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At least 883 records · Page 49

Atomistically-informed modeling of point defect clustering and evolution in irradiated ThO 2

A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO 2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster configuration. A high-order adaptive time-integration has been used to solve the model. The predicted loop density and their average size is in good agreement with reported experimental observations for proton irradiated ThO 2 at 600°C. In conclusion, the model did not predict void evolution due to the sluggish kinetics of cation vacancies, explaining the absence of voids in proton irradiated ThO 2 (and other oxides) at relatively low temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effects of cluster expansion on the locations of phase transition boundary as a first step to quantify uncertainty in first principles statistical mechanics framework

Predicting phase diagrams from first principle calculations eliminates the need of tedious experimental trials and errors. Fully automating first principle phase diagram calculations without any sort of human intervention has been a long daunting task and troubling scientific communities for decades. This grand problem remains not fully resolved, largely due to the vastly high-dimensional parameter space associated with density functional theory, cluster expansion, lattice Monte Carlo, and the substantial uncertainty propagating through a set of complex simulations. As a first step to tackle this grand problem, we reported a first demonstration of how sensitive phase boundary locations can be to various cluster expansion fittings and input DFT training data. To the best knowledge of the authors, this study reported the first ever attempt to quantify uncertainty in first principles statistical mechanics framework. In addition, a semi-automated phase transition detection algorithm has been devised in this paper to deal with the associated statistical errors and uncertainties from Monte Carlo method and its predecessor DFT calculations and cluster expansions. This algorithm has been applied in a classical cluster expansion Mg-Cd binary alloy system to detect phase transitions at various locations of phase diagram using different cluster expansions to demonstrate its predictive power and quantify uncertainties. The results suggested that using Chebyshev basis function shifted the transition locations toward the dilute solid solution phase and expanded the phase stability of concentrated ordered phases to wider composition range. The addition of perturbed defect configurations into training data set lowered the order-disorder transition temperature to be away from true transition temperature, suggesting the transition nature is indeed configurational disorder dominated rather than defect assisted. Finally, we found that the weighting has negligible effect on the transition locations, except for the case of using Chebyshev basis function to fit all non-weighted configurations that can be susceptible to Monte Carlo sampling hysteresis.

36 MATERIALS SCIENCE↗

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

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗

Cluster dynamics modeling of irradiation growth in single crystal Zr

Irradiation growth of single-crystal Zr is modeled with a reduced set of cluster dynamics equations. Nucleation and growth of basal and prismatic dislocation loops are both accounted for in the model. Equations are developed for the time evolution of single point defects, a limited number of point defect clusters, interstitial and vacancy loop nucleation rates, as well as for the growth of vacancy loops on basal planes and interstitial loops on prismatic planes. Reduction of the usual infinite hierarchy of cluster dynamics equations to the simple set studied here is justified on the physical basis of the stability of small loops once nucleated. This simplified cluster dynamics model with a small number of adjustable parameters avoids the complexity of explicit representation of higher order point defect clusters. The model shows consistency with experimental observations of the following aspects: (1) the growth rates of Zr crystals along the a- and c-axes; (2) the onset dose for breakaway irradiation growth; (3) the saturation dislocation loop densities of vacancy and interstitial loops; (4) the effects of cold work and temperature on irradiation growth.

36 MATERIALS SCIENCE↗

Cluster dynamics simulation of xenon diffusion during irradiation in UO 2

Diffusion of fission gas in UO 2 nuclear fuel impacts several important performance metrics, such as fission gas release, swelling, and thermal conductivity. Current empirical models of fission gas release have significant uncertainty, some of which derives from the bulk diffusion rate and its dependence on, for example, fuel chemistry and irradiation. In this work, we have applied the previously-developed Free Energy Cluster Dynamics (FECD) methodology in the code Centipede to calculate xenon cluster concentrations in UO 2 under intrinsic (high temperature) and irradiation-enhanced (intermediate temperature) conditions in order to develop a model of the xenon diffusion coefficient based on the atomic scale mechanisms responsible for transport. While the diffusion mechanism for xenon in UO 2 is adequately described by the Xe + U 2 O vacancy cluster for intrinsic conditions, a similar process is not capable of capturing measured in-pile fission gas diffusivity at intermediate temperatures. Therefore, a different diffusion mechanism must dominate under this regime. Using calculated atomistic data, we have shown that irradiation-enhanced diffusion at intermediate temperatures occurs via the larger Xe + U 4 O y vacancy clusters, which have lower migration barriers and increase in concentration by several orders of magnitude compared to intrinsic conditions. This mechanism is enabled by the increased uranium vacancy concentration under irradiation due to Frenkel pair production. In addition, the fast migration of uranium interstitials with two attached oxygen interstitials lowers the total uranium interstitial concentration through reactions with sinks. This allows the extended defects, such as Xe + U 4 O y vacancy clusters, to maintain high concentrations by limiting annihilation with attached vacancies. Furthermore, predictions using the Xe + U 4 O y diffusion mechanism are in good agreement with experiment, albeit with some differences in the Arrhenius slope, which we believe may be related to either experimental or model parameter uncertainty. Lastly, an analytical expression suitable for application in fuel performance simulations was derived to capture the predictions of the Centipede simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Polynomial Scaling Localized Active Space Unitary Selective Coupled Cluster Singles and Doubles

We present a polynomial-scaling algorithm for the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. In this approach, cluster excitations are selected based on a threshold ϵ determined by the absolute gradients of the LAS-UCCSD energy with respect to cluster amplitudes. Using the generalized Wick’s theorem for multireference wave functions, we derive the gradient expression as a polynomial function of one-, two-, and three-body reduced density matrices and 1- and 2-electron integrals, valid for any multireference wave function. The resulting gradient implementation exhibits a memory scaling of 𝒪(N 6 ), with N spin orbitals in the combined active space of all fragments. The variational quantum eigensolver is used to optimize the selected cluster excitations on a quantum simulator. Furthermore, by plotting the energy error, defined as the difference between the LAS-USCCSD and corresponding CASCI energies, against the inverse cluster amplitude selection threshold (ϵ –1 ) for polyene chains containing 2 to 5 π-bond units, we establish a relationship between the energy error and the threshold. To further validate the accuracy of LAS-USCCSD, we computed the cis–trans isomerization energy of stilbene (a 20-qubit system) and the magnetic coupling constant of the tris-hydroxo-bridged chromium dimer [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ (evaluated as both 12- and 20-qubit systems) using the Qiskit-Qulacs simulator. Assessing such examples is important to determine the practical feasibility of quantum simulations for chemically realistic systems. Toward this goal, with the LAS-USCCSD algorithm we estimated the quantum resources required for simulating an active space of (30e,22o) in [Cr 2 (OH) 3 (NH 3 ) 6 ] 3+ , a size that remains beyond the reach of current quantum simulators for accurate treatment.

Algorithms↗

Photoelectron Spectroscopy and Computational Study on Microsolvated [B 10 H 10 ] 2– Clusters and Comparisons to Their [B 12 H 12 ] 2– Analogues

Microhydrated closo-Boranes have attracted great interests due to their superchaotropic activity related to well-known Hofmeister effect and important applications in biomedical and battery fields. In this work, we report a combined negative ion photoelectron spectroscopy and quantum chemical investigation on hydrated closo-decaborate clusters [B 10 H 10 ] 2- ·nH 2 O (n = 1 – 7) with a direct comparison to their analogues [B 12 H 12 ] 2- ·nH 2 O and free water clusters. A single H 2 O molecule is found sufficient to stabilize the intrinsically unstable [B 10 H 10 ] 2- dianion. The first two water molecules strongly interact with the solute forming B-H···H-O dihydrogen bonds while additional water molecules show substantially reduced binding energies. Unlike [B 12 H 12 ] 2- ·nH 2 O possessing highly structured water network with the attached H 2 O molecules arranged in a unified pattern by maximizing B-H···H-O dihydrogen bonding, distinct structural arrangements of the water clusters within [B 10 H 10 ] 2– ·nH 2 O are achieved with the water cluster networks from trimer to heptamer resembling free water clusters. Such a distinct difference arises from the variations in size, symmetry, and charge distributions between these two dianions. Finally, the present finding again confirms the structural diversity of hydrogen-bonding networks in microhydrated closo-boranes and enrich our understanding of aqueous borate chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Many-Body Expansion for Metals: II. Nonadditive Terms in Clusters Composed of Metals with n s 1 , n s 2 , and n s 2 p 1 Configurations

The many-body expansion (MBE) was applied to homometallic and heterometallic trimers of metals with ns 1 , ns 2 , and ns 2 p 1 configurations to investigate its convergence, the magnitude and nature (stabilizing/destabilizing) of the individual terms and seek an understanding of their variation across the different families of clusters. In particular, we examined the series of alkali metals (Li 3 , Na 3 , K 3 , Li 2 Na, LiNa 2 ), alkali metal borides (Li 2 B and LiB 2 ), and alkaline earth metals (Be 3 , Be 2 Mg, BeMg 3 , and Mg 3 ) trimers, as well as sodium clusters Na n , n = 2–5. Here, we found that there is no uniform contribution (stabilizing or destabilizing) across the series in the different families of trimers. For instance, the 2-B term stabilizes the ground states of the Na 3 (doublet), Na 4 (singlet), and Na 5 (doublet) clusters, and the 3-B term destabilizes them; however, the opposite holds for the quartet state of the Li 3 , Li 2 Na, LiNa 2 , and Na 3 clusters (destabilizing 2-B, stabilizing 3-B). Substituting Li with B in the quartet state of Li 3 results in a significant reduction of the 3-B term amounting to 16% (Li 2 B) and 5% (LiB 3 ) of the binding energy. On the contrary, the ground states of the alkaline earth metal clusters (Be 3 , Be 2 Mg, BeMg 3 , and Mg 3 ) are stabilized by the 3-B term, while the 2-B term destabilizes them. Overall, we find that the 3-B terms significantly stabilize the high-spin multiplicity states of the ns 1 configurations and the low-spin states of the ns 2 configurations. Finally, as the size of the metal increases, the contribution of the 3-B term to the binding energy decreases due to the longer metal–metal bond distances.

Alkali metals↗

ReaxFF Parameter Set for Boron Clusters and Icosahedral Boron Crystals: Comparison with Density Functional Theory and Machine-Learning Potentials

Icosahedral boron materials, which include regular icosahedra of 12 boron atoms have gained increasing attention due to their potential applications as superhard materials, semiconductors, and energy storage media. However, the synthesis of high quality crystals of these materials has been a major barrier to the development of these applications. To enable computational prediction of synthesis conditions yielding high-quality icosahedral boron crystals, herein we tested and refined a set of ReaxFF parameters for the nucleation and growth of such crystals. We focused on matching the relative energies of small boron clusters obtained by density functional theory since such small clusters and similar motifs are likely present in crystal nuclei and at the interface of growing crystals. Using a training set of B 80 clusters, including a low-energy core–shell structure containing a B 12 icosahedron core and a high-energy single-shell structure produced in preliminary ReaxFF simulations, the ReaxFF parameter set was refined to better reproduce energies calculated by density functional theory (DFT). Among existing ReaxFF parameter sets and the machine-learning interatomic potentials MACE-MP-0, MACE-MP-0b3, MACE-MPA-0, PFP v7.0.0, and SevenNet-MF-ompa, only our new parameter set and PFP v7.0.0 correctly ranked these B 80 clusters. This refinement led to improved agreement with DFT for a test set of 58 clusters consisting of 8–103 boron atoms. Furthermore, our refined parameter set yielded greater local icosahedral structure than the previously existing ReaxFF parameter set for larger scale simulations of crystallization from supercooled liquid boron. Additionally, simulations of solid boron in contact with molten nickel using our refined ReaxFF parameters yielded a boron solubility value that agrees moderately well with experimental expectations, while the previous boron parameters gave a value that was much too low.

boron↗

Di- and Tetrameric Molybdenum Sulfide Clusters Activate and Stabilize Dihydrogen as Hydrides

NaY zeolite-encapsulated dimeric (Mo 2 S 4 ) and tetrameric (Mo 4 S 4 ) molybdenum sulfide clusters stabilize hydrogen as hydride binding to Mo atoms. Density functional theory (DFT) calculations and adsorption measurements suggest that stabilization of hydrogen as sulfhydryl (SH) groups, as typical for layered MoS 2 , is thermodynamically disfavored. Competitive adsorption of H 2 and ethene on Mo was probed by quantifying adsorbed CO on partly hydrogen and/or ethene covered samples with IR spectroscopy. During hydrogenation, experiment and theory suggest that Mo is covered predominately with ethene and sparsely with hydride. DFT calculations further predict that under reaction conditions, each Mo x S y cluster can activate only one H 2 , suggesting that the entire cluster (irrespective of its nuclearity) acts as one active site for hydrogenation. The nearly identical turnover frequencies (24.7 ± 3.3 mol ethane ·h -1 ·mol cluster -1 ), apparent activation energies (31-32 kJ·mol -1 ), and reaction orders (~0.5 in ethene and ~1.0 in H 2 ) show that the active sites in both clusters are catalytically indistinguishable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data–Driven Velocity Model Evaluation Using K–Means Clustering

In this work, we develop a data-driven clustering method to evaluate a velocity model using surface wave velocity dispersion. This is done by first computing theoretical dispersion curves for 1-D velocity profiles of all the grid locations and then splitting the resulting dispersion curves into a certain number of groups via the K-means clustering. The observed dispersion curves are also clustered following the same procedure and the velocity model is assessed by comparing the spatial patterns obtained for the observed and synthetic data sets. The method is applied to evaluate two community velocity models in southern California, CVM-S4.26 and CVM-H15.1, using phase velocity maps derived for 3–16 s Rayleigh waves. We found a good correlation in the spatial distribution of clusters between the result of CVM-S4.26 and that of the observed data, suggesting that the CVM-S4.26 fits the observed dispersion maps better than the CVM-H15.1 in terms of features extracted from the clustering analysis.

58 GEOSCIENCES↗

Synchrotron intensity gradient revealing magnetic fields in galaxy clusters

Magnetic fields and their dynamical interplay with matter in galaxy clusters contribute to the physical properties and evolution of the intracluster medium. However, the current understanding of the origin and properties of cluster magnetic fields is still limited by observational challenges. In this article, we map the magnetic fields at hundreds-kpc scales of five clusters RXC J1314.4-2515, Abell 2345, Abell 3376, MCXC J0352.4-7401, and El Gordo using the synchrotron intensity gradient technique in conjunction with high-resolution radio observations from the Jansky Very Large Array (JVLA) and the Karoo Array Telescope (MeerKAT). We demonstrate that the magnetic field orientation of radio relics derived from synchrotron intensity gradient is in agreement with that obtained with synchrotron polarization. Most importantly, the synchrotron intensity gradient is not limited by Faraday depolarization in the cluster central regions and allows us to map magnetic fields in the radio halos of RXC J1314.4-2515 and El Gordo. We find that magnetic fields in radio halos exhibit a preferential direction along the major merger axis and show turbulent structures at higher angular resolution. The results are consistent with expectations from numerical simulations, which predict turbulent magnetic fields in cluster mergers that are stirred and amplified by matter motions.

79 ASTRONOMY AND ASTROPHYSICS↗

Atacama Cosmology Telescope measurements of a large sample of candidates from the Massive and Distant Clusters of WISE Survey

Galaxy clusters are an important tool for cosmology, and their detection and characterization are key goals for current and future surveys. Using data from the Wide-field Infrared Survey Explorer (WISE), the Massive and Distant Clusters of WISE Survey (MaDCoWS) located 2839 significant galaxy overdensities at redshifts 0.7 ≲ z ≲ 1.5, which included extensive follow-up imaging from the Spitzer Space Telescope to determine cluster richnesses. Concurrently, the Atacama Cosmology Telescope (ACT) has produced large area millimeter-wave maps in three frequency bands along with a large catalog of Sunyaev-Zeldovich (SZ)-selected clusters as part of its Data Release 5 (DR5). Aims. We aim to verify and characterize MaDCoWS clusters using measurements of, or limits on, their thermal SZ effect signatures. Here, we also use these detections to establish the scaling relation between SZ mass and the MaDCoWS-defined richness.

79 ASTRONOMY AND ASTROPHYSICS↗

Filaments in and between galaxy clusters at low and mid-frequency with the SKA

Context. Understanding the magnetised Universe is a major challenge in modern astrophysics, and cosmic magnetism has been acknowledged as one of the key scientific drivers of the most ambitious radio instrument ever planned, the Square Kilometre Array. Aims. With this work, we aim to investigate the potential of the Square Kilometre Array and its precursors and pathfinders in the study of magnetic fields in galaxy clusters and filaments through diffuse synchrotron radio emission. Galaxy clusters and filaments of the cosmic web are indeed unique laboratories in which to investigate turbulent fluid motions and large-scale magnetic fields in action, and much of what is known about magnetic fields in galaxy clusters comes from sensitive radio observations. Methods. Based on cosmological magneto-hydrodynamic simulations, we predict radio properties (total intensity and polarisation) of a pair of galaxy clusters connected by a cosmic-web filament. Results. We use our theoretical expectations to explore the potential of polarimetric observations to study large-scale structure magnetic fields in the frequency ranges 50–350 MHz and 950–1760 MHz. We also present predictions for galaxy cluster polarimetric observations with the Square Kilometre Array precursors and pathfinders, such as the LOw frequency ARray 2.0 and the MeerKAT+ telescope. Conclusions. Our findings point out that polarisation observations are particularly powerful for the study of large-scale magnetic fields, since they are not significantly affected by confusion noise. The unprecedented sensitivity and spatial resolution of the intermediatefrequency radio telescopes make them the favourite instruments for the study of these sources through polarimetric data, potentially allowing us to understand if the energy density of relativistic electrons is in equipartition with the magnetic field or rather coupled with the thermal gas density. Our results show that low-frequency instruments also represent a precious tool to study diffuse synchrotron emission in total intensity and polarisation.

79 ASTRONOMY AND ASTROPHYSICS↗

Computational studies of structural, energetic, and electronic properties of pure Pt and Mo and mixed Pt/Mo clusters: Comparative analysis of characteristics and trends

The added technological potential of bimetallic clusters and nanoparticles, as compared to their pure (i.e., one-component) counterparts, stems from the ability to further fine-tune their properties and, consequently, functionalities through a simultaneous use of the “knobs” of size and composition. The practical realization of this potential can be greatly advanced by the knowledge of the correlations and relationships between the various characteristics of bimetallic nanosystems on the one hand and those of their pure counterparts as well as pure constituent components on the other hand. Here, in this study, we present results of a density functional theory based study of pure Pt n and Mo n clusters aimed at revisiting and exploring further their structural, electronic, and energetic properties. These are then used as a basis for analysis and characterization of the results of calculations on two-component Pt n-m Mo m clusters. The analysis also includes establishing relationships between the properties of the Pt n-m Mo m clusters and those of their Pt n-m and Mo m components. One of the particularly intriguing findings suggested by the calculated data is a linear dependence of the average binding energy per atom in sets of Pt n-m Mo m clusters that have the same fixed number m of Mo atoms and different number n-m of Pt atoms on the fractional content (n-m)/n of Pt atoms. We derive an analytical model that establishes the fundamental basis for this linearity and expresses its parameters—the m-dependent slope and intercept—in terms of characteristic properties of the constituent components, such as the average binding energy per atom of Mo m and the average per-atom adsorption energy of the Pt atoms on Mo m . The conditions of validity and degree of robustness of this model and of the linear relationship predicted by it are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mass-selected ion–molecule cluster beam apparatus for ultrafast photofragmentation studies

We describe an apparatus for investigating the excited-state dissociation dynamics of mass-selected ion–molecule clusters by mass-resolving and detecting photofragment-ions and neutrals, in coincidence, using an ultrafast laser operating at high repetition rates. The apparatus comprises a source that generates ion–molecule clusters, a time-of-flight spectrometer, and a mass filter that selects the desired anions, and a linear-plus-quadratic reflectron mass spectrometer that discriminates the fragment anions after the femtosecond laser excites the clusters. The fragment neutrals and anions are then captured by two channeltron detectors. The apparatus performance is tested by measuring the photofragments: I – , CF 3 I – , and neutrals from photoexcitation of the ion–molecule cluster CF 3 I·I – using femtosecond UV laser pulses with a wavelength of 266 nm. Here, the experimental results are compared with our ground state and excited state electronic structure calculations as well as the existing results and calculations, with particular attention to the generation mechanism of the anion fragments and dissociation channels of the ion–molecule cluster CF 3 I·I – in the charge-transfer excited state.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Influence of counterion substitution on the properties of imidazolium-based ionic liquid clusters

Due to their unique physiochemical properties that may be tailored for specific purposes, ionic liquids (ILs) have been investigated for various applications, including chemical separations, catalysis, energy storage, and space propulsion. The different cations and anions comprising ILs may be selected to optimize a range of desired properties, such as thermal stability, ionic conductivity, and volatility, leading to the designation of certain ILs as designer “green” solvents. The effect of counterions on the properties of ILs is of both fundamental scientific interest and technological importance. Herein, we report a systematic experimental and theoretical investigation of the size, charge, stability toward dissociation, and geometric/electronic structure of 1-ethyl-3-methyl imidazolium (EMIM)-based IL clusters containing two different atomic counterions (i.e., bromide [Br − ] and iodide [I − ]). This work extends our studies of EMIM + cations with atomic chloride (Cl − ) and molecular tetrafluoroborate (BF 4 − ) anions reported previously by Baxter et al. [Chem. Mater. 34, 2612 (2022)] and Zhang et al . [J. Phys. Chem. Lett. 11, 6844 (2020)], respectively. Distributions of anionic IL clusters were generated in the gas phase using electrospray ionization and characterized by high mass resolution mass spectrometry, energy-resolved collision-induced dissociation, and negative ion photoelectron spectroscopy experiments. The experimental results reveal anion-dependent trends in the size distribution, relative abundance, ionic charge state, stability toward dissociation, and electron binding energies of the IL clusters. Complementary global optimization theory provides molecular-level insights into the bonding and electronic structure of a selected subset of clusters, including their low energy structures and electrostatic potential maps, and how these fundamental characteristics are influenced by anion substitution. Collectively, our findings demonstrate how the fundamental properties of ILs, which determine their suitability for many applications, may be tuned by substituting counterions. These observations are critical in the sub-nanometer cluster size regime where phenomena do not scale predictably to the bulk phase, and each atom counts toward determining behavior.

cluster↗

Estimating cluster masses from SDSS multiband images with transfer learning

ABSTRACT The total masses of galaxy clusters characterize many aspects of astrophysics and the underlying cosmology. It is crucial to obtain reliable and accurate mass estimates for numerous galaxy clusters over a wide range of redshifts and mass scales. We present a transfer-learning approach to estimate cluster masses using the ugriz-band images in the SDSS Data Release 12. The target masses are derived from X-ray or SZ measurements that are only available for a small subset of the clusters. We designed a semisupervised deep learning model consisting of two convolutional neural networks. In the first network, a feature extractor is trained to classify the SDSS photometric bands. The second network takes the previously trained features as inputs to estimate their total masses. The training and testing processes in this work depend purely on real observational data. Our algorithm reaches a mean absolute error (MAE) of 0.232 dex on average and 0.214 dex for the best fold. The performance is comparable to that given by redMaPPer, 0.192 dex. We have further applied a joint integrated gradient and class activation mapping method to interpret such a two-step neural network. The performance of our algorithm is likely to improve as the size of training data set increases. This proof-of-concept experiment demonstrates the potential of deep learning in maximizing the scientific return of the current and future large cluster surveys.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗