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At least 1,261 records · Page 70

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗

The Salinity Retrieval Algorithms for the NASA Aquarius Version 5 and SMAP Version 3 Releases

The Aquarius end-of-mission (Version 5) salinity data set was released in December 2017. This article gives a comprehensive overview of the main steps of the Level 2 salinity retrieval algorithm. In particular, we will discuss the corrections for wind induced surface roughness, atmospheric oxygen absorption, reflected galactic radiation and side-lobe intrusion from land surfaces. Most of these corrections have undergone major updates from previous versions, which has helped mitigating temporal and zonal biases. Our article also discusses the ocean target calibration for Aquarius Version 5. We show how formal error estimates for the Aquarius retrievals can be obtained by perturbing the input to the algorithm. The performance of the Aquarius Version 5 salinity retrievals is evaluated against salinity measurements from the ARGO network and the HYCOM model. When stratified as function of sea surface temperature or sea surface wind speed, the difference between Aquarius Version 5 and ARGO is within +/-0.1 psu. The estimated global RMS uncertainty for monthly 100 km averages is 0.128 psu for the Aquarius Version 5 retrievals. Finally, we show how the Aquarius Version 5 salinity retrieval algorithm is adapted to retrieve salinity from the Soil-Moisture Active Passion (SMAP) mission.

retrieval algorithm↗

The Salinity Retrieval Algorithms for the NASA Aquarius Version 5 and SMAP Version 3 Releases

The Aquarius end-of-mission (Version 5) salinity data set was released in December 2017. This article gives a comprehensive overview of the main steps of the Level 2 salinity retrieval algorithm. In particular, we will discuss the corrections for wind induced surface roughness, atmospheric oxygen absorption, reflected galactic radiation and side-lobe intrusion from land surfaces. Most of these corrections have undergone major updates from previous versions, which has helped mitigating temporal and zonal biases. Our article also discusses the ocean target calibration for Aquarius Version 5. We show how formal error estimates for the Aquarius retrievals can be obtained by perturbing the input to the algorithm. The performance of the Aquarius Version 5 salinity retrievals is evaluated against salinity measurements from the ARGO network and the HYCOM model. When stratified as function of sea surface temperature or sea surface wind speed, the difference between Aquarius Version 5 and ARGO is within +-0.1 psu. The estimated global RMS uncertainty for monthly 100 km averages is 0.128 psu for the Aquarius Version 5 retrievals. Finally, we show how the Aquarius Version 5 salinity retrieval algorithm is adapted to retrieve salinity from the Soil-Moisture Active Passion (SMAP) mission.

calibration↗

Instrument Offset Optimization Technique for Airborne Doppler Wind Lidar Profiling Algorithm

This paper presents the instrument offset optimization technique for the Doppler Aerosol Wind Lidar (DAWN) profiling algorithm at NASA Langley Research Center (LaRC). The 2 um Doppler wind Lidar system at LaRC has a long history of research development and airborne campaigns. The core of the wind Lidar data processing is Airborne Wind Profiling Algorithm for Doppler Wind Lidar (APOLO), which was developed at LaRC. The extraction of wind parameters from the airborne Doppler wind Lidar data is challenging due to many factors such as the speed of aircraft, and the errors in instrument installation and calibration. It is unavoidable to prevent the adverse impact of calibration error and instrument installation offset on the performance of wind parameter estimation in the algorithm. Due to the unsteady environment where the data are collected, even a small offset will result in nonsensical results in the parameter estimation process. A brief introduction of APOLO and the overview of the optimization techniques are presented in this paper.

Wind profile↗

A Segmentation Algorithm for Characterizing Rise and Fall Segments in Seasonal Cycles: an Application to Xco2 to Estimate Benchmarks and Assess Model Bias

There is more useful information in the time series of satellite-derived column-averaged carbon dioxide (XCO2) than is typically characterized. Often, the entire time series is treated at once without considering detailed features at shorter timescales, such as nonstationary changes in signal characteristics – amplitude, period and phase. In many instances, signals are visually and analytically differentiable from other portions in a time series. Each rise (increasing) and fall (decreasing) segment in the seasonal cycle is visually discernable in a graph of the time series. The rise and fall segments largely result from seasonal differences in terrestrial ecosystem production, which means that the segment's signal characteristics can be used to establish observational benchmarks because the signal characteristics are driven by similar underlying processes. We developed an analytical segmentation algorithm to characterize the rise and fall segments in XCO2 seasonal cycles. We present the algorithm for general application of the segmentation analysis and emphasize here that the segmentation analysis is more generally applicable to cyclic time series. We demonstrate the utility of the algorithm with specific results related to the comparison between satellite- and model-derived XCO2 seasonal cycles (2009–2012) for large bioregions across the globe. We found a seasonal amplitude gradient of 0.74–0.77 ppm for every 10∘ of latitude in the satellite data, with similar gradients for rise and fall segments. This translates to a south–north seasonal amplitude gradient of 8 ppm for XCO2, about half the gradient in seasonal amplitude based on surface site in situ CO2 data (∼19 ppm). The latitudinal gradients in the period of the satellite-derived seasonal cycles were of opposing sign and magnitude (−9 d per 10∘ latitude for fall segments and 10 d per 10∘ latitude for rise segments) and suggest that a specific latitude (∼2∘ N) exists that defines an inversion point for the period asymmetry. Before (after) the point of asymmetry inversion, the periods of rise segments are lesser (greater) than the periods of fall segments; only a single model could reproduce this emergent pattern. The asymmetry in amplitude and the period between rise and fall segments introduces a novel pattern in seasonal cycle analyses, but, while we show these emergent patterns exist in the data, we are still breaking ground in applying the information for science applications. Maybe the most useful application is that the segmentation analysis allowed us to decompose the model biases into their correlated parts of biases in amplitude, period and phase independently for rise and fall segments. We offer an extended discussion on how such information about model biases and the emergent patterns in satellite-derived seasonal cycles can be used to guide future inquiry and model development.

segmentation algorithm↗

Dust Aerosol Retrieval Over the Oceans With the MODIS/VIIRS Dark Target Algorithm: 2. Nonspherical Dust Model

The Dark‐target (DT) aerosol algorithm retrieves spectral Aerosol Optical Depth (AOD) and other aerosol properties from Moderate‐resolution Imaging Spectrometer (MODIS) reflectance observations. Over the ocean, the DT algorithm is known to contain scattering‐angle‐dependent biases in its retrievals of AOD, Angstrom Exponent (AE), and Fine Mode Fraction (FMF) for dust aerosols. Following a two‐step strategy to improve the DT retrieval of dust over ocean, for which the first step is to identify dusty pixels (reported in “Part 1”), in this “Part 2,” we report on construction of a new dust model lookup table (LUT) and the strategy for applying it within the existing DT algorithm. In particular, we evaluate different characterizations of dust optical properties from a variety of frameworks and databases, and compare them with the current DT retrieval assumptions. Substituting the standard operational LUT with a spheroid dust model with identified dusty pixels shows significant improvement when compared with collocated AERONET‐identified dusty pixels. Specifically, the application of the new dust model to dusty pixels reduces their AOD bias from 0.06 to 0.02 while improving the fraction of retrievals within expected error from 64% to 82%. At the same time, the overall bias in AE is reduced from 0.13 to 0.06, and the scattering‐angle‐dependent AE bias is largely eliminated. In testing on two full months of data (April and July), the new retrieval will reduce the monthly mean AOD by up to 0.1 and 0.2 in the north Atlantic and Arabian seas, respectively. The average AE and FMF are also reduced in these dust heavy regions

dust aerosol retrieval↗

A Three-Step Semi Analytical Algorithm (3SAA) for Estimating Inherent Optical Properties Over Oceanic, Coastal, and Inland Waters From Remote Sensing Reflectance

We present a three-step inverse model (3SAA) for estimating the inherent optical properties (IOPs) of surface waters from the remote sensing reflectance spectra, Rrs(). The derived IOPs include the total (a()), phytoplankton (aphy()), and colored detrital matter (acdm()), absorption coefficients, and the total (bb()) and particulate (bbp()) backscattering coefficients. The first step uses an improved neural network approach to estimate the diffuse attenuation coefficient of downwelling irradiance from Rrs. a() and bbp() are then estimated using the LS2 model (Loisel et al., 2018), which does not require spectral assumptions on IOPs and hence can assess a() and bb() at any wavelength at which Rrs() is measured. Then, an inverse optimization algorithm is combined with an optical water class (OWC) approach to assess aphy() and acdm() from anw().The proposed model is evaluated using an in situ dataset collected in open oceanic, coastal, and inland waters. Comparisons with other standard semi-analytical algorithms (QAA and GSM), as well as match-up exercises, have also been performed. The applicability of the algorithm on OLCI observations was assessed through the analysis of global IOPs spatial patterns derived from 3SAA and GSM. The good performance of 3SAA is manifested by median absolute percentage differences (MAPD) of 13%, 23%, 34% and 34% for bbp(443), anw(443), aphy(443) and acdm(443), respectively for oceanic waters. Due to the absence of spectral constraints on IOPs in the inversion of total IOPs, and the adoption of an OWC-based approach, the performance of 3SAA is only slightly degraded in bio-optical complex inland waters.

ocean color↗

Quantum-Accelerated Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees

We present two algorithms in the Quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability; one for producing an approximately optimal Steiner Tree, and one for producing an exact spanning arborescence of minimum weight, the analog of a Minimum Spanning Tree in a directed graph, each of which uses O~(n^(1/4)) rounds of communication and O~(n^(9/4)) messages, achieving a lower round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. The CONGEST distributed computational model allows limited-sized messages to be transmitted within a network described by a communication graph of size n in a series of rounds to address a computational problem. The size limitation for such messages isO(log(n)) bits at each edge of the communication graph per round. The communication graph in the CONGEST-CLIQUE model is fully connected. In the Quantum CONGEST-CLIQUE model, at most O(log(n)) classical and quantum bits (qubits) can be communicated across each edge of the communication graph per round. At a high level, we achieve these results by combining classical algorithms with fast quantum subroutines. These speedups further contribute to understanding what problems can be solved more efficiently when we allow quantum communication in this CONGEST-CLIQUE model of distributed computation.

quantum distributed algorithms↗

A Tuned Ocean Color Algorithm for the Arctic Ocean: A Solution for Waters With High CDM Content

The Arctic Ocean (AO) is the most river-influenced ocean. Located at the land-sea interface wherein phytoplankton blooms are common, Arctic coastal waterbodies are among the most affected regions by climate change. Given phytoplankton are critical for energy transfer supporting marine food webs, accurate estimation of chlorophyll a concentration (Chl), which is frequently used as a proxy of phytoplankton biomass, is critical for improving our knowledge of the Arctic marine ecosystem and its response to the ongoing climate change. Due to the unique and complex bio-optical properties of the AO, efforts are still needed to obtain more accurate Chl estimates, especially for coastal waters with high colored detrital material (CDM) content. In this study, we optimized the the Garver-Siegel-Maritorena (GSM) algorithm, using an Arctic bio-optical dataset comprised of seven wavelengths (the original GSM wavelengths plus 625 nm). Results suggested that our tuned algorithm, denoted GSMA, outperformed an alternative AO GSM algorithm denoted AO.GSM, but the accuracy of Chl estimates was only improved by 8%. In addition, GSMA showed appreciable robustness when assessed using a satellite image and two non-Arctic coastal datasets.

Arctic↗

Biased degenerate ground-state sampling of small Ising models with converged quantum approximate optimization algorithm

The quantum alternating operator ansatz, a generalization of the quantum approximate optimization algorithm (QAOA), is a quantum algorithm used for approximately solving combinatorial optimization problems. QAOA typically uses the transverse field mixer as the driving Hamiltonian. One of the interesting properties of the transverse field driving Hamiltonian is that it results in nonuniform sampling of degenerate ground states of optimization problems. In this study, we numerically examine the fair sampling properties of the transverse field mixer QAOA, and Grover mixer QAOA (GM-QAOA), which provides theoretical guarantees of fair sampling of degenerate optimal solutions, up to a large enough p such that the mean expectation value converges to an optimal approximation ratio of 1. This comparison is performed with high-quality heuristically computed, but not necessarily optimal, QAOA angles, which give strictly monotonically improving solution quality as p increases. These angles are computed using the Julia based numerical simulation software JuliQAOA. Fair sampling of degenerate ground states is quantified using the Shannon entropy of the ground-state amplitudes distribution. The fair sampling properties are reported on several quantum signature Hamiltonians from previous quantum annealing fair sampling studies. Small random fully connected spin glasses are shown, which exhibit exponential suppression of some degenerate ground states with transverse field mixer QAOA. The transverse field mixer QAOA simulations show that some problem instances clearly saturate the Shannon entropy of 0 with a maximally biased distribution that occurs when the learning converges to an approximation ratio of 1 while other problem instances never deviate from a maximum Shannon entropy (uniform distribution) at any p step. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An algorithm for detecting and quantifying disturbance and recovery in high-frequency time series

Determining when a disturbance has occurred, its severity, and when the system recovered, is important to numerous questions in the aquatic sciences. This problem can be conceptualized as the timing and degree of perturbation from a typical state, and when the system returns to that typical state. We present an algorithm for detecting disturbance and recovery designed for high-frequency time series, e.g., data produced by automated sampling devices in instrumented buoys and flux towers. The algorithm quantifies differences in the empirical cumulative distribution functions of moving windows over reference and evaluation periods, and is sensitive to changes in the mean, variance, and higher statistical moments. Tests on simulated data show it accurately identifies disturbance and recovery. Three case studies illustrate the application of our algorithm in different empirical settings. A case study on dissolved oxygen in a Florida, USA estuary following a hurricane identified the disturbance and recovery 73 d later. A case study on air temperature and net ecosystem exchange in the Florida everglades identified cold snaps coinciding with periods of reduced carbon uptake. A case study on rotifer abundance following zebra mussel invasion in the Hudson River, NY showed rotifer collapse following invasion and recovery over a decade later. Methods such as ours can improve understanding response to disturbance and facilitate comparative and synthetic study of disturbance impacts across ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗

Algorithm advances and applications of time‐dependent first‐principles simulations for ultrafast dynamics

Abstract Far from equilibrium phenomenon is a central theme of contemporary material research. Such phenomenon can exhibit itself in atomic structure and dynamics, but very often it also happens as non‐equilibrium phenomenon in the electronic structure. In ab initio material simulation, density functional theory (DFT) has played an essential role in studying electronic ground state problems. For excited states, besides many‐body perturbation theory, another powerful tool is the time dependent DFT (TDDFT) method. In particular, the real‐time TDDFT (rt‐TDDFT) method can be used to simulate many non‐equilibrium phenomena directly. Here we introduce our works on some algorithm advances based on our recently rt‐TDDFT method. This method uses the plane‐wave basis set, and significantly accelerates its efficiency by increasing the time step from 0.1–1 as in traditional methods to 0.2–0.5 fs. The noncollinear magnetic moments and spin–orbit coupling have also been included in our rt‐TDDFT method. Furthermore, a Boltzmann‐TDDFT algorithm has been developed to solve the hot carrier overheating problem in Ehrenfest dynamics, and a natural orbital branching algorithm has been developed to overcome the mean‐field approximation in Ehrenfest dynamics nuclear trajectory, thus allows stochastic multiple paths in chemical reactions. Utilizing these methods, we have studied the photoinduced ultrafast demagnetization, ultrafast phase transition, energy transfer between plasmon and hot carriers, as well as the high‐energy ion implantation and low‐energy atomic diffusion in semiconductors. We believe the tools as the ones introduced here can enable us to study a wide range of phenomena which are of great interest in modern day material research. This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Liu, Wen‐Hao↗

Using a Genetic Algorithm to Optimize Configurations in a Data-Driven Application

Users of highly-configurable software systems often want to optimize a particular objective such as improving a functional outcome or increasing system performance. One approach is to use an evolutionary algorithm. However, many applications today are data-driven, meaning they depend on inputs or data which can be complex and varied. Hence, a search needs to be run (and re-run) for all inputs, making optimization a heavy-weight and potentially impractical process. In this paper, we explore this issue on a data-driven highly-configurable scientific application. We build an exhaustive database containing 3,000 configurations and 10,000 inputs, leading to almost 100 million records as our oracle, and then run a genetic algorithm individually on each of the 10,000 inputs. We ask if (1) a genetic algorithm can find configurations to improve functional objectives; (2) whether patterns of best configurations over all input data emerge; and (3) if we can we use sampling to approximate the results. We find that the original (default) configuration is best only 34% of the time, while clear patterns emerge of other best configurations. Out of 3,000 possible configurations, only 112 distinct configurations achieve the optimal result at least once across all 10,000 inputs, suggesting the potential for lighter weight optimization approaches. We show that sampling of the input data finds similar patterns at a lower cost.

Sinha, Urjoshi↗

Measurements of the groomed jet radius and momentum splitting fraction with the soft drop and dynamical grooming algorithms in pp collisions at $ \sqrt{s}$ = 5.02 TeV

This article presents measurements of the groomed jet radius and momentum splitting fraction in pp collisions at $\sqrt{s}$ = 5.02 TeV with the ALICE detector at the Large Hadron Collider. Inclusive charged-particle jets are reconstructed at midrapidity using the anti-k T algorithm for transverse momentum 60 < p$_{T}^{ch jet}$ < 80 GeV/c. We report results using two different grooming algorithms: soft drop and, for the first time, dynamical grooming. For each grooming algorithm, a variety of grooming settings are used in order to explore the impact of collinear radiation on these jet substructure observables. These results are compared to perturbative calculations that include resummation of large logarithms at all orders in the strong coupling constant. We find good agreement of the theoretical predictions with the data for all grooming settings considered.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A unified funnel restoration SQP algorithm

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.

Kiessling, David [Katholieke Univ. Leuven, Heverle↗

A Pattern Recognition Algorithm for Quantum Annealers

Abstract The reconstruction of charged particles will be a key computing challenge for the high-luminosity Large Hadron Collider (HL-LHC) where increased data rates lead to a large increase in running time for current pattern recognition algorithms. An alternative approach explored here expresses pattern recognition as a quadratic unconstrained binary optimization (QUBO), which allows algorithms to be run on classical and quantum annealers. While the overall timing of the proposed approach and its scaling has still to be measured and studied, we demonstrate that, in terms of efficiency and purity, the same physics performance of the LHC tracking algorithms can be achieved. More research will be needed to achieve comparable performance in HL-LHC conditions, as increasing track density decreases the purity of the QUBO track segment classifier.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

ResNet and CycleGAN for pulse shape discrimination of He-4 detector pulses: Recovering pulses conventional algorithms fail to label unanimously

Pulse shape discrimination (PSD) capable detectors, such as He-4, that respond to neutron and gamma-ray 7 interactions have a threshold deposited energy value below which n/γ discrimination vanishes when using 8 conventional PSD algorithms. Recent attempts in applying supervised learning based artificial neural 9 networks for PSD use the pulses in the separated regions to train the networks so they can be used to classify 10 another set of separated pulses. In doing so, pulses previously indistinguishable are not recovered for 11 classification, which would have increased the number of neutron and gamma-ray pulses that could be used 12 for further analysis. Assuming the reason why conventional PSD algorithms have unseparated regions is 13 because the parameter space of the algorithms fail to capture the intrinsic (but subtle) distinguishing 14 behavior of some of the neutron and gamma-ray pulses, a cycle-consistent generative adversarial network 15 (CycleGAN) was trained to amplify those differences and extract well separated neutron and gamma-ray 16 clusters. Results show that, once the network is trained with pulses from separated and unseparated regions, 17 it was able to transform the pulses in the unseparated region to improve the PSD. Subsequent n/γ 18 classification was performed using deep residual network (ResNet) that takes pulses with 512 data points 19 as an input. Two different ResNets were explored – simple ResNet and modified ResNet which takes 20 segmented pulse inputs in the first layer and the corresponding time axis values in the last hidden layer. 21 The later approach enables the network to extract time correlated pulse features to enhance its ability to 22 capture the pulse behaviors relevant for PSD. Although it achieves slightly lower accuracy, 99.41% versus 23 99.89%, based on simply counting the number of correct n/γ labels assigned, compared to the simple 24 ResNet, the modified ResNets architecture was able to decreases the cross-entropy loss function by half, 25 which implies that the correct n/γ labels assigned are less likely to be accidental. PSD parameter 26 distributions based on n/γ classification by ResNet before and after transforming unseparated pulses using 27 CycleGAN show that by enhancing the separation between neutrons and gamma-rays, the transformation 28 helps improve the performance of classifier networks that are trained using labeled dataset. The 29 enhancement of neutron and gamma-ray separation by the CycleGAN increased the PSD figure of merit 30 (FOM) by up to 70% in some regions. Here, the results show that, if a given detector achieves clear separation 31 between neutron and gamma-ray pulses in any energy region, such neural network approaches can help 32 lower the energy threshold for the separation and increasing the number of neutron and gamma-ray pulses 33 that can be used for further analysis.

4He↗