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At least 343 records · Page 19

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part A. Analysis and model validation on ASDEX Upgrade

We discuss how the combination of experimental observations and rapid modeling has enabled to improve understanding of the tokamak ramp-down phase in ASDEX Upgrade. A series of dedicated experiments has been performed, to disentangle the effect of individual actuators like plasma current, auxiliary heating and plasma shaping. Optimized discharge termination strategies with increased margin with respect to radiative and vertical stability limits are proposed and tested in experiment. Radiative collapse of the edge $T$ $e$ profile after the HL back-transition is avoided by initially maintaining auxiliary heating during L-mode, showing beneficial effects even after the auxiliary heating is turned off. The capability of the RAPTOR code to model the time evolution of the internal inductance $\ell$ $i3$ has been validated, including the effect of a change in the $I$ $p$ ramp-down rate and the HL transition timing. The reduction of $\ell$ $i3$ caused by rapid compression of the plasma cross-section has been quantitatively recovered in simulations. Successful modeling of the $\ell$ $i3$ time evolution is essential to optimize ramp-down scenarios for future fusion reactors, for which vertical stability and power balance control will be more challenging.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling plasma-induced surface charge effects on CO 2 activation by single atom catalysts supported on reducible and irreducible metal oxides

Abstract The accumulation of negative surface charge on catalytic surfaces in the presence of low-temperature plasma (LTP) could influence catalytic performance. However, it is difficult to disentangle the role of surface charging and other LTP catalytic effects in experiment. Herein, we use density functional theory (DFT) modeling to understand the effect of plasma-induced surface charging on CO 2 activation by atomically dispersed single atom (SA) catalysts on both reducible and irreducible metal oxide supports. We model CO 2 adsorption strength and CO 2 dissociation barriers for Co 1 , Ni 1 , Cu 1 , Rh 1 , Pd 1 , and Ag 1 SAs on both reducible and irreducible supports, namely, CeO 2 (100), TiO 2 (101), and γ -Al 2 O 3 (110), to elucidate trends. We find that accumulated surface charge on the SA increases the CO 2 adsorption strength and decreases the CO 2 dissociation barrier for all studied SA/support combinations. For both charged and uncharged (neutral) systems, SAs on the reducible CeO 2 (100) support generally adsorb CO 2 more weakly compared to when on irreducible supports like γ -Al 2 O 3 (110). SAs on γ -Al 2 O 3 (110) typically have larger barriers for CO 2 dissociation for both charged and uncharged systems compared to TiO 2 (101) and CeO 2 (100). The magnitude of surface charging effects on CO 2 binding energies and dissociation barriers depends sensitively on both the SA and the support. In some cases, the CO 2 activation trends qualitatively change between neutral and charged systems for a fixed SA across different supports. This DFT modeling study demonstrates that surface charging should be considered in strong electric fields because it can have a large effect on molecule adsorption and bond-breaking on catalytic surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Decoupling plasma, catalyst, and gaseous mechanisms for non-oxidative methane conversion

Direct non-oxidative methane (CH 4 ) conversion to value-added hydrogen (H 2 ) and C 2 products remains hindered by fundamental catalytic scaling constraints and rapid surface deactivation at elevated temperatures. Plasma-enabled catalysis offers a promising route to overcome the thermodynamic and kinetic barriers of direct non-oxidative methane upgrading at mild conditions, yet control over C–C product selectivity and catalyst stability remains elusive. Here, we establish a unified mechanistic framework including Langmuir–Hinshelwood (L–H) and Langmuir–Rideal (L–R) mechanisms that disentangles the roles of plasma excitation (including vibrationally activated species and radicals), surface temperature (T sur ), and catalyst binding energy in steering CH 4 conversion to H 2 and C 2 hydrocarbons. Through a combination of density functional theory (DFT) informed microkinetic modeling, in situ and ex situ surface characterization, and product quantification under dielectric barrier discharge conditions, we show that vibrationally excited CH 4 lowers activation barriers selectively for dissociative chemisorption, enabling surface activation across a wide range of transition metal catalysts at low thermal energy input. We find that once CH 4 is dissociatively chemisorbed, the branching between C 2 H 2 , C 2 H 4 , and C 2 H 6 is governed by surface properties (carbon binding energy, T sur , etc), regardless of plasma excitation. The DFT informed microkinetic model decouples the effects of molecular activation from surface properties and indentifies operating windows that maximize target yields while suppressing carbon accumulation and subsequent catalytic inactivation. Experiments on polycrystalline Cu/Al 2 O 3 , Ni/Al 2 O 3 , and Pt/Al 2 O 3 validate these predictions, revealing catalyst-dependent branching toward ethane or ethylene and distinct deactivation profiles. We unify these trends into a generalized three-dimensional plasma-thermal-catalytic design space, from which reduced descriptors such as T vib /T sur in the limit of vibrationally excited L–H pathways emerge as predictive metrics. These results enable rational tuning of methane conversion pathways and unlock selective C 2 formation using earth-abundant metals under mild plasma conditions.

catalyst inactivation↗

Crystal structure and magnetism of actinide oxides: a review

In actinide systems, the 5f electrons experience a uniquely delicate balance of effects and interactions having similar energy scales, which are often difficult to properly disentangle. This interplay of factors such as the dual nature of 5f-states, strong electronic correlations, and strong spin–orbit coupling results in electronically unusual and intriguing behavior such as multi-k antiferromagnetic ordering, multipolar ordering, Mott-physics, mixed valence configurations, and more. Despite the inherent allure of their exotic properties, the exploratory science of even the more basic, binary systems like the actinide oxides has been limited due to their toxicity, radioactivity, and reactivity. In this article, we provide an overview of the available synthesis techniques for selected binary actinide oxides, including the actinide dioxides, sesquioxides, and a selection of higher oxides. For these oxides, here we also review and evaluate the current state of knowledge of their crystal structures and magnetic properties. In many aspects, substantial knowledge gaps exist in the current body of research on actinide oxides related to understanding their electronic ground states. Bridging these gaps is vital for improving not only a fundamental understanding of these systems but also of future nuclear technologies. To this end, we note the experimental techniques and necessary future investigations which may aid in better elucidating the nature of these fascinating systems.

36 MATERIALS SCIENCE↗

Astrophysics & cosmology from line intensity mapping vs galaxy surveys

Line intensity mapping (LIM) proposes to efficiently observe distant faint galaxies and map the matter density field at high redshift. Building upon the formalism in a companion paper, we first highlight the degeneracies between cosmology and astrophysics in LIM. We discuss what can be constrained from measurements of the mean intensity and redshift-space power spectra. With a sufficient spectral resolution, the large-scale redshift-space distortions of the 2-halo term can be measured, helping to break the degeneracy between bias and mean intensity. With a higher spectral resolution, measuring the small-scale redshift-space distortions disentangles the 1-halo and shot noise terms. Additionally, cross-correlations with external galaxy catalogs or lensing surveys further break degeneracies. We derive requirements for experiments similar to SPHEREx, HETDEX, CDIM, COMAP and CONCERTO. We then revisit the question of the optimality of the LIM observables, compared to galaxy detection, for astrophysics and cosmology. We use a matched filter to compute the luminosity detection threshold for individual sources. We show that LIM contains information about galaxies too faint to detect, in the high-noise or high-confusion regimes. We quantify the sparsity and clustering bias of the detected sources and compare them to LIM, showing in which cases LIM is a better tracer of the matter density. We extend previous work by answering these questions as a function of Fourier scale, including for the first time the effect of cosmic variance, pixel-to-pixel correlations, luminosity-dependent clustering bias and redshift-space distortions.

79 ASTRONOMY AND ASTROPHYSICS↗

Exploring the MeV sky with a combined coded mask and Compton telescope: the Galactic Explorer with a Coded aperture mask Compton telescope (GECCO)

The sky at MeV energies is currently poorly explored. Here we present an innovative mission concept that builds upon the heritage of past and current missions improving the sensitivity and, very importantly, the angular resolution. This consists in combining a Compton telescope and a coded-mask telescope. We delineate the motivation for such a concept and we define the scientific goals for such a mission. The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel concept for a next-generation telescope covering hard X-ray and soft gamma-ray energies. The potential and importance of this approach that bridges the observational gap in the MeV energy range are presented. With the unprecedented angular resolution of the coded mask telescope combined with the sensitive Compton telescope, a mission such as GECCO can disentangle the discrete sources from the truly diffuse emission. Individual Galactic and extragalactic sources are detected. This also allows to understand the gamma-ray Galactic center excess and the Fermi Bubbles, and to trace the low-energy cosmic rays, and their propagation in the Galaxy. Nuclear and annihilation lines are spatially and spectrally resolved from the continuum emission and from sources, addressing the role of low-energy cosmic rays in star formation and galaxy evolution, the origin of the 511 keV positron line, fundamental physics, and the chemical enrichment in the Galaxy. Such an instrument also detects explosive transient gamma-ray sources, which, in turn, enables identifying and studying the astrophysical objects that produce gravitational waves and neutrinos in a multi-messenger context. By looking at a poorly explored energy band it also allows discoveries of new astrophysical phenomena.

79 ASTRONOMY AND ASTROPHYSICS↗

Modified gravitational wave propagation with higher modes and its degeneracies with lensing

Low-energy alternatives to General Relativity (GR) generically modify the phase of gravitational waves (GWs) during their propagation. As detector sensitivities increase, it becomes key to understand how these modifications affect the GW higher modes and to disentangle possible degeneracies with astrophysical phenomena. We apply a general formalism — the WKB approach — for solving analytically wave propagation in the spatial domain with a modified dispersion relation (MDR). We compare this WKB approach to applying a stationary phase approximation (SPA) in the temporal domain with time delays associated to the group or particle velocity. To this end, we extend the SPA to generic signals with higher modes, keeping careful track of reference phases and arrival times. We find that the WKB approach coincides with the SPA using the group velocity, in agreement with the principles of wave propagation. We then explore the degeneracies between a GW propagation with an MDR and a strongly-lensed GW in GR, since the latter can introduce a frequency-independent phase shift which is not degenerate with source parameters in the presence of higher modes. We find that for a particular MDR there is an exact degeneracy for wave propagation, unlike with the SPA for particle propagation. For the other cases, we search for the values of the MDR parameters that minimize the χ 2 and conclude that strongly-lensed GR GWs could be misinterpreted as GWs in modified gravity. As a result, future MDR constraints with higher mode GWs should include the possibility of frequency-independent phase shifts, allowing for the identification of modified gravity and strong lensing distortions at the same time.

79 ASTRONOMY AND ASTROPHYSICS↗

Polarization formalism for ALP-induced X-ray emission from magnetars

Missions like NASA's Imaging X-ray Polarimetry Explorer (IXPE) are poised to provide an unprecedented view of the Universe in polarized X-rays. Polarization probes physical anisotropies, a fact exploited by particle physicists to look for the anisotropic a E∙B operator in the axion-like-particle (ALP) Lagrangian. Such studies have typically focused on polarization in the radio and microwaves, through local or cosmic birefringence effects. To such polarization studies we add X-rays emanating from magnetars — a class of neutron stars with near-critical strength magnetic fields — that are important targets for IXPE. ALPs produced in the neutron star core convert to X-rays in the magnetosphere; such X-rays are polarized along the direction parallel to the dipolar magnetic field at the point of conversion. Here, we develop the full theoretical formalism for ALP-induced polarization in the presence of dipolar magnetic fields. For uncorrelated photon and ALP production mechanisms, we completely disentangle the ALP contributions to the Stokes parameters in terms of the ALP intensity, the ALP-to-photon conversion probability, and the ALP-induced birefringence. In the proper limit, our results demonstrate that the inclusion of ALPs suppresses the observed degree of circular polarization compared to its pure astrophysical value. Our results can also be used to impose limits on ALP couplings with IXPE polarization data from magnetars 4U 0142+61 and 1RXS J170849.0-400910, the subject of upcoming work.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing fundamental constant oscillation in the Galactic Center with S-Star Spectroscopy

Astrophysical spectroscopy provides a powerful probe of spacetime variations of fundamental constants, as atomic and ionic emission and absorption lines depend sensitively on the fine-structure constant. In particular, coherent temporal oscillations induced by an ultralight scalar background produce characteristic, time-resolved signatures that can be robustly disentangled from intrinsic variability. In the Galactic Center, such scalar backgrounds can be substantially enhanced, either through the formation of dense scalar clouds powered by black hole rotational energy extraction or as ultralight scalar dark matter forming a soliton-like core. These scalar configurations generically induce oscillations of the fine-structure constant, with periods set by the scalar mass and spatial profiles determined by the scalar wavefunction and its coupling to the electromagnetic sector. We show that precise, time-resolved spectroscopy of S-stars orbiting the supermassive black hole Sgr A^* provides a sensitive test of these effects, enabling constraints on quadratic scalar-photon couplings in the exceptionally high boson-density environment of the Galactic Center.

Bai, Zhaoyu [Weizmann Inst.] (ORCID:00000002075815↗

Brighter-fatter Effect in Near-infrared Detectors—III. Fourier-domain Treatment of Flat Field Correlations and Application to WFIRST

Weak gravitational lensing has emerged as a leading probe of the growth of cosmic structure. However, the shear signal is very small and accurate measurement depends critically on our ability to understand how non-ideal instrumental effects affect astronomical images. The Wide-Field Infrared Survey Telescope (WFIRST) will fly a focal plane containing 18 Teledyne H4RG-10 near-infrared detector arrays, which present different instrument calibration challenges from previous weak lensing observations. Previous work [Paper I: Hirata & Choi, PASP, 132, 014501 (2020); and Paper II: Choi & Hirata, PASP, 132, 014502 (2020)] has shown that correlation functions of flat field images, including cross-correlations between different time slices that are enabled by the non-destructive read capability of the infrared detectors, are effective tools for disentangling linear and nonlinear inter-pixel capacitance (IPC) and the brighter-fatter effect (BFE). Here we present a Fourier-domain treatment of the flat field correlations, which allows us to expand the previous formalism to all orders in IPC, BFE, and classical nonlinearity. We show that biases in simulated flat field analyses in Paper I are greatly reduced through the use of this formalism. We then apply this updated formalism to flat field data from three WFIRST flight candidate detectors, and explore the robustness to variations in the analysis. We find that the BFE is present in all three detectors, and that its contribution to the flat field correlations dominates over the nonlinear IPC, in accordance with the results from Paper II on a development detector. The magnitude of the BFE is such that the effective area of a pixel is increased by (3.54 ± 0.03) × 10 -7 for every electron deposited in a neighboring pixel (sensor chip assembly [SCA] 20829, statistical error, not IPC-deconvolved). We compare IPC maps from flat field autocorrelation measurements to those obtained from the single pixel reset method and find a median difference of 0.113% for SCA 20829. After further diagnosis of this difference, we ascribe it largely to an additional source of cross-talk, the vertical trailing pixel effect, and recommend further work to develop a model for this effect. These results represent a significant step toward calibration of the non-ideal effects in WFIRST detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

Xenon doping of Liquid Argon in ProtoDUNE Single Phase: first results

Doping Liquid Argon (LAr) with xenon is a known technique to shift the light emitted by argon (128 nm) to a longer wavelength to ease its detection. The largest Xenon doping test ever performed in a LArTPC was carried out in ProtoDUNE Single Phase (ProtoDUNE-SP) at the CERN Neutrino Platform. The response of such a large TPC (7701 of Liquid Argon and 4401 of fiducial mass) has been studied using the ProtoDUNE Photon Detection System (PDS) and a dedicated setup installed before the run. With the first, it was possible to study the light detected in the system as a function of the xenon concentration and to characterise the light collection efficiency with respect to the track position. With the second system it was possible to disentangle the LAr (128 nm) light from the xenon (178 nm) light using two dedicated X-ARAPUCA modules. The run was fully satisfactory, it was possible to measure directly the increase of the xenon light component during doping; furthermore most of the LAr light quenched by impurities was fully recovered even at small Xenon concentration (< 20 ppm in mass). A study of the collected scintillation light as a function of the track position showed an improvement of the detector response uniformity.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Scintillator ageing of the T2K near detectors from 2010 to 2021

The T2K experiment widely uses plastic scintillator as a target for neutrino interactions and an active medium for the measurement of charged particles produced in neutrino interactions at its near detector complex. Over 10 years of operation the measured light yield recorded by the scintillator based subsystems has been observed to degrade by 0.9–2.2% per year. Extrapolation of the degradation rate through to 2040 indicates the recorded light yield should remain above the lower threshold used by the current reconstruction algorithms for all subsystems. This will allow the near detectors to continue contributing to important physics measurements during the T2K-II and Hyper-Kamiokande eras. Additionally, work to disentangle the degradation of the plastic scintillator and wavelength shifting fibres shows that the reduction in light yield can be attributed to the ageing of the plastic scintillator. The long component of the attenuation length of the wavelength shifting fibres was observed to degrade by 1.3–5.4% per year, while the short component of the attenuation length did not show any conclusive degradation.

47 OTHER INSTRUMENTATION↗

The scintillator surface detector of the Pierre Auger observatory

Data collected so far by the Pierre Auger Observatory have enabled major advances in ultra-high energy cosmic ray physics and demonstrated that improved determination of masses of primary cosmic-ray particles, preferably on an event-by-event basis, is necessary for understanding their origin and nature. Improvement in primary mass measurements was the main motivation for the upgrade of the Pierre Auger Observatory, called AugerPrime. As part of this upgrade, scintillator detectors are added to the existing water-Cherenkov surface detector stations. By making use of the differences in detector response to the electromagnetic particles and muons between scintillator and water-Cherenkov detectors, the electromagnetic and muonic components of cosmic-ray air showers can be disentangled. Since the muonic component is sensitive to the primary mass, such combination of detectors provides a powerful way to improve primary mass composition measurements over the original Auger surface detector design. In this paper, the so-called Scintillator Surface Detectors are discussed, including their design characteristics, production process, testing procedure and deployment in the field.

Detector design and construction technologies and ↗

Distinct roles of land cover in regulating spatial variabilities of temperature responses to radiative effects of aerosols and clouds

Surface temperature responses to radiative perturbations due to aerosols and clouds are complicated by the land surface properties. To disentangle these complexities, this study, from a terrestrial surface energy budget perspective, isolates the underlying biophysical processes from the instantaneous radiative effects of aerosols and clouds on surface temperature using the National Center for Atmospheric Research Community Earth System Model version 1.2.1. It is found that in comparison with the global heterogeneous distributions of instantaneous radiative perturbations at the surface induced by aerosols and clouds, the spatial variations of the corresponding surface temperature responses to aerosol direct radiative effects (DRE) during the daytime and cloud radiative effects (CRE) during the nighttime are amplified. It is because of the consistent global distribution of the local surface climate sensitivity (a function of land cover properties such as surface roughness and Bowen ratio) with those of daytime DRE and nighttime CRE. By applying identical anthropogenic aerosol and precursor emissions over eight major past, present and projected future anthropogenic aerosol emitting regions (i.e. Brazil, China, East Africa, India, Indonesia, South Africa, United States and Western Europe), surface temperature responses to aerosol radiative cooling in the daytime and cloud radiative warming in the nighttime over these regions positively regulated by local surface climate sensitivities are prominent.

54 ENVIRONMENTAL SCIENCES↗

Rapidly changing high-latitude seasonality: implications for the 21st century carbon cycle in Alaska

Seasonal variations in high-latitude terrestrial carbon (C) fluxes are predominantly driven by air temperature and radiation. At present, high-latitude net C uptake is largest during the summer. Recent observations and modeling studies have demonstrated that ongoing and projected climate change will increase plant productivity, microbial respiration, and growing season lengths at high-latitudes, but impacts on high-latitude C cycle seasonality (and potential feedbacks to the climate system) remain uncertain. Here we use ecosys, a well-tested and process-rich mechanistic ecosystem model that we evaluate further in this study, to explore how climate warming under an RCP8.5 scenario will shift C cycle seasonality in Alaska throughout the 21st century. The model successfully reproduced recently reported large high-latitude C losses during the fall and winter and yet still predicts a high-latitude C sink, pointing to a resolution of the current conflict between process-model and observation-based estimates of high-latitude C balance. We find that warming will result in surprisingly large changes in net ecosystem exchange (NEE; defined as negative for uptake) seasonality, with spring net C uptake overtaking summer net C uptake by year 2100. This shift is driven by a factor of 3 relaxation of spring temperature limitation to plant productivity that results in earlier C uptake and a corresponding increase in magnitude of spring NEE from –19 to –144 gC m –2 season –1 by the end of the century. Although a similar relaxation of temperature limitation will occur in the fall, radiation limitation during those months will limit increases in C fixation. Additionally, warmer soil temperatures and increased carbon inputs from plants lead to combined fall and winter C losses (163 gC m –2 ) that are larger than summer net uptake (123 gC m –2 season –1 ) by year 2100. However, this increase in microbial activity leads to more rapid N cycling and increased plant N uptake during the fall and winter months that supports large increases in spring NPP. Due to the large increases in spring net C uptake, the high-latitude atmospheric C sink is projected to sustain throughout this century. Our analysis disentangles the effects of key environmental drivers of high-latitude seasonal C balances as climate changes over the 21st century.

54 ENVIRONMENTAL SCIENCES↗

Optimizing training trajectories in variational autoencoders via latent Bayesian optimization approach *

Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and/or regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g. balancing the Kullback–Leibler and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive-to-train models, here we have explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrated for joint-VAE with rotational invariances. We have demonstrated an application of this method for finding joint discrete and continuous rotationally invariant representations for modified national institute of standards and technology database (MNIST) and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter trajectory optimization of other ML models.

42 ENGINEERING↗

A robust estimator of mutual information for deep learning interpretability

Abstract We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Combining variational autoencoders and physical bias for improved microscopy data analysis *

Electron and scanning probe microscopy produce vast amounts of data in the form of images or hyperspectral data, such as electron energy loss spectroscopy or 4D scanning transmission electron microscope, that contain information on a wide range of structural, physical, and chemical properties of materials. To extract valuable insights from these data, it is crucial to identify physically separate regions in the data, such as phases, ferroic variants, and boundaries between them. In order to derive an easily interpretable feature analysis, combining with well-defined boundaries in a principled and unsupervised manner, here we present a physics augmented machine learning method which combines the capability of variational autoencoders to disentangle factors of variability within the data and the physics driven loss function that seeks to minimize the total length of the discontinuities in images corresponding to latent representations. Our method is applied to various materials, including NiO-LSMO, BiFeO 3 , and graphene. The results demonstrate the effectiveness of our approach in extracting meaningful information from large volumes of imaging data. The customized codes of the required functions and classes to develop phyVAE is available at https://github.com/arpanbiswas52/phy-VAE.

97 MATHEMATICS AND COMPUTING↗