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DOE OSTI2025

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

For quantum matter, eigenstate entanglement entropies obey an area law or log-area law at low energies and small subsystem sizes and cross over to volume laws for high energies and large subsystems. This transition is captured by crossover functions, which assume a universal scaling form in quantum critical regimes. We demonstrate this for the harmonic lattice model, which describes quantized lattice vibrations and is a regularization for free scalar field theories, modeling, e.g., spin-0 bosonic particles. In one dimension, the ground-state entanglement obeys a log-area law. For dimensions d ≥ 2, it displays area laws, even at criticality. The distribution of excited-state entanglement entropies is found to be sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. Numerically, we determine crossover scaling functions for the quantum critical regime of the model and do a large-deviation analysis. We show how infrared singularities of the system can be handled and how to access the thermodynamic limit using a perturbative trick for the covariance matrix. Eigenstates for quasi-free bosonic systems are not Gaussian. Here, we resolve this problem by considering appropriate squeezed states instead. For these, entanglement entropies can be evaluated efficiently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Monte Carlo control loops for cosmic shear cosmology with DES Year 1 data

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of background galaxies and requires precise control of systematic errors. Monte Carlo control loops (MCCL) is a forward modeling method designed to tackle this problem. It relies on the ultra fast image generator (UFig) to produce simulated images tuned to match the target data statistically, followed by calibrations and tolerance loops. Here, we present the first end-to-end application of this method, on the Dark Energy Survey (DES) Year 1 wide field imaging data. We simultaneously measure the shear power spectrum $C_ℓ$ and the redshift distribution $n(z)$ of the background galaxy sample. The method includes maps of the systematic sources, point spread function (PSF), an approximate Bayesian computation (ABC) inference of the simulation model parameters, a shear calibration scheme, and a fast method to estimate the covariance matrix. We find a close statistical agreement between the simulations and the DES Y1 data using an array of diagnostics. In a nontomographic setting, we derive a set of $C_ℓ$ and $n(z)$ curves that encode the cosmic shear measurement, as well as the systematic uncertainty. Following a blinding scheme, we measure the combination of $Ω_m$, $σ_8$, and intrinsic alignment amplitude $A_{IA}$, defined as $S_8D_{IA}=σ_8(Ω_m/0.3)^{0.5}D_{IA}$, where $D_{IA}=1-0.11(A_{IA}-1)$. We find $S_8D_{IA}=0.8954_{-0.039}^{+0.054}$, where systematics are at the level of roughly 60% of the statistical errors. We discuss these results in the context of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that this method and its fast runtime offer good prospects for cosmic shear measurements with future wide-field surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Return of the templates: Revisiting the Galactic Center excess with multimessenger observations

The Galactic center excess (GCE) remains one of the most intriguing discoveries from the Fermi Large Area Telescope (LAT) observations. We revisit the characteristics of the GCE by first producing a new set of high-resolution galactic diffuse gamma-ray emission templates. This diffuse emission, which accounts for the bulk of the observed gamma rays, is ultimately due to cosmic-ray interactions with the interstellar medium. Using recent high-precision cosmic-ray observations, in addition to the continuing Fermi-LAT observations and observations from lower energy photons, we constrain the properties of the galactic diffuse emission. We describe a large set of diffuse gamma-ray emission templates which account for a very wide range of initial assumptions on the physical conditions in the inner galaxy. The broad properties of the GCE that we find in this work are qualitatively unchanged despite the introduction of this new set of templates, though its quantitative features appear mildly different than those obtained in previous analyses. In particular, we find a high-energy tail at higher significance than previously reported. This tail is very prominent in the northern hemisphere, and less so in the southern hemisphere. This strongly affects one prominent interpretation of the excess: known millisecond pulsars are incapable of producing this high-energy emission, even in the relatively softer southern hemisphere, and are therefore disfavored as the sole explanation of the GCE. The annihilation of dark matter particles of mass 40 - 7 + 10 GeV (95% CL) to b quarks with a cross-section of ⟨ σ A v ⟩ = 1. 4 - 0.3 + 0.6 × 10 - 26 cm 3 s − 1 provides a good fit to the excess especially in the relatively cleaner southern sky. Dark matter of the same mass range annihilating to b quarks or heavier dark matter particles annihilating to heavier Standard Model bosons can combine with millisecond pulsars to provide a good fit to the southern hemisphere emission as well, as can a broken power-law spectrum which would be related to recent cosmic-ray burst activity. As part of this paper, we make publicly available all of our templates and the data covariance matrix we have generated to account for systematic uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Measurement of the CMB temperature power spectrum and constraints on cosmology from the SPT-3G 2018 T T , T E , and E E dataset

We present a sample-variance-limited measurement of the temperature power spectrum ( T T ) of the cosmic microwave background using observations of a ∼ 1500 deg 2 field made by the SPT-3G in 2018. We report multifrequency power spectrum measurements at 95, 150, and 220 GHz covering the angular multipole range 750 ≤ ℓ < 3000 . We combine this T T measurement with the published polarization power spectrum measurements from the 2018 observing season and update their associated covariance matrix to complete the SPT-3G 2018 T T / T E / E E dataset. This is the first analysis to present cosmological constraints from SPT T T , T E , and E E power spectrum measurements jointly. We blind the cosmological results and subject the dataset to a series of consistency tests at the power spectrum and parameter level. We find excellent agreement between frequencies and spectrum types and our results are robust to the modeling of astrophysical foregrounds. We report results for Λ CDM and a series of extensions, drawing on the following parameters: the amplitude of the gravitational lensing effect on primary power spectra A L , the effective number of neutrino species N eff , the primordial helium abundance Y P , and the baryon clumping factor due to primordial magnetic fields b . We find that the SPT-3G 2018 T T / T E / E E data are well fit by Λ CDM with a probability to exceed of 15%. For Λ CDM , we constrain the expansion rate today to H 0 = 68.3 ± 1.5 km s - 1 Mpc - 1 and the combined structure growth parameter to S 8 = 0.797 ± 0.042 . The SPT-based results are effectively independent of Planck, and the cosmological parameter constraints from either dataset are within < 1 σ of each other. The addition of temperature data to the SPT-3G T E / E E power spectra improves constraints by 8–27% for each of the Λ CDM cosmological parameters. When additionally fitting A L , N eff , or N eff + Y P , the posteriors of these parameters tighten by 5–24%. In the case of primordial magnetic fields, complete T T / T E / E E power spectrum measurements are necessary to break the degeneracy between b and n s , the spectral index of primordial density perturbations. We report a 95% confidence upper limit from SPT-3G data of b < 1.0 . The cosmological constraints in this work are the tightest from SPT primary power spectrum measurements to date and the analysis forms a new framework for future SPT analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Neural network based emulation of galaxy power spectrum covariances: A reanalysis of BOSS DR12 data

We train neural networks to quickly generate redshift-space galaxy power spectrum covariances from a given parameter set (cosmology and galaxy bias). This covariance emulator utilizes a combination of traditional fully connected network layers and transformer architecture to accurately predict covariance matrices for the high redshift, north galactic cap sample of the BOSS DR12 galaxy catalog. We run simulated likelihood analyses with emulated and brute-force computed covariances, and we quantify the network’s performance via two different metrics: (1) difference in Χ 2 and (2) likelihood contours for simulated BOSS DR 12 analyses. We find that the emulator returns excellent results over a large parameter range. We then use our emulator to perform a reanalysis of the BOSS HighZ NGC galaxy power spectrum, and find that varying covariance with cosmology along with the model vector produces Ω m = $0.27⁢6$$^{+0.013}_{–0.015}$, H 0 = 70.2 ± 1.9 km/s/Mpc, and σ 8 = $0.67⁢4$$^{+0.058}_{–0.077}$. These constraints represent an average 0.46⁢σ shift in best-fit values and a 5% increase in constraining power compared to fixing the covariance matrix (Ω m = 0.293 ± 0.017, H 0 = 70.3 ± 2.0 km/s/Mpc, σ 8 = $0.70⁢2$$^{+0.063}_{–0.075}$). As a result, this work demonstrates that emulators for more complex cosmological quantities than second-order statistics can be trained over a wide parameter range at sufficiently high accuracy to be implemented in realistic likelihood analyses.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Bootstrap-determined p values in lattice QCD

We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p -value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling T 2 methods based on the conventional χ 2 statistic do not apply, such as for uncorrelated fits. Specifically, we analyze q 2 , defined as the correlated χ 2 statistic obtained using an arbitrary covariance matrix estimator, and show how to use the bootstrap as a data-driven method to determine the expected distribution of q 2 for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p -value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p -value of estimating population parameters from a single ensemble of N samples. The overall method is accurate up to a 1 / N bias which we do not attempt to quantify. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Cosmology From CMB Lensing and Delensed EE Power Spectra Using 2019-2020 SPT-3G Polarization Data

From CMB polarization data alone we reconstruct the CMB lensing power spectrum, comparable in overall constraining power to previous temperature-based reconstructions, and an unlensed E -mode power spectrum, with clear detections of the third through tenth acoustic peaks. The observations, taken in 2019 and 2020 with the South Pole Telescope (SPT) and the SPT-3G camera, cover 1500 deg 2 at 95, 150, and 220 GHz with arcminute resolution and roughly 4.9 µ K-arcmin coadded noise in polarization. The power spectrum estimates, together with systematic parameter estimates and a joint covariance matrix, follow from a Bayesian analysis using the Marginal Unbiased Score Expansion (MUSE) method. The E -mode spectrum at ℓ > 2000 and lensing spectrum at L > 350 are the most precise to date. Assuming the ΛCDM model, and using only these SPT data and priors on τ and absolute calibration from Planck, we find H 0 = 66.81 ± 0.81 km/s/Mpc, comparable in precision to the Planck determination and in 5.4 σ tension with the most precise H 0 inference derived via the distance ladder. We also find S 8 ≡ σ 8 (Ω m /0.3) 0.5 = 0.850 ± 0.017, providing further independent evidence of a slight tension with low-redshift structure probes. The ΛCDM model provides a good simultaneous fit to the combined Planck, ACT, and SPT data, and thus passes a powerful test. Combining these CMB datasets with BAO observations, we explore extensions to the ΛCDM model. We find that the effective number of neutrino species, spatial curvature, and primordial helium fraction are consistent with standard model values, and that the 95% confidence upper limit on the neutrino mass sum is 0.075 eV, close to the minimum sum expected from observations of solar and atmospheric neutrino oscillations. The SPT data are consistent with the somewhat weak (< 3 σ ) preference for excess lensing power seen in Planck and ACT data relative to predictions of the ΛCDM model given the combined Planck, ACT, and BAO data sets. Finally, we also detect at greater than 3 σ the influence of non-linear evolution in the CMB lensing power spectrum and discuss it in the context of the S 8 tension. Forthcoming SPT-3G analyses will feature deeper and wider observations in temperature and polarization, providing even tighter constraints and more powerful tests of the ΛCDM model.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Hadronic vacuum polarization for the muon 𝑔 − 2 from lattice QCD: Complete short and intermediate windows

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment 𝑎 𝜇 in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to 𝑎 𝜇 , respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong-isospin breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark-connected contribution, we obtain 𝑎$^{𝑙⁢𝑙,SD}_{𝜇⁡}$(conn) = 48.139⁢(11) stat ⁢(91) syst ⁢[92] total × 10 −10 and 𝑎$^{𝑙⁢𝑙,W}_{𝜇}$⁡(conn) = 206.90⁢(14) stat ⁢(61) syst ⁢[63] total × 10 −10 . We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are 𝑎$^{SD}_{𝜇}$ = 69.05⁢(1) stat⁢ (21) syst ⁢[21] total × 10 −10 and 𝑎$^{W}_{𝜇}$ = 236.45⁢(17) stat⁢ (83) syst ⁢[85] total × 10 −10 . This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes

We introduce a framework for simulating, on an ( n + 1 )-qubit quantum computer, the action of a Gaussian bosonic (GB) circuit on a state over 2 n modes. Specifically, we encode the initial bosonic state’s expectation values over quadrature operators (and their covariance matrix) as an input qubit state. This is then evolved by a quantum circuit that effectively implements the symplectic propagators induced by the GB gates. We find families of GB circuits and initial states leading to efficient quantum simulations. For this purpose, we introduce a dictionary that maps between GB and qubit gates such that particle- (non-particle-) preserving GB gates lead to real- (imaginary-) time evolutions at the qubit level. For the special case of particle-preserving circuits, we present a bounded-error-quantum-polynomial time (BQP)-complete GB decision problem, indicating that GB evolutions of Gaussian states on exponentially many modes are as powerful as universal quantum computers. We also perform numerical simulations of an interferometer on ∼ 8 × 10 9 modes, illustrating the power of our framework. Published by the American Physical Society 2025

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗

DOE OSTI2026

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

DOE OSTI2022

Fast Gaussian Process Estimation for Large-Scale In Situ Inference using Convolutional Neural Networks

Exascale computing will bring with it significant I/O limitations. One foreseeable consequence of such restrictions is that the user can save only a small fraction of complex simulation data to disk for subsequent analysis. An alternative is to fit statistical models to data in situ, that is, inside the simulation as it runs. This option requires extremely fast statistical estimation to avoid slowing down the simulation. Gaussian processes (GPs) have state-of-the-art predictive performance for modeling spatial data. However, standard estimation methods for GPs scale quite poorly to large data sets as parameter estimation requires inverting a covariance matrix to the size of the data set. In the presented work, we use a convolutional neural network (CNN) to predict the GP parameters for a spatial data set, from a simulation or otherwise, rather than optimize the parameters directly. Here, our presented case study models spatial data from E3SM, the Department of Energy’s Exascale climate model. The CNN is trained on synthetic data simulated from GP models with known parameters and then applied to data from the climate simulation. In the presented examples, the neural network scheme produces parameter estimates that compare well with standard methods such as maximum likelihood estimation in predictive performance but is obtained four orders of magnitude faster.

big data↗

DOE OSTI2024

Preparing an on-Demand Cloud Processing Workflow for NISAR Ecosystems Science Products

In preparation for the NISAR launch and data collection in 2024, the NISAR Project Science Team is building workflows for each Science Team discipline (Ecosystems, Cryosphere, and Solid Earth). This abstract focuses on the Ecosystem disciplines and the development of on-demand cloud-processing workflows for wetlands inundation, forest biomass, agricultural active crop area, and forest disturbance. The workflow simulates NISAR data using UAVSAR or ALOS-2 Single Look Complex data, which are processed to Level 2 geocoded polarimetric covariance matrix products using InSAR Scientific Computing Environment 3.0 software and to Level 3 science products using the Algorithm Theoretical Basis Documents. In this presentation, we describe these workflows and efforts to improve efficiency and data accessibility by using a cloud processing system. We present preliminary sample products from each Ecosystem discipline: inundation, forest biomass, crop area, and forest disturbance.

Christensen, Alexandra↗

DOE OSTI2021

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Gaussian Process Regression under Computational and Epistemic Misspecification

Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper investigates the effect of such kernel approximations on the interpolation error. We introduce a unified framework to analyze Gaussian process regression under important classes of computational misspecification: Karhunen-Loève expansions that result in low-rank kernel approximations, multiscale wavelet expansions that induce sparsity in the covariance matrix, and finite element representations that induce sparsity in the precision matrix. Furthermore, our theory also accounts for epistemic misspecification in the choice of kernel parameters.

Gaussian process regression↗