Machine Learning for Probabilistic Model with Random Coefficients
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Computationally efficient surrogate modeling↗
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Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.
54 ENVIRONMENTAL SCIENCES↗
Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs
Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The metallicity’s fundamental dependence on both local and global galactic quantities
ABSTRACT We study the scaling relations between gas-phase metallicity, stellar mass surface density (Σ*), star formation rate surface density (ΣSFR), and molecular gas surface density ($\Sigma _{{\rm H}_2}$) in local star-forming galaxies on scales of a kpc. We employ optical integral field spectroscopy from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, and ALMA data for a subset of MaNGA galaxies. We use partial correlation coefficients and Random Forest regression to determine the relative importance of local and global galactic properties in setting the gas-phase metallicity. We find that the local metallicity depends primarily on Σ* (the resolved mass–metallicity relation, rMZR), and has a secondary anticorrelation with ΣSFR (i.e. a spatially resolved version of the ‘Fundamental Metallicity Relation’, rFMR). We find that $\Sigma _{{\rm H}_2}$ is less important than ΣSFR in determining the local metallicity. This result indicates that gas accretion, resulting in local metallicity dilution and local boosting of star formation, is unlikely to be the primary origin of the rFMR. The local metallicity depends also on the global properties of galaxies. We find a strong dependence on the total stellar mass (M*) and a weaker (inverse) dependence on the total SFR. The global metallicity scaling relations, therefore, do not simply stem out of their resolved counterparts; global properties and processes, such as the global gravitational potential well, galaxy-scale winds and global redistribution/mixing of metals, likely contribute to the local metallicity, in addition to local production and retention.
79 ASTRONOMY AND ASTROPHYSICS↗
Stellar mass, not dynamical mass nor gravitational potential, drives the mass–metallicity relationship
The widely known relation between stellar mass and gas metallicity [mass–metallicity relation (MZR)] in galaxies is often ascribed to the higher capability of more massive systems to retain metals against the action of galactic outflows. In this scenario the stellar mass would simply be an indirect proxy of the dynamical mass or of the gravitational potential. We test this scenario by using a sample of more than 1000 star-forming galaxies from the MaNGA (Mapping Nearby Galaxies at Apache Point Observatory) survey for which dynamical masses have been accurately determined. By using three different methods (average dispersion, partial correlation coefficients, and random forest), we unambiguously find that the gas metallicity depends primarily and fundamentally on the stellar mass. Once the dependence on stellar mass is taken into account, there is little or no dependence on either dynamical mass or gravitational potential (and, if anything, the metallicity dependence on the latter quantities is inverted). Our result indicates that the MZR is not caused by the retention of metals in more massive galaxies. The direct, fundamental dependence of metallicity on stellar mass suggests the much simpler scenario in which the MZR is just a consequence of the stellar mass being proportional to the integral of metals production in the galaxy.
79 ASTRONOMY AND ASTROPHYSICS↗
Data Driven Correlated Noise Simulation for the ICEBERG LArTPC
Accurate electronic-noise simulation is essential for low-energy physics in liquid-argon TPCs. More realistic noise modeling allows us to better tune reconstruction algorithms and more reliably assess and optimize signal-detection thresholds. We present a data-driven noise simulation framework developed for the ICEBERG test stand for DUNE that generates synthetic noise waveforms that reproduce both (i) the measured per-channel magnitude of the Fast Fourier Transform (FFT) and (ii) frequency-dependent channel-to-channel correlations observed in ICEBERG noise data. Using a dedicated noise-only dataset, we build a compact noise model containing per-channel FFT-magnitude targets together with a small set of band-wise cross-wire color matrices. White noise is generated in the frequency domain by drawing circular-symmetric complex Gaussian coefficients with random phases and scaling them to match the measured FFT-magnitude targets, and cross-wire correlations are subsequently imposed using the stored color matrices. The model and algorithm were integrated into the LArSoft + Wire-Cell Toolkit simulation chain and validated by comparing waveform structure, frequency-domain spectra, and band-limited correlation matrices from simulated noise and ICEBERG data. This approach can be extended to other LArTPC operating conditions.
Ghosh, Avik [Iowa State U.]↗
Thermodynamic modeling of aqueous acetic acid, butyric acid, and lactic acid solutions
Based on the activity coefficient – fugacity coefficient approach, a rigorous thermodynamic modeling study is presented for accurate correlation of vapor-liquid equilibrium data of aqueous solutions of acetic acid (293 to 391 K), butyric acid (325 to 436 K), lactic acid (378 to 409 K), and acetic acid + butyric acid binary mixture (358 to 421 K). In addition, the pH data of the three aqueous, single carboxylic acid solutions were measured at 298 to 328 K and successfully correlated. Given that these aqueous carboxylic acid solutions exhibit various degrees of association behavior in both vapor and liquid phases, the thermodynamic models considered for this study include the Redlich-Kwong equation of state (RK-EoS) and the Hayden-O’Connell equation of state (HOC-EoS) for the vapor phase fugacity coefficients and the electrolyte non-random two-liquid model (eNRTL) and the association electrolyte non-random two-liquid model (AeNRTL) for the liquid phase activity coefficients. The combination of the HOC-EoS for the vapor phase and the AeNRTL model for the liquid phase is found to provide the best correlation results, consistent with the fact that the HOC-EoS and the AeNRTL model explicitly account for association behaviors in the vapor phase and the liquid phase, respectively.
09 BIOMASS FUELS↗
The impact of curation errors in the PDBBind Database on machine learning predictions of protein–protein binding affinity
The PDBBind database has been widely utilized for the computational prediction of protein–protein binding affinities. While the accuracy of the PDBBind-curated equilibrium dissociation constants (K D ) has been reported for the protein–ligand subset of the PDBBind database, the curation accuracy has not been reported for the protein–protein subset. Here, we present a detailed manual analysis for the subset of PDBBind records with PubMed Central Open Access primary publications and find that ~19% of these records had K D values that were not supported by their primary publications. The impact of these putative curation errors on the machine learning-based prediction of K D from experimental protein–protein 3D structures was evaluated and correcting the curation errors improved the Pearson correlation coefficient between measured and random forest-predicted log 10 (K D ) values by ~8 percentage points. This finding underscores the importance of dataset accuracy for computational modelling and highlights the need for more stringent curation processes when extracting information from the scientific literature.
59 BASIC BIOLOGICAL SCIENCES↗
Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion
In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between existing vertices. Specifically, at each time step t, either a new vertex is added with probability f(t), or an edge is added between two existing vertices with probability 1 – f(t). We establish concentration inequalities for the global clustering and clique number of the resulting graphs under the assumption that f(t) is a regularly varying function at infinity with index of regular variation –$\gamma$, where $\gamma$ $\in$ [0, 1). Finally, we also demonstrate an inverse relation between these two statistics: the clique number is essentially the reciprocal of the global clustering coefficient.
97 MATHEMATICS AND COMPUTING↗
Multipoint Correlations in Poisson Media
Multipoint correlations in randomly heterogeneous composite media are determined by the probability that a set of points belong to specific phases. They determine a wide range of macroscopic transport properties such as conductivity, dielectric constant, diffusion coefficient, and transmittance. The Poisson model—a random tesselation of space by hyperplanes—provides realistic descriptions of heterogeneous media in, e.g., radiation-transport applications; yet, until now, it has lacked closed-form expressions for its multipoint correlations. We resolve this problem by presenting an exact solution for the multipoint correlations in the Poisson model. By comparing it to Monte Carlo simulations of four-point correlations in three dimensions, we demonstrate the accuracy of our solution. In conclusion, we visualize the multipoint correlations and discuss their features.
Amorphous materials↗
Controlled thermal coefficient product system and method
A controlled thermal coefficient product manufacturing system and method is disclosed. The disclosed product relates to the manufacture of metallic material product (MMP) having a thermal expansion coefficient (TEC) in a predetermined range. The disclosed system and method provides for a first material deformation (FMD) of the MMP that comprises at least some of a first material phase (FMP) wherein the FMP comprises martensite randomly oriented and a first thermal expansion coefficient (FTC). In response to the FMD at least some of the FMP is oriented in at least one predetermined orientation. Subsequent to deformation, the MMP comprises a second thermal expansion coefficient (STC) that is within a predetermined range and wherein the thermal expansion of the MMP is in at least one predetermined direction. The MMP may be comprised of a second material phase (SMP) that may or may not transform to the FMP in response to the FMD.
Monroe, James Alan↗
Quantification of modeling uncertainty in the Rayleigh damping model
Understanding and accurately characterizing energy dissipation mechanisms in civil structures during earthquakes is an important element of seismic assessment and design. The most commonly used model is attributed to Rayleigh. This paper proposes a systematic approach to quantify the uncertainty associated with Rayleigh's damping model. Bayesian calibration with embedded model error is employed to treat the coefficients of the Rayleigh model as random variables using modal damping ratios. Through a numerical example, we illustrate how this approach works and how the calibrated model can address modeling uncertainty associated with the Rayleigh damping model.
42 ENGINEERING↗
Investigating the ecological fallacy through sampling distributions constructed from finite populations
Correlation coefficients and linear regression values computed from group averages can differ from correlation coefficients and linear regression values computed using individual scores. This observation known as the ecological fallacy often assumes that all the individual scores are available from a population. In many situations, one must use a sample from the larger population. In such cases, the computed correlation coefficient and linear regression values will depend on the sample that is chosen and the underlying sampling distribution. The sampling distribution of correlation coefficients and linear regression values for group averages will be identical to the sampling distribution for individuals for normally distributed variables for random samples drawn from infinitely large continuous distributions. However, data that is acquired in practice is often acquired when sampling without replacement from a finite population. Our objective is to demonstrate through Monte Carlo simulations that the sampling distributions for correlation and linear regression will also be similar for individuals and group averages when sampling without replacement from normally distributed variables. These simulations suggest that when a random sample from a population is selected, the correlation coefficients and linear regression values computed from individual scores will not be more accurate in estimating the entire population values compared to samples when group averages are used as long as the sample size is the same.
97 MATHEMATICS AND COMPUTING↗
Analysis of Correlation between Cold Weather Meteorological Variables and Electricity Outages
The significance of the impact of weather on the electric grid has grown as climate change continues to increase the frequency and intensity of extreme weather events. In recent years (2021-2022) in particular, extreme winter weather has affected the grid in locations in the US rarely exposed to extreme low temperatures, snow and icing conditions. Here we analyze the correlation between cold weather meteorological variables and electricity outages during two large winter storm events, Uri (February 2021) and Landon (February 2022) using Random Forest machine learning and Pearson’s correlation coefficient. Our geographical focus across the two storms is the state of Texas. Extrapolation of the method to winter weather impacts over other years and additional locations is proposed.
Dumas, Melissa↗
Stochastic modeling and statistical calibration with model error and scarce data
This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.
Bayesian inference↗
Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers
We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. Here we study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using the Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.
79 ASTRONOMY AND ASTROPHYSICS↗
GenMod: A generative modeling approach for spectral representation of PDEs with random inputs
Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.
97 MATHEMATICS AND COMPUTING↗
Quasiparticle self-consistent GW band structures and phase transitions of LiAlO 2 in tetrahedrally and octahedrally coordinated structures
In this work, a first-principles computational study is presented of various phases of LiAlO 2 . The relative total energies and equations of state of the α, β, and γ phases are determined after structural relaxation of each phase. The β and γ tetrahedral phases are found to be very close in energy and lattice volume with the γ phase having the lowest energy. The octahedral α phase is a high-pressure phase and the transition pressure from the γ and β phases to α is determined to be about 1 GPa. The electronic band structures of each phase at their own equilibrium volume are determined using the quasiparticle self-consistent (QS) GW method as well as using the 0.8 Σ approach in which the QS GW self-energy is reduced by a factor of 0.8 to correct for the underscreening of W in QS GW. The effective masses of the band edges and the nature of the band gaps are presented. The lowest energy γ phase is found to have a pseudodirect gap of 7.69 eV. The gap is direct at Γ but corresponds to a dipole forbidden transition. The imaginary part of the dielectric function and the absorption coefficient are calculated in the long-wavelength limit and the random phase approximation, without local field or electron-hole interaction effects for each phase, and their anisotropies are discussed. Si doping on the Al site is investigated as a possible n-type dopant in γ-LiAlO 2 using a 128-atom supercell corresponding to 3.125% Si on the Al sublattice in the generalized gradient approximation and a smaller 16-atom cell with 25% Si in the QS GW approximation. The Si is found to significantly perturb the conduction band and lower the gap but a clearly separated deep donor defect level is not found. However, the donor binding energy is still expected to be relatively deep, on the order of a few tenths eV in the hydrogenic effective mass approximation.
36 MATERIALS SCIENCE↗