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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Freely jointed chain models with extensible links

We report analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Advanced Analytical Methodologies Enable Feedstock Screening and Correlation to Pyrolysis Yields and Catalytic Upgrading

Pyrolysis of lignocellulosic biomass can serve as a powerful pathway for the generation of renewable fuels and industrial products. However, procurement of some biomass may be costly, especially when there is competition for alternative uses. Forestry and agricultural byproducts may serve as valuable pyrolysis feedstocks due to their high availability and low cost. Although waste products may fill demand for affordable pyrolysis feedstocks, they are often high in ash and extractives which contribute to unfavorable changes in pyrolysis vapor composition, as well as end products. The work presented here investigates the correlations between various pine anatomical fractions to understand their effect on pyrolysis oil composition for forest residues. Analytical pyrolysis coupled to direct analysis by molecular beam mass spectrometry (MBMS) provides real-time monitoring of pyrolysis vapor composition, even for compounds that are not amenable to gas chromatography. Statistical analysis of MBMS data from the fast pyrolysis (FP) of clean pine, cambium, twigs and branches, needles, bark, and a forest residue samples revealed that bark and needles made the greatest differences in the vapor composition of forest residues during pyrolysis and were enriched in resin acids, furfural derivatives, and ions that have been previously observed from catalysis corresponding to ash content. These results were also compared to catalytic fast pyrolysis (CFP) using a platinum on titania catalyst, and correlations between FP and CFP products were observed for the anatomical fractions. The forest residues and corresponding anatomical fractions from a stand of 23-year-old pine will be converted by fast pyrolysis in a bench-scale 2-inch fluidized-bed reactor, and statistical correlations between the bench-scale products and analytical-scale pyrolysis vapors will be shown. This work highlights the power of advanced analytical methodologies in determining the contributions of vapor components to catalytic pyrolysis outcomes for mixed feedstocks and demonstrates the use of analytical methodologies to better screen feedstocks prior to pyrolysis.

analytical↗
DOE OSTI2023

Infinite neural network quantum states: entanglement and training dynamics

We study infinite limits of neural network quantum states (∞-NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For ∞-NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an ∞-NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. ∞-NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.

quantum state supervised learning↗
DOE OSTI2023

Measuring photometric redshifts for high-redshift radio source surveys

With the advent of deep, all-sky radio surveys, the need for ancillary data to make the most of the new, high-quality radio data from surveys like the Evolutionary Map of the Universe (EMU), GaLactic and Extragalactic All-sky Murchison Widefield Array survey eXtended, Very Large Array Sky Survey, and LOFAR Two-metre Sky Survey is growing rapidly. Radio surveys produce significant numbers of Active Galactic Nuclei (AGNs) and have a significantly higher average redshift when compared with optical and infrared all-sky surveys. Thus, traditional methods of estimating redshift are challenged, with spectroscopic surveys not reaching the redshift depth of radio surveys, and AGNs making it difficult for template fitting methods to accurately model the source. Machine Learning (ML) methods have been used, but efforts have typically been directed towards optically selected samples, or samples at significantly lower redshift than expected from upcoming radio surveys. This work compiles and homogenises a radio-selected dataset from both the northern hemisphere (making use of Sloan Digital Sky Survey optical photometry) and southern hemisphere (making use of Dark Energy Survey optical photometry). We then test commonly used ML algorithms such as k-Nearest Neighbours (kNN), Random Forest, ANNz, and GPz on this monolithic radio-selected sample. We show that kNN has the lowest percentage of catastrophic outliers, providing the best match for the majority of science cases in the EMU survey. We note that the wider redshift range of the combined dataset used allows for estimation of sources up to z = 3 before random scatter begins to dominate. When binning the data into redshift bins and treating the problem as a classification problem, we are able to correctly identify ≈ 76% of the highest redshift sources—sources at redshift z > 2.51 —as being in either the highest bin (z > 2.51) or second highest (z = 2.25).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multi-objective Bayesian active learning for MeV-ultrafast electron diffraction

Ultrafast electron diffraction using MeV energy beams(MeV-UED) has enabled unprecedented scientific opportunities in the study of ultrafast structural dynamics in a variety of gas, liquid and solid state systems. Broad scientific applications usually pose different requirements for electron probe properties. Due to the complex, nonlinear and correlated nature of accelerator systems, electron beam property optimization is a time-taking process and often relies on extensive hand-tuning by experienced human operators. Algorithm based efficient online tuning strategies are highly desired. Here, we demonstrate multi-objective Bayesian active learning for speeding up online beam tuning at the SLAC MeV-UED facility. The multi-objective Bayesian optimization algorithm was used for efficiently searching the parameter space and mapping out the Pareto Fronts which give the trade-offs between key beam properties. Such scheme enables an unprecedented overview of the global behavior of the experimental system and takes a significantly smaller number of measurements compared with traditional methods such as a grid scan. This methodology can be applied in other experimental scenarios that require simultaneously optimizing multiple objectives by explorations in high dimensional, nonlinear and correlated systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Multiplicative Shot-Noise: A New Route to Stability of Plastic Networks

Fluctuations of synaptic weights, among many other physical, biological, and ecological quantities, are driven by coincident events of two “parent” processes. Here we propose a multiplicative shot-noise model that can capture the behaviors of a broad range of such natural phenomena, and analytically derive an approximation that accurately predicts its statistics. We apply our results to study the effects of a multiplicative synaptic plasticity rule that was recently extracted from measurements in physiological conditions. Using mean-field theory analysis and network simulations, we investigate how this rule shapes the connectivity and dynamics of recurrent spiking neural networks. The multiplicative plasticity rule is shown to support efficient learning of input stimuli, and it gives a stable, unimodal synaptic-weight distribution with a large fraction of strong synapses. The strong synapses remain stable over long times but do not “run away.” Our results suggest that the multiplicative shot-noise offers a new route to understand the tradeoff between flexibility and stability in neural circuits and other dynamic networks.

59 BASIC BIOLOGICAL SCIENCES↗
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

Worldwide Physics-Based Lifetime Prediction of c-Si Modules Due to Solder-Bond Failure

Lifetime prediction of the fielded c-Si solar modules due to location-specific weather conditions has been an important topic of photovoltaic research and the economic viability of solar energy. Data analytic techniques such as the performance ratio method, Statistical clear sky model, and Suns-Vmp methods quantify the degradation from measured data of a solar farm, however, the nonlinear time-dependence and correlated degradations make it difficult to use the empirical degradation rates for ultimate lifetime projection. In this article, we propose a complementary physics-based model to predict the solder bond failure caused by mechanical stress associated with the variations of the temperature. Integrating the worldwide weather information from NASA/NSRDB databases, the model predicts the location-specific output-power degradation and the lifetime of a module due to solder bond failure. The model parameters are calibrated against qualification tests involving thermal cycling of specific batches of modules from a specific technology/manufacturer. The results may be summarized as: 1) Modules installed at higher latitudes show a longer lifetime due to reduced damage accumulation. 2) The reduction of temperature fluctuation close to large bodies of water, such as seashores, increases solder bond lifetime significantly. 3) Relatively speaking, modules installed close to the Tropic of Cancer/Capricorn (23.5 degrees North/South) suffer from a higher solder bond damage and have a shorter lifetime, suggesting a conservative design. This model should serve as a building block of a comprehensive reliability framework that can predict the lifetime of a module that experiences simultaneous and correlated degradation mechanisms involving yellowing, corrosion, and potential-induced degradation.

14 SOLAR ENERGY↗
DOE OSTI2023

Modeling single-molecule stretching experiments using statistical thermodynamics

Single-molecule stretching experiments are widely utilized within the fields of physics and chemistry to characterize the mechanics of individual bonds or molecules, as well as chemical reactions. Analytic relations describing these experiments are valuable, and these relations can be obtained through the statistical thermodynamics of idealized model systems representing the experiments. Since the specific thermodynamic ensembles manifested by the experiments affect the outcome, primarily for small molecules, the stretching device must be included in the idealized model system. Though the model for the stretched molecule might be exactly solvable, including the device in the model often prevents analytic solutions. In the limit of large or small device stiffness, the isometric or isotensional ensembles can provide effective approximations, but the device effects are missing. Here a dual set of asymptotically correct statistical thermodynamic theories are applied to develop accurate approximations for the full model system that includes both the molecule and the device. In conclusion, the asymptotic theories are first demonstrated to be accurate using the freely jointed chain model and then using molecular dynamics calculations of a single polyethylene chain.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Concentration-Discharge Relationships in the Six Largest Arctic Rivers, 2003-2019

This dataset provides the results of the analysis of the relationship of dissolved analyte concentrations and river discharges in the six largest Arctic rivers across the global panarctic region (see Figure 1 in documentation file *.pdf). Long-term measurements of dissolved analyte concentrations and river discharge have been collected for each of the Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers by the Arctic Great Rivers Observatory (ArcticGRO) project from ~2003-present (Shiklomanov, 2021). The relationship of dissolved analyte concentrations and discharges in each river was characterized by statistical analysis of the slope of the log(concentration) vs log(discharge) (b), the coefficient of variation ratio (CVc/CVq), the 2.5% and 97.5% confidence intervals of b, and assigning a chemostatic, flushing, diluting, or non-systematic behavior category according to Koger (2018). The summary of these analyses for all six rivers is provided in one .csv file. The concentrations of 20 dissolved analytes and discharge measurement data for the individual Kolyma, Lena, Mackenzie, Ob, Yenisey, and Yukon rivers are also provided with this dataset. There are seven *.csv files; one for each river plus the statistical summary. These public ArcticGRO data at "https://www.arcticgreatrivers.org" (Shiklomanov, 2021) were downloaded on Feb 13, 2020, but each river has different measurement dates over the sampling and analysis period. The ArcticGRO metadata document (*.pdf) downloaded on Feb 13, 2020 is also included in this dataset. The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research. The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska. Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Modeling intrinsic galaxy alignment in the MICE simulation

The intrinsic alignment (IA) of galaxies is potentially a major limitation in deriving cosmological constraints from weak lensing surveys. In order to investigate this effect, we assign intrinsic shapes and orientations to galaxies in the light-cone output of the MICE simulation, spanning ~ 5000 deg 2 and reaching redshift Z = 1.4. This assignment is based on a semianalytic IA model that uses photometric properties of galaxies as well as the spin and shape of their host halos. Advancing on previous work, we include more realistic distributions of galaxy shapes and a luminosity-dependent galaxy-halo alignment. The IA model parameters are calibrated against COSMOS and BOSS LOWZ observations. The null detection of IA in observations of blue galaxies is accounted for by setting random orientations for these objects. We compare the two-point alignment statistics measured in the simulation against predictions from the analytical IA models NLA and TATT over a wide range of scales, redshifts, and luminosities for red and blue galaxies separately. We find that both models fit the measurements well at scales above 8h -1 Mpc, while TATT outperforms NLA at smaller scales. The IA parameters derived from our fits are in broad agreement with various observational constraints from red galaxies. Finally, we build a realistic source sample, mimicking DES Year 3 observations and use it to predict the IA contamination to the observed shear statistics. We find this prediction to be within the measurement uncertainty, which might be a consequence of the random alignment of blue galaxies in the simulation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Statistical mechanics of kinks on a gliding screw dislocation

The ability of a body-centered-cubic metal to deform plastically is limited by the thermally activated glide motion of screw dislocations, which are line defects with a mobility exhibiting complex dependence on temperature, stress, and dislocation segment length. We derive an analytical expression for the velocity of dislocation glide, based on a statistical mechanics argument, and identify an apparent phase transition marked by a crossover temperature above which the activation energy for glide effectively halves, changing from the formation energy of a double kink to that of a single kink. The analysis is in quantitative agreement with direct kinetic Monte Carlo simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Pressure Effects on the Relaxation of an Excited Ethane Molecule in High-Pressure Bath Gases

Here, we use molecular dynamics to calculate the rotational and vibrational energy relaxation of C 2 H 6 in Ar, Kr, and Xe bath gases over a pressure range of 10 to 400 atm and at temperatures of 300 K and 800 K. The C 2 H 6 is instantaneously excited by 80 kcal/mol randomly distributed into both vibrational and rotational modes. The computed relaxation rates show little sensitivity to the identity of the noble gas in the bath. Vibrational relaxation rates show a non-linear pressure dependence at 300 K. At 800 K the reduced range of bath gas densities covered by the range of pressures do not yet show any non-linearity in the pressure dependence. Rotational relaxation is characterized with two relaxation rates. The slower rate is comparable to the vibrational relaxation rate. The faster rate has a linear pressure dependence at 300 K but an irregular, nonlinear pressure dependence at 800 K. To understand this, a model was developed based on approximating the periodic box used in the molecular dynamics simulations by an equal-volume collection of cubes where each cube is sized to allow only single occupancy by the noble gas or the molecule. Combinatorial statistics then leads to a pressure and temperature dependent analytic distribution of the bath gas species the molecule encounters in a collision. This distribution, the dissociation energy of molecule/bath gas complexes and bath gas clusters, and the computed energy release per collision combine to show that only at 300 K is the energy release sufficient to dissociate likely complexes and clusters. This suggests that persistent and pressure-dependent clusters and complexes at 800 K may be responsible for the non-linear pressure dependence of rotational relaxation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

ADDGALS: Simulated Sky Catalogs for Wide Field Galaxy Surveys

Abstract We present a method for creating simulated galaxy catalogs with realistic galaxy luminosities, broadband colors, and projected clustering over large cosmic volumes. The technique, denoted Addgals (Adding Density Dependent GAlaxies to Lightcone Simulations), uses an empirical approach to place galaxies within lightcone outputs of cosmological simulations. It can be applied to significantly lower-resolution simulations than those required for commonly used methods such as halo occupation distributions, subhalo abundance matching, and semi-analytic models, while still accurately reproducing projected galaxy clustering statistics down to scales of r ∼ 100 h −1 kpc . We show that Addgals catalogs reproduce several statistical properties of the galaxy distribution as measured by the Sloan Digital Sky Survey (SDSS) main galaxy sample, including galaxy number densities, observed magnitude and color distributions, as well as luminosity- and color-dependent clustering. We also compare to cluster–galaxy cross correlations, where we find significant discrepancies with measurements from SDSS that are likely linked to artificial subhalo disruption in the simulations. Applications of this model to simulations of deep wide-area photometric surveys, including modeling weak-lensing statistics, photometric redshifts, and galaxy cluster finding, are presented in DeRose et al., and an application to a full cosmology analysis of Dark Energy Survey (DES) Year 3 like data is presented in DeRose et al. We plan to publicly release a 10,313 square degree catalog constructed using Addgals with magnitudes appropriate for several existing and planned surveys, including SDSS, DES, VISTA, Wide-field Infrared Survey Explorer, and Rubin Observatory’s Legacy Survey of Space and Time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Analytical Bit-Error Model of NAND Flash Memories for Dosimetry Application

In this work, we provide an analytical model for the total ionizing dose (TID) effects on the bit error statistics of commercial flash memory chips. We have validated the model with experimental data collected by irradiating several commercial NAND flash memory chips from different technology nodes. We find that our analytical model can project bit errors at higher TID values (~ 20 krad(Si)) from measured data at lower TID values (<1 krad(Si)). Based on our model and the measured data, we have formulated basic design rules for using a commercial flash memory chip as a dosimeter. We discuss the impact of NAND chip-to-chip variability, noise margin and the intrinsic errors on the dosimeter design using detailed experimentation.

3-D NAND↗
DOE OSTI2021

Correlative analysis of structure and chemistry of Li x FePO 4 platelets using 4D-STEM and X-ray ptychography

Lithium iron phosphate (Li x FePO 4 ), a cathode material used in rechargeable Li-ion batteries, phase separates upon de/lithiation under equilibrium. The interfacial structure and chemistry within these cathode materials affects Li-ion transport, and therefore battery performance. Here, correlative imaging of Li x FePO 4 was performed using four-dimensional scanning transmission electron microscopy (4D-STEM), scanning transmission X-ray microscopy (STXM), and X-ray ptychography in order to analyze the local structure and chemistry of the same particle set. Over 50,000 diffraction patterns from 10 particles provided measurements of both structure and chemistry at a nanoscale spatial resolution (16.6–49.5 nm) over wide (several micron) fields-of-view with statistical robustness. Li x FePO 4 particles at varying stages of delithiation were measured to examine the evolution of structure and chemistry as a function of delithiation. In lithiated and delithiated particles, local variations were observed in the degree of lithiation even while local lattice structures remained comparatively constant, and calculation of linear coefficients of chemical expansion suggest pinning of the lattice structures in these populations. Partially delithiated particles displayed broadly core–shell-like structures, however, with highly variable behavior both locally and per individual particle that exhibited distinctive intermediate regions at the interface between phases, and pockets within the lithiated core that correspond to FePO 4 in structure and chemistry. The results provide insight into the Li x FePO 4 system, subtleties in the scope and applicability of Vegard’s law (linear lattice parameter-composition behavior) under local versus global measurements, and demonstrate a powerful new combination of experimental and analytical modalities for bridging the crucial gap between local and statistical characterization.

25 ENERGY STORAGE↗
DOE OSTI2023

A First Principles Approach to Spectral Phonon Transport in Heterostructures

Understanding thermal transport across interfaces which give rise to a thermal resistance (also known as Kapitza resistance) is a critical issue affecting the development of nanotechnologies. Much modern and emergent nanotechnology consist of adjacent materials, and phonon mediated heat transfer governs thermal behavior across internal interfaces in these devices. The physics of thermal transport in solids are governed both by phenomena occurring at the atomic scale and interactions with the material's microstructure. The forecasting of fundamental quantities such as temperature, heat flux and thermal conductivity typically employs the semi-classical Boltzmann transport equation to predict the macroscopic behavior of materials in terms of the microscopic dynamics of its heat carriers. Kapitza resistance was first discovered in liquid helium experiments and has led to a fundamental research thrust in micro and nano-scale heat transport, the behavior of thermal carriers across internal interfaces. Thermal interfacial resistance (TIR) is a widely studied phenomenon, first engaged by Swartz and Pohl through their development of the acoustic and diffuse mismatch methods, then continued through myriad efforts with varying methods and approaches in an attempt to resolve carrier behavior at thermal interfaces. Many of the fundamental approaches to TIR have been at the nanoscale, and research is conducted with molecular dynamics (MD) and density functional theory (DFT) methods. The limitations of these methods is system size; atomistic methods tend to be limited to system sizes of 100,000 atoms or less. Larger length-scale methods have also been pursued, based on the principles of acoustic or diffuse mismatch, but not all include simulation of TIR using a full phonon band spectrum, or temperature dependent methods. Our approach to enabling phonon transport in layered materials draws upon our previous work of demonstrating spectrally coupled phonon transport in homogeneous and heterogeneous materials. We use a semi-analytical approach in which the Bose-Einstein (B-E) statistics set the strength of the phonon radiance in a frequency group, but the B-E statistics are informed with information from the transport system. The B-E statistics in a single frequency group feels the influence of all the groups through the spatial temperature. We also include a new field term which is an indicator of the amount of non-equilibrium behavior of the phonon spectrum---this is added to the phonon source term in all groups to ensure closure and conservation of energy, as the phonon groups in the transport system and the analytical systems are coupled. This work builds upon our previous approach by adding a phonon coupling term at an internal interface, using the principles of the DMM through transmission and reflection coefficients. In this work, the coefficients are determined through computing a common temperature at the interface, influenced by the phonon band structure of both materials, in effect, providing mixing between the two material systems and using the common temperature to set the strength of the phonon radiance at the boundaries on either side of the interface. Our approach uses material properties computed along various crystallographic orientations, and while some isotropy is built into the interface condition, the material properties weight the phonon distributions in the proper crystalline direction. Greater resolution of phonon behavior in proximity to an interface, and more accurate predictions of TIR are obtained. While it is true the assumption of diffuse mismatch can yield inconsistent results compared to experiment especially at low temperatures, this work focuses on room temperature and beyond effects, for future applications in nuclear fuel, or thermoelectric devices; a modified mismatch approach may be feasible if applied properly. Additionally, our methods focus on bridging mesoscale to engineering scale

36 MATERIALS SCIENCE↗
DOE OSTI2025

Uncertainty propagation in feed-forward neural network models

We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.

MLP networks↗