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DOE OSTI2020

An accurate perturbative approach to redshift space clustering of biased tracers in modified gravity

We extend the scale-dependent Gaussian Streaming Model (GSM) to produce analytical predictions for the anisotropic redshift-space correlation function for biased tracers in modified gravity models. Employing the Convolution Lagrangian Perturbation Theory (CLPT) re-summation scheme, with a local Lagrangian bias schema provided by the peak-background split formalism, we predict the necessary ingredients that enter the GSM, the real-space halo pairwise velocity and the pairwise velocity dispersion. We further consider effective field theory contributions to the pairwise velocity dispersion in order to model correctly its large scale behavior. We apply our method on two widely-considered modified gravity models, the chameleon-screened ƒ(R) Hu-Sawicki model and the nDGP Vainshtein model and compare our predictions against state-of-the-art N-body simulations for these models. We demonstrate that the GSM approach to predict the monopole and the quadrupole of the redshift-space correlation function for halos, gives very good agreement with the simulation data, for a wide range of screening mechanisms, levels of screening and halo masses at z = 0.5 and z = 1. Our work shows the applicability of the GSM, for cosmologies beyond GR, demonstrating that it can serve as a powerful predictive tool for the next stage of cosmological surveys like DESI, Euclid, LSST and WFIRST.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Global centroid moment tensor solutions in a heterogeneous earth: the CMT3D catalogue

SUMMARY For over 40 yr, the global centroid-moment tensor (GCMT) project has determined location and source parameters for globally recorded earthquakes larger than magnitude 5.0. The GCMT database remains a trusted staple for the geophysical community. Its point-source moment-tensor solutions are the result of inversions that model long-period observed seismic waveforms via normal-mode summation for a 1-D reference earth model, augmented by path corrections to capture 3-D variations in surface wave phase speeds, and to account for crustal structure. While this methodology remains essentially unchanged for the ongoing GCMT catalogue, source inversions based on waveform modelling in low-resolution 3-D earth models have revealed small but persistent biases in the standard modelling approach. Keeping pace with the increased capacity and demands of global tomography requires a revised catalogue of centroid-moment tensors (CMT), automatically and reproducibly computed using Green's functions from a state-of-the-art 3-D earth model. In this paper, we modify the current procedure for the full-waveform inversion of seismic traces for the six moment-tensor parameters, centroid latitude, longitude, depth and centroid time of global earthquakes. We take the GCMT solutions as a point of departure but update them to account for the effects of a heterogeneous earth, using the global 3-D wave speed model GLAD-M25. We generate synthetic seismograms from Green's functions computed by the spectral-element method in the 3-D model, select observed seismic data and remove their instrument response, process synthetic and observed data, select segments of observed and synthetic data based on similarity, and invert for new model parameters of the earthquake’s centroid location, time and moment tensor. The events in our new, preliminary database containing 9382 global event solutions, called CMT3D for ‘3-D centroid-moment tensors’, are on average 4 km shallower, about 1 s earlier, about 5 per cent larger in scalar moment, and more double-couple in nature than in the GCMT catalogue. We discuss in detail the geographical and statistical distributions of the updated solutions, and place them in the context of earlier work. We plan to disseminate our CMT3D solutions via the online ShakeMovie platform.

58 GEOSCIENCES↗

DOE OSTI2022

How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates

Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Blinded challenge for precision cosmology with large-scale structure: Results from effective field theory for the redshift-space galaxy power spectrum

An accurate theoretical template for the galaxy power spectrum is key for the success of ongoing and future spectroscopic surveys. We examine to what extent the effective field theory (EFT) of large-scale structure is able to provide such a template and correctly estimate cosmological parameters. To that end, we initiate a blinded challenge to infer cosmological parameters from the redshift-space power spectrum of high-resolution mock catalogs mimicking the BOSS galaxy sample but covering a 100 times larger cumulative volume. This gigantic simulation volume allows us to separate systematic bias due to theoretical modeling from the statistical error due to sample variance. The challenge is to measure three unknown input parameters used in the simulation: the Hubble constant, the matter density fraction, and the clustering amplitude. We present analyses done by two independent teams, who have fitted the mock simulation data generated by yet another independent group. This allows us to avoid any confirmation bias by analyzers and to pin down possible tuning of the specific EFT implementations. Both independent teams have recovered the true values of the input parameters within subpercent statistical errors corresponding to the total simulation volume.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Surface and Atmospheric Heating Responses to Spectrally Resolved Albedo of Frozen and Liquid Water Surfaces

Abstract Multiple Earth system models (ESMs) discretize surface albedo into two semi‐broadbands comprising the UV/visible and near‐infrared (NIR) wavelengths. Here, we use an offline single‐column radiative transfer model to investigate the radiative effects of spectrally resolving the surface albedo. We use the Snow, Ice, and Aerosol Radiative model, extended to simulate liquid water, to calculate snow, ice, and liquid water albedo. We flux‐weight the hyperspectral albedo into the coarser spectral bands used by the atmospheric shortwave radiative transfer model. We establish representative atmospheric profiles for the three surface types and compare their shortwave fluxes and atmospheric warming rates with the spectrally resolved albedo to those calculated with the semi‐broadband approximation. Spectrally resolved surface albedo over snow and ice reduces atmospheric warming by darkening the albedo of NIR bands, correcting the too‐strong surface absorption in visible bands, and too‐weak surface absorption in shortwave infrared bands caused by the semi‐broadband approximation. We explore the effects on surface and atmospheric warming rates of varying solar zenith angle, cloud cover, relative humidity, and snow grain/air bubble radii. The semi‐broadband albedo biases can exceed 10% and 2% for the surface and atmospheric net flux respectively, being particularly strong under conditions which alter the distributions of surface insolation (i.e., cloud cover or increased atmospheric water vapor). These results show that transmitting a higher resolution spectral radiation field between the atmosphere and surface reduces biases in surface absorption and atmospheric heating present in ESMs that currently use the semi‐broadband approximation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Noise from undetected sources in Dark Energy Survey images

ABSTRACT For ground-based optical imaging with current CCD technology, the Poisson fluctuations in source and sky background photon arrivals dominate the noise budget and are readily estimated. Another component of noise, however, is the signal from the undetected population of stars and galaxies. Using injection of artifical galaxies into images, we demonstrate that the measured variance of galaxy moments (used for weak gravitational lensing measurements) in Dark Energy Survey (DES) images is significantly in excess of the Poisson predictions, by up to 30 per cent, and that the background sky levels are overestimated by current software. By cross-correlating distinct images of ‘empty’ sky regions, we establish that there is a significant image noise contribution from undetected static sources (US), which, on average, are mildly resolved at DES resolution. Treating these US as a stationary noise source, we compute a correction to the moment covariance matrix expected from Poisson noise. The corrected covariance matrix matches the moment variances measured on the injected DES images to within 5 per cent. Thus, we have an empirical method to statistically account for US in weak lensing measurements, rather than requiring extremely deep sky simulations. We also find that local sky determinations can remove most of the bias in flux measurements, at a small penalty in additional, but quantifiable, noise.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Understanding Biases in Sample Preparation Techniques for Coupled Scanning Electron Microscopy and MAMA PuO 2 Morphological Analysis

In this project, the scanning electron microscopy (SEM) sampling method used during the statistical design study (SDS) was investigated to determine if any sampling biases were present in the analyzed data. Using standard particle size distribution powders from the National Institute of Standards and Technology (NIST 1984 standard reference material) with the origin wet dispersion method, it was determined that a bias to smaller particles was present. This was supported by theoretical calculations using Stokes’ law to determine the settling rate of spherical particles of roughly the same size and mass as those found in the SDS. Based on the theoretical calculations, it was determined that the settling rate for each of the 76 powder sets in the SDS could be unique based on specific particle shape and mass distributions, making a universal correction factor/formula not applicable. Therefore, priority shifted to developing an improved wet dispersion method that significantly reduced the particle settling rate for all particle size and shapes. This was achieved by replacing the original solvent (isopropyl alcohol) with a heavy liquid (lithium heteropolytungstates), which dramatically slowed the settling rate and allowed for the capture of a suitable homogeneous aliquot. SEM imaging and Morphological Analysis for Material Attribution (MAMA) software analysis were conducted on the NIST standard, and the SEM/MAMA data were compared to data captured by a dynamic image analysis particle size analyzer. The resulting data confirmed that the new wet dispersion method does indeed deliver an improved representative aliquot to the SEM stub. For instance, in the NIST certificate, the average particle size is ~17.1 µm ± 2.2 µm with a normal distribution. The initial wet dispersion method resulted in a drastically reduced average particle size of 6.1 µm in addition to a non-representative heavy bi-modal distribution whereas the improved LST wet dispersion method resulting in an average particle size that was much closer to the NIST certificate (12.7 µm) with a similar normal distribution. Although the improved method was still short of the NIST certificate average, atomic force microscopy analysis determined that the resulting ~20-25% reduction in size was due to particles sinking into the carbon sticky tape used for SEM imaging. It is believed that that this bias can be calibrated in a much more predicable manner than the original settling rate bias. In addition, the matching normal distribution curves between the NIST certificate and the heavy liquid method indicate a much-improved representative aliquot has been sampled and imaged. A surrogate CeO 2 powder was used to reflect PuO 2 more accurately and to aid in implementing radiological controls and shielding. The resulting data sets from the SEM/MAMA method and the particle size analyzer give almost identical average particle sizes and particle distribution statistics. Future work will re-analyze several select runs from the SDS to determine if morphological signatures can be found with the improved sampling method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Emulating galaxy and peculiar velocity clustering on non-linear scales

We explore the potential of cross-correlating galaxies and peculiar velocities on non-linear scales to enhance cosmological constraints. Leveraging the ABACUSSUMMIT simulation suite and the halo occupation distribution (HOD) formalism, we trained emulator models to describe the non-linear clustering of galaxies and velocities in redshift space. Our analysis demonstrates that combining galaxy and peculiar velocity clustering provides tighter constraints on both HOD and cosmological parameters, particularly on σ8 and w0. We further applied our models to realistic mock catalogues, reproducing the expected density and peculiar velocity errors of type-Ia supernovae, Tully-Fisher and fundamental plane measurements for the combined ZTF and DESI measurements. While systematic biases arise in the HOD parameters, the cosmological constraints remain unbiased, yielding a 3.8% precision measurement on fσ 8 compared to 4.7% when using galaxy clustering alone. We demonstrate that while combining tracers with realistic velocity measurements still yields an improvement, the gains are diminished, highlighting the need for further efforts to reduce velocity measurement uncertainties and correct observational systematics on small scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Investigating the linkage between simulated precipitation climatology and ENSO-related precipitation anomaly based on multi-model and perturbed parameter ensembles

It remains a challenge for climate models to correctly capture the relationship between precipitation and ENSO. This studyexamines the linkage between the simulated precipitation climatology and ENSO-related precipitation anomaly during borealwinter based on the multi-model ensemble from the Atmospheric Model Intercomparison Project Phase 5 (AMIP5) and perturbedparameter ensemble (PPE) with the Beijing Climate Center (BCC) atmospheric model. The AMIP5 models have large biases insimulating the tropical precipitation anomaly during El Niño, such as the shifts of the Inter-Tropical Convergence Zone (ITCZ)and South Pacific Convergence Zone (SPCZ). The inter-model differences show that the precipitation change in response to seasurface temperature (SST) change increases with enhanced precipitation climatology. The ENSO-related precipitation anomalycan also be related to the spatial distribution of the mean-state precipitation. The simulated ITCZ/SPCZ displacements aresignificantly correlated with the spatial precipitation-SST relationship in the mean state. Models with stronger mean-stateprecipitation-SST relationship also produce stronger SPCZ/ITCZ displacements. The mean-state tropical precipitation also hasstrong impacts on the ENSO-related precipitation anomalies over East Asia. In the BCC PPE, the connection between the mean-state precipitation and ENSO-related precipitation anomaly is overall consistent with that in AMIP5. Parameters associated withthe low-cloud and deep convection processes are the most influential ones for the precipitation simulations in BCC. Comparedwith the version in AMIP5, the new BCC model can better simulate the precipitation climatology and the relationship betweenENSO and precipitation over southern China. These results have important implications for model development and model-basedclimate predictions.

Yang, Ben↗

DOE OSTI2025

Measurement of event shapes in minimum-bias events from proton-proton collisions at $\sqrt{s}$ = 13

A measurement of event-shape variables is presented, using a data sample produced in a special run with approximately one inelastic proton-proton collision per bunch crossing. The data were collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 64 μ⁢b −1 . A number of observables related to the overall distribution of charged particles in the collisions are corrected for detector effects and compared with simulations. Inclusive event-shape distributions, as well as differential distributions of event shapes as functions of charged-particle multiplicity, are studied. None of the models investigated are able to satisfactorily describe the data. Moreover, there are significant features common amongst all generator setups studied, particularly showing data being more isotropic than any of the simulations. Multidimensional unfolded distributions are provided, along with their correlations.

Chekhovsky, V. [Yerevan Physics Institute]↗

DOE OSTI2024

Enhancing quantum annealing accuracy through replication-based error mitigation *

Abstract Quantum annealers like those manufactured by D-Wave Systems are designed to find high quality solutions to optimization problems that are typically hard for classical computers. They utilize quantum effects like tunneling to evolve toward low-energy states representing solutions to optimization problems. However, their analog nature and limited control functionalities present challenges to correcting or mitigating hardware errors. As quantum computing advances towards applications, effective error suppression is an important research goal. We propose a new approach called replication based mitigation (RBM) based on parallel quantum annealing (QA). In RBM, physical qubits representing the same logical qubit are dispersed across different copies of the problem embedded in the hardware. This mitigates hardware biases, is compatible with limited qubit connectivity in current annealers, and is well-suited for currently available noisy intermediate-scale quantum annealers. Our experimental analysis shows that RBM provides solution quality on par with previous methods while being more flexible and compatible with a wider range of hardware connectivity patterns. In comparisons against standard QA without error mitigation on larger problem instances that could not be handled by previous methods, RBM consistently gets better energies and ground state probabilities across parameterized problem sets.

Djidjev, Hristo N. (ORCID:0000000192868824)↗

DOE OSTI2023

Color Transformations of Photometric Measurements of Galaxies in Optical and Near-infrared Wide-field Imaging Surveys*

Abstract Over the past 2 decades, wide-field photometric surveys in optical and infrared domains reached a nearly all-sky coverage thanks to numerous observational facilities operating in both hemispheres. However, subtle differences among exact realizations of Johnson and SDSS photometric systems require one to convert photometric measurements into the same system prior to analysis of composite data sets originating from multiple surveys. It turns out that the published photometric transformations lead to substantial biases when applied to integrated photometry of galaxies from the corresponding catalogs. Here we present photometric transformations based on piece-wise linear approximations of integrated photometry of galaxies in the optical surveys SDSS, DECaLS, BASS, MzLS, DES, DELVE, KiDS, VST ATLAS, and the near-infrared surveys UKIDSS, UHS, VHS, and VIKING. We validate our transformations by constructing k -corrected color–magnitude diagrams of non-active galaxies and measuring the position and tightness of the “red sequence.” We also provide transformations for aperture magnitudes and show how they are affected by the image quality difference among the surveys. We present the implementation of the derived transformations in python and idl and also a web-based color transformation calculator for galaxies. By comparing DECaLS and DES, we identified systematic issues in DECaLS photometry for extended galaxies, which we attribute to the photometric software package used by DECaLS. As an application of our method, we compiled two multi-wavelength photometric catalogs for over 200,000 low- and intermediate-redshift galaxies originating from CfA FAST and Hectospec spectral archives.

Astronomy & Astrophysics↗

DOE OSTI2025

Reducing Long‐Standing Surface Ozone Overestimation in Earth System Modeling by High‐Resolution Simulation and Dry Deposition Improvement

The overestimation of surface ozone concentration in low‐resolution global atmospheric chemistry and climate models has been a long‐standing issue. We first update the ozone dry deposition scheme in both high‐ (0.25°) and low‐resolution (1°) Community Earth System Model (CESM) version 1.3 runs, by adding the effects of leaf area index and correcting the sunlit and shaded fractions of stomatal resistances. With this update, 5‐year‐long summer simulations (2015–2019) using the low‐resolution CESM still exhibit substantial ozone overestimation (by 6.0–16.2 ppbv) over the U.S., Europe, eastern China, and ozone pollution hotspots. The ozone dry deposition scheme is further improved by adjusting the leaf cuticle conductance, reducing the mean ozone bias by 19%, and increasing the model resolution further reduces the ozone overestimation by 43%. We elucidate the mechanism by which model grid spacing influences simulated ozone, revealing distinctive pathways in urban versus rural areas. In rural areas, grid spacing mainly affects daytime ozone levels, where additional NO x emissions from nearby urban areas result in an ozone boost and overestimation in low‐resolution simulations. In contrast, over urban areas, daytime ozone overestimation follows a similar mechanism due to the influence of volatile organic compounds from surrounding rural areas. However, nighttime ozone overestimation is closely linked to weakened NO titration owing to the redistribution of urban NO x to rural areas. Additionally, stratosphere‐troposphere exchange may also contribute to reducing ozone bias in high‐resolution simulations, warranting further investigation. This optimized high‐resolution CESM may enhance understanding of ozone formation mechanisms, sources, and changes in a warming climate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

A unified thermionic and thermionic-field emission (TE–TFE) model for ideal Schottky reverse-bias leakage current

We present a unified thermionic emission (TE) and thermionic-field emission (TFE) model for the ideal reverse-bias leakage current in Schottky junctions. The unified TE–TFE analytical model advances upon previous analytical TFE models by Murphy–Good and Padovani–Stratton, which are the two most widely adopted models by the community, in two major aspects: (i) the applicability of the TFE expression therein is extended to near-zero surface electric fields by an error-function correction, allowing for the calculation of the total current by a nontrivial sum of TE (over-the-barrier current) and TFE (below-the-barrier current) contributions; therefore, an accurate description of the TE-to-TFE transition region is captured analytically for the first time; (ii) image-force lowering is considered with much-simpler correction terms. Comparisons with the reference numerical model show that the unified TE–TFE model has excellent accuracy, as well as a 10 000× reduction in computation time. The unified model is further tested against experimental data from Schottky barrier diodes based on Si, 4H-SiC, GaN, and β-Ga 2 O 3 , revealing accurate extractions of barrier heights and correct descriptions of the ideal reverse leakage characteristics. With the extended applicable range, improved accuracy, and computational efficiency, the unified TE–TFE model is highly valuable for the design and analysis of devices based on Schottky junctions, as well as for potential integration in technology computer-aided design (TCAD) tools.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Illumination correction of dyed fabric based on extreme learning machine with improved ant lion optimizer

Abstract In order to eliminate the influence of scene illumination on the evaluation of the color difference of dyed fabrics, this paper proposes a dyed fabric illumination correction algorithm based on the extreme learning machine (ELM) with grey wolf optimizer (GWO)‐optimized ant lion optimizer (ALO). Firstly, the Grey Edge framework is used to extract the features of the dyed fabric image as the input vector. Then, to improve the optimization ability of the ALO algorithm, the GWO algorithm is used to provide a set of optimized initial populations to the ALO algorithm, and then the improved ALO algorithm is used to optimize the parameters of the ELM. Finally, the proposed GWO‐ALO‐ELM algorithm is used to correct the illumination of the dyed fabric, and restore the graphics to the effect display under standard illumination through the diagonal reduction model. Compared with the experimental results of GWO‐ELM, ALO‐ELM, backpropagation (BP), ELM, random vector function link (RVFL), and other algorithms, it can be seen that the GWO‐ALO‐ELM algorithm proposed in this paper has good predictive value and quasi‐bias effect, and good stability.

Zhou, Zhiyu↗

DOE OSTI2024

Evaluation of WSR-88D Level III and MRMS Rainfall Estimates Against Rain Gauge Observations at the Savannah River Site

Rainfall data for the Savannah River Site (SRS) has been historically measured by rain gauges. These instruments serve as ground truth for most climatological and weather applications; however, gauge measurements are prone to errors or biases under certain weather conditions. Rainfall estimates from radar reflectivity values have been developed and improved over the years and serve as an alternative or supplement for gauge measurements. This study compares measurements from tipping bucket rain gauges with rainfall estimates from the NOAA NWS WSR-88D Level III hourly rainfall product and the Multi-Radar Multi-Sensor (MRMS) gauge-corrected precipitation estimate. Results show good agreement between radar derived amounts and ground measurements, with MRMS values showing correlation coefficients of 0.60-0.95 and RMSE values of less than 1.0 cm (0.4 in). The WSR-88D Level III estimates result in correlation coefficients of 0.46-0.86 and RMSE values of less than 1.3 cm (0.5 in). Few outliers are observed for each data pair and are evaluated against precipitation classification products (WSR-88D Hybrid Hydrometeor Classification product and MRMS Precipitation Flag product). The rain gauges used in this study are not part of the Hydrometeorological Automated Data System (HADS) network used to correct the MRMS estimates and therefore, results of this work provide an independent validation of the MRMS gauge correction scheme.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Sensitivity of Cloud-Radiative Effects to Cloud Fraction Parametrizations in Tropical, Mid-Latitude and Arctic Kilometre-Scale Simulations

The Regional Atmosphere (RA) configuration of the Met Office Unified Model currently requires different cloud fraction parametrizations (CFP) for tropical and midlatitude simulations. To explore the scope for unification of these two RA configurations, this paper presents a detailed evaluation of simulations over tropical, midlatitude and arctic domains, with two different diagnostic CFPs, a prognostic CFP, and no CFP at all. Furthermore, a novel, hybrid approach was used that treats liquid cloud diagnostically and ice cloud prognostically. Using observations from three U.S. Department of Energy Atmospheric Radiation Measurement supersites, it is shown that none of these CFPs stands out as superior over all domains. Over the frequently overcast Arctic, the all-or-nothing approach best captures the cloud radiative properties. Conversely, CFPs are of benefit in regions with frequent partial cloudiness, such as the midlatitudes and the tropics. However, their improved cloud radiative properties often hide an error compensation. All models underestimate overcast, low-base cloud with small water paths in convective environments. In addition, mid-latitude overcast, low-base, optically thick clouds in the morning, possibly associated with overnight convection, are frequently too broken. Diagnostic schemes compensate for these errors by producing spurious, scattered afternoon cloud, which could be due to a correct cloud response to too eager convective initiation. Winter clouds over the midlatitudes are improved when liquid cloud is represented diagnostically with a bimodal saturation-departure PDF, without error compensation. While it is difficult to unify the RA across the globe around a single CFP scheme, the newly proposed Hybrid scheme performs reasonably well for cloud cover across all regions. It also exhibits SW biases that are smaller than most other configurations and is less affected by excessive liquid water paths and compensating errors than fully diagnostic schemes. Surface precipitation is fairly insensitive to the CFP in the simulations shown here.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

When and why PINNs fail to train: A neural tangent kernel perspective

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. Here in this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗