memory efficiency.

Chung, Ming-Ying↗

NASA NTRS1993

Programmable noise bandwidth reduction by means of digital averaging

Predetection noise bandwidth reduction is effected by a pre-averager capable of digitally averaging the samples of an input data signal over two or more symbols, the averaging interval being defined by the input sampling rate divided by the output sampling rate. As the averaged sample is clocked to a suitable detector at a much slower rate than the input signal sampling rate the noise bandwidth at the input to the detector is reduced, the input to the detector having an improved signal to noise ratio as a result of the averaging process, and the rate at which such subsequent processing must operate is correspondingly reduced. The pre-averager forms a data filter having an output sampling rate of one sample per symbol of received data. More specifically, selected ones of a plurality of samples accumulated over two or more symbol intervals are output in response to clock signals at a rate of one sample per symbol interval. The pre-averager includes circuitry for weighting digitized signal samples using stored finite impulse response (FIR) filter coefficients. A method according to the present invention is also disclosed.

Poklemba, John J.↗

NASA NTRS2010

Universal Decoder for PPM of any Order

A recently developed algorithm for demodulation and decoding of a pulse-position- modulation (PPM) signal is suitable as a basis for designing a single hardware decoding apparatus to be capable of handling any PPM order. Hence, this algorithm offers advantages of greater flexibility and lower cost, in comparison with prior such algorithms, which necessitate the use of a distinct hardware implementation for each PPM order. In addition, in comparison with the prior algorithms, the present algorithm entails less complexity in decoding at large orders. An unavoidably lengthy presentation of background information, including definitions of terms, is prerequisite to a meaningful summary of this development. As an aid to understanding, the figure illustrates the relevant processes of coding, modulation, propagation, demodulation, and decoding. An M-ary PPM signal has M time slots per symbol period. A pulse (signifying 1) is transmitted during one of the time slots; no pulse (signifying 0) is transmitted during the other time slots. The information intended to be conveyed from the transmitting end to the receiving end of a radio or optical communication channel is a K-bit vector u. This vector is encoded by an (N,K) binary error-correcting code, producing an N-bit vector a. In turn, the vector a is subdivided into blocks of m = log2(M) bits and each such block is mapped to an M-ary PPM symbol. The resultant coding/modulation scheme can be regarded as equivalent to a nonlinear binary code. The binary vector of PPM symbols, x is transmitted over a Poisson channel, such that there is obtained, at the receiver, a Poisson-distributed photon count characterized by a mean background count nb during no-pulse time slots and a mean signal-plus-background count of ns+nb during a pulse time slot. In the receiver, demodulation of the signal is effected in an iterative soft decoding process that involves consideration of relationships among photon counts and conditional likelihoods of m-bit vectors of coded bits. Inasmuch as the likelihoods of all the m-bit vectors of coded bits mapping to the same PPM symbol are correlated, the best performance is obtained when the joint mbit conditional likelihoods are utilized. Unfortunately, the complexity of decoding, measured in the number of operations per bit, grows exponentially with m, and can thus become prohibitively expensive for large PPM orders. For a system required to handle multiple PPM orders, the cost is even higher because it is necessary to have separate decoding hardware for each order. This concludes the prerequisite background information. In the present algorithm, the decoding process as described above is modified by, among other things, introduction of an lbit marginalizer sub-algorithm. The term "l-bit marginalizer" signifies that instead of m-bit conditional likelihoods, the decoder computes l-bit conditional likelihoods, where l is fixed. Fixing l, regardless of the value of m, makes it possible to use a single hardware implementation for any PPM order. One could minimize the decoding complexity and obtain an especially simple design by fixing l at 1, but this would entail some loss of performance. An intermediate solution is to fix l at some value, greater than 1, that may be less than or greater than m. This solution makes it possible to obtain the desired flexibility to handle any PPM order while compromising between complexity and loss of performance.

Moision, Bruce E.↗

NASA NTRS2005

Coupled Receiver/Decoders for Low-Rate Turbo Codes

been proposed for receiving weak single- channel phase-modulated radio signals bearing low-rate-turbo-coded binary data. Originally intended for use in receiving telemetry signals from distant spacecraft, the proposed receiver/ decoders may also provide enhanced reception in mobile radiotelephone systems. A radio signal of the type to which the proposal applies comprises a residual carrier signal and a phase-modulated data signal. The residual carrier signal is needed as a phase reference for demodulation as a prerequisite to decoding. Low-rate turbo codes afford high coding gains and thereby enable the extraction of data from arriving radio signals that might otherwise be too weak. In the case of a conventional receiver, if the signal-to-noise ratio (specifically, the symbol energy to one-sided noise power spectral density) of the arriving signal is below approximately 0 dB, then there may not be enough energy per symbol to enable the receiver to recover properly the carrier phase. One could solve the problem at the transmitter by diverting some power from the data signal to the residual carrier. A better solution . a coupled receiver/decoder according to the proposal . could reduce the needed amount of residual carrier power. In all that follows, it is to be understood that all processing would be digital and the incoming signals to be processed would be, more precisely, outputs of analog-to-digital converters that preprocess the residual carrier and data signals at a rate of multiple samples per symbol. The upper part of the figure depicts a conventional receiving system, in which the receiver and decoder are uncoupled, and which is also called a non-data-aided system because output data from the decoder are not used in the receiver to aid in recovering the carrier phase. The receiver tracks the carrier phase from the residual carrier signal and uses the carrier phase to wipe phase noise off the data signal. The receiver typically includes a phase-locked loop (PLL) or Costas loop that requires no delay or perhaps a single sample delay. The lower part of the figure depicts a basic coupled receiver/decoder . a data-aided system that would implement an iterative receiving/decoding process. The receiver would include a PLL or a Wiener filter that, to the extent possible, would track the residual carrier signal, wipe phase noise off the data signal, then send the result to the turbo decoder. Recovery of timing could be effected by, for example, a digital transition tracking loop (DTTL) or other, similar loop. The first iteration of turbo decoding would yield soft data symbols, which would be sent back to the receiver for use in softly wiping off the data signal in an effort to recover the residual carrier signal. The wiped signal would contain a relatively large carrier-phase component that could be tracked by use of a second Wiener filter.

Hamkins, Jon↗

NASA NTRSDate not supplied

Application of Variable Data Rate (VDR) Towards Channel Optimization

Recognizing the vagaries of channel impediments, one way to optimize aggregate channel information throughput is to maintain a constant symbol rate but vary the modulation scheme and/or the codec rate. The CCSDS VCM and ACM standards promulgation relies upon this kind of an approach. We offer a considerably simpler alternative for spacecraft that are not parked in geo-stationary orbit, one that can rely upon conventional spacecraft housekeeping schedules to change spacecraft and ground operations and will minimize the possibility of requiring any spacecraft hardware accommodations to incorporate. We suggest the use of varying the physical symbol rate within the channel to both initiate acquisition earlier in a pass and retain the link longer as the pass tends toward loss of signal. There is nothing new in what we propose, just a recognition of what has been successful in the past and employed in multiple missions. Integrating over the periodicity of orbit repetition, we shall show that any link that is dependent primarily on a varying range from spacecraft to ground only requires a maximum of five symbol rate transitions in order to optimize total information throughput. By applying these symbol rate transitions using almost rigid rules, we anticipate doubling the information throughput for conventional LEO sun-synchronous orbits. We provide other examples as well.

variable data rate↗

NASA NTRSDate not supplied

Application of Variable Data Rate (VDR) Towards Channel Optimization

Variable Data Rate↗

DOE OSTI2024

Modeling plasticity-mediated void growth at the single crystal scale: A physics-informed machine learning approach

Modeling the evolution of voids during plastic flow as well as their effects on plastic dissipation is critical for both component manufacturing and lifetime estimation purposes. To this end, we propose a rate-dependent constitutive model to homogenize the effects of semi-randomly distributed voids on single crystal plasticity whilst capturing void interaction and plastic anisotropy. Here, this present work focuses on the case of face centered cubic crystals to introduce an anisotropic gauge function applicable within the crystal plasticity formalism. The approach combines analytical methods to describe the micromechanics of the system in combination with symbolic regression to capture analytically intractable mechanisms from data. The hybrid framework uses a physics-informed genetic programming-based symbolic regression algorithm to solve a multiform optimization problem simultaneously producing a new gauge function and a new strain rate equation. This is also a multi-objective optimization problem with many competing objectives. A new search and selection step is introduced to the genetic algorithm that promotes convergence toward a global solution that better satisfies all the objectives. Overall, the symbolic equations produced leverage data-driven methods to achieve greater accuracy than comparable alternatives on an analytically intractable problem while maintaining model transparency.

36 MATERIALS SCIENCE↗

NASA NTRS2003

Bimanual cross-talk during reaching movements is primarily related to response selection, not the specification of motor parameters

Simultaneous reaching movements made with the two hands can show a considerable increase in reaction time (RT) when they differ in terms of direction or extent, compared to when the movements involve the same direction and extent. This cost has been attributed to cross-talk in the specification of the motor parameters for the two hands. However, a recent study [Diedrichsen, Hazeltine, Kennerley, & Ivry, (2001). Psychological Science, 12, 493-498] indicates that when reaching movements are cued by the onset of the target endpoint, no compatibility effects are observed. To determine why directly cued movements are immune from interference, we varied the stimulus onset asynchrony for the two movements and used different combinations of directly cued and symbolically cued movements. In two experiments, compatibility effects were only observed when both movements were symbolically cued. No difference was found between compatible and incompatible movements when both movements were directly cued or when one was directly cued and the other was symbolically cued. These results indicate that interference is not related to the specification of movement parameters but instead emerges from processes associated with response selection. Moreover, the data suggest that cross-talk, when present, primarily shortens the RT of the second movement on compatible trials rather than lengthening this RT on incompatible trials.

Randomized Controlled Trial↗

DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗

DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗

DOE OSTI2026

Secure Wireless Communication Using Distributed Coherent Transmission and Spatial Signal Decomposition

We present a new approach to secure wireless communications using coherent distributed transmission of signals that are spatially decomposed between a two-element distributed antenna array. High-accuracy distributed coordination of microwave wireless systems supports the ability to transmit different parts of a signal from separate transmitters such that they combine coherently at a designated destination. In this article, we explore this concept using a two-element coherent distributed phased array where each of the two transmitters sends a separate component of a communication signal, where each symbol is decomposed into a sum of two pseudorandom signal vectors, the coherent summation of which yields the intended symbol. By directing the transmission to an intended receiver using distributed beamforming, the summation of the two vector components is largely confined to a spatial region at the destination receiver. We implement the technique in a $50−λ$ array operating at 3 GHz. We evaluate the symbol error rate (SER) in 2-D space through simulation and measurement, showing that the approach yields a spatially confined secure region where the information is recoverable (i.e., the received signal has low SER), and outside of which the information is unrecoverable (high SER). The proposed system is also compared against a traditional beamforming system where each node sends the same data. We validate experimentally that our approach achieves a low SER of 0.0082 at broadside and an SER above 0.25 at all other locations compared to a traditional beamforming approach that achieves a SER of 0 at all locations measured.

Engineering - Electronic and electrical engineerin↗

DOE OSTI2021

AI-Batt (Autonomous Identification of Battery Life Models) [SWR 21-36]

Autonomous Identification of Battery Life Models (AI-Batt) AI-Batt is a MATLAB code base for developing lifetime models for batteries from accelerated aging data. The code base provides many functions for processing, visualizing, and modeling battery aging data, making the data processing, exploration, and modeling workflow substantially faster. These tools are tailored for working with battery aging data sets, which usually consist of many separate time-series for each cell, with many test conditions and possible replicates at each condition, which makes it difficult to simply process or visualize the data set. Complex modeling tasks, such as cross-validation, sensitivity analysis, and uncertainty quantification have been implemented to enable thorough statistical investigation of model predictions. Additionally, several machine-learning algorithms are implemented to autonomously identify suitable models via symbolic regression. Data processing functions automatically cast data from the struct data type, which is commonly used to store experimental data, but is not an acceptable input for most algorithms, to the table data type, which can be easily used as input to any optimization algorithm. Also, the data can be separated into time-invariant and time-variant data tables, which is helpful for exploring the data set as well as developing separate models for time-variant and time-invariant aging mechanisms. For example, in aging tests with constant temperature, temperature is a time-invariant experimental condition. Visualization tools enable plotting of data, model fits, and model simulations possible with single-line function calls, empowering data exploration of complex data sets with both time-varying and time-invariant trends. Plots can be automatically generated for the whole data set, or separated by data group (groups of test replicates) or individual data series. Data points or data series can be automatically colored by the value of a variable with a variety of color maps, and model predictions can also be colored by the value of a fit statistic. Comparisons between data sets and the predictions/simulations of different models on the same data set can be easily plotted as well. Distributions of parameter values from bootstrap resampling can be plotted to visualize the reliability of parameter estimation, or determine any correlations between parameters. Modeling tools handle the complex task of creating and parsing symbolic equations for modeling battery lifetime. Equations are parsed to grab relevant data variables, parameter values, or specified sub-models for input into optimization, evaluation, or simulation functions. Models can be optimized locally (one set of parameters for each data series), bi-level (some parameters shared across the data set), or globally (single set of parameters for all data). Functions implementing symbolic regression algorithms help users to discover effective model equations, even in poorly sampled, high-dimensional data.

Smith, Kandler↗

DOE OSTI2023

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Datasets and U-Net Model for "A Deep Learning Based Framework to Identify Undocumented Orphaned Oil and Gas Wells from Historical Maps: a Case Study for California and Oklahoma"

This dataset has results and the model associated with the publication Ciulla et al., (2024). It contains a U-Net semantic segmentation model (unet_model.h5) and associated code implemented in tensorflow 2.0 for the model training and identification of oil and gas well symbols in USGS historical topographic maps (HTMC). Given a quadrangle map (7.5 minutes), downloadable at this url: https://ngmdb.usgs.gov/topoview/, and a list of coordinates of the documented wells present in the area, the model returns the coordinates of oil and gas symbols in the HTMC maps. For reproducibility of our workflow, we provide a sample map in California and the documented well locations for the entire State of California (CalGEM_AllWells_20231128.csv) downloaded from https://www.conservation.ca.gov/calgem/maps/Pages/GISMapping2.aspx. Additionally, the locations of 1,301 potential undocumented orphaned wells identified using our deep learning framework or the counties of Los Angeles and Kern in California, and Osage and Oklahoma in Oklahoma are provided in the file found_potential_UOWs.zip. The results of the visual inspection of satellite imagery in Osage County is in the file visible_potential_UOWs.zip. The dataset also includes a custom tool to validate the detected symbols in the HTMC maps (vetting_tool.py). More details about the methodology can be found in the associated paper: Ciulla, F., Santos, A., Jordan, P., Kneafsey, T., Biraud, S.C., and Varadharajan, C. (2024) A Deep Learning Based Framework to Identify Undocumented Orphaned Oil and Gas Wells from Historical Maps: a Case Study for California and Oklahoma. Accepted for publication in Environmental Science and Technology. The geographical coordinates provided correspond to the locations of potential undocumented orphaned oil and gas wells (UOWs) extracted from historical maps. The actual presence of wells need to be confirmed with on-the-ground investigations. For your safety, do not attempt to visit or investigate these sites without appropriate safety training, proper equipment, and authorization from local authorities. Approaching these well sites without proper personal protective equipment (PPE) may pose significant health and safety risks. Oil and gas wells can emit hazardous gasses including methane, which is flammable, odorless and colorless, as well as hydrogen sulfide, which can be fatal even at low concentrations. Additionally, there may be unstable ground near the wellhead that may collapse around the wellbore. This dataset was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

Artificial Intelligence↗

DOE OSTI2022

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1973

Hexagonal multiple phase-and-amplitude-shift-keyed signal sets

Selection of a particular signal set array for a bandwidth-constrained multiple phase-and-amplitude-shift-keyed (MPASK) communication system for a linear additive Gaussian noise channel requires consideration of factors such as average and/or peak power vs symbol error probability, signal amplitude dynamic range, simplicity of generation and detection, and number of bit errors per symbol error (Gray code properties). A simple technique is presented for generating and optimally detecting the honeycomb (hexagonal) signal set, i.e., the signal set that has the tightest sphere-packing properties. The symbol and bit error probability performance of this set is compared to other two-dimensional signal sets that have been investigated in the literature, and is shown to be slightly superior from an average power standpoint. The paper concludes with a comparison of all of these signal sets from the standpoint of the factors listed above.

Simon, M. K.↗