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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Design and Synthesis of PtPdNiCoMn High‐Entropy Alloy Electrocatalyst for Enhanced Alkaline Hydrogen Evolution Reaction: A Theoretically Supported Predictive Design Approach

Electrocatalytic hydrogen generation requires a multifunctional electrocatalyst with abundant active sites to drive multielectron transfer reactions. High entropy alloys (HEA) are five or more-elements with high configurational entropy are considered unique materials for next-generation electrocatalysts. Here, in this work, based on new screening guidelines for catalyst selections that combine density-functional theory calculated Gibbs formation-enthalpy with bond length and electronegativity variance, a novel HEA electrocatalyst consisting of five elements, namely, Pt, Pd, Ni, Co, and Mn has been designed. By simple room temperature electrodeposition, the designed catalyst is prepared and its hydrogen evolution reaction (HER) is explored and validated through experimental and theoretical approaches. The HEA demonstrated a superior HER activity with an overpotential of 22.6 mV at -10 mA cm -2 which outperforms Pt/C commercial catalyst. No evident degradation of the material is detected even after 100 hours of continuous operation under high current density. Moreover, the HEA has shown exceptional performance in harsh electrolyte conditions such as in simulated seawater and actual seawater. Remarkably, the density-functional theory calculated Gibbs formation-enthalpy is small (≈0 eV) compared to Pt/C placing the new HEA near the apex of Trasatti's model of Volcano plot, which is also suggestive of superior HER activity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Integrating Characteristic Arctic Vegetation in a Land Surface Model Improves Representation of Carbon Dynamics Across a Tundra Landscape

Arctic warming is altering vegetation and carbon dynamics with global implications, yet Earth System Model (ESM) predictions in the Arctic remain highly uncertain, in part due to historically limited data for model parameterization and validation. As such, ESMs typically represent Arctic ecosystems in an oversimplified manner. Recently, nine plant functional types (PFTs) designed to realistically represent tundra vegetation were integrated into the Energy Exascale Earth System Model (E3SM) Land Model (ELM) and parameterized using plot-scale observations from a single site. Additional evaluation was needed to determine their transferability across the Arctic. Here, in this study, we evaluated whether refined representation of tundra vegetation improved model accuracy by conducting spatially explicit 100 × 100 m resolution ELM simulations on Alaska's Seward Peninsula. Simulations with the default two-PFT configuration and with the nine Arctic-specific PFTs were benchmarked against observations of net ecosystem exchange, gross primary production, and aboveground biomass from multiple data streams including an eddy covariance flux tower, flux chambers, and aircraft and unoccupied aerial system hyperspectral remote sensing. Evaluation revealed that Arctic-specific PFT simulations produced more realistic landscape-level carbon exchanges, and better captured observed heterogeneity in biomass and productivity, explaining 60%–70% of spatial variance (R 2 = 0.6–0.7) compared to just 12%–18% (R 2 = 0.12–0.18) with the default configuration. However, the refined model failed to reproduce observed aboveground biomass for highly productive alder-willow communities, requiring further evaluation of carbon allocation parameterizations for tall shrubs that are increasingly expanding across tundra landscapes. Our results demonstrate that enhanced representation of vegetation heterogeneity boosts predictive understanding of tundra carbon dynamics, facilitating regional to pan-Arctic model and remote-sensing scaling.

Murphy, Bailey A. [Oak Ridge National Laboratory (↗
DOE OSTI2025

Geothermal well testing pressure prediction by using a hybrid transformer model system: FORGE well use case

Geothermal has huge potential to become an indispensable component in achieving the goal of sustainable energy economy, given its capability to provide consistent baseload power to the electric grid. Injection tests are crucial in geothermal energy system as they naturally help to evaluate reservoir properties, understand fluid flow and even enhance reservoir performance. In this research, we developed a hybrid model system that integrates machine learning (ML) regression, a physics-based mathematical model, and transformer deep learning. Trained and validated using FORGE injection test dataset, this system can forecast the pressure variations both upward and downward over time. The pressure prediction achieved prediction accuracy within 3-6% variance of true pressure values. The system can significantly save time and reduce costs by testing only a few cycles and then using model predictions for further analysis, instead of conducting additional real injection cycle tests. The developed model system also holds promise for designing injection test processes and maintaining well production in geothermal energy. Presented at the IMAGE ‘25 Conference led by Shell.

FORGE↗
DOE OSTI2024

Jet classification using high-level features from anatomy of top jets

Recent advancements in deep learning models have significantly enhanced jet classification performance by analyzing low-level features (LLFs). However, this approach often leads to less interpretable models, emphasizing the need to understand the decision-making process and to identify the high-level features (HLFs) crucial for explaining jet classification. To address this, we consider the top jet tagging problems and introduce an analysis model (AM) that analyzes selected HLFs designed to capture important features of top jets. Our AM mainly consists of the following three modules: a relation network analyzing two-point energy correlations, mathematical morphology and Minkowski functionals for generalizing jet constituent multiplicities, and a recursive neural network analyzing subjet constituent multiplicity to enhance sensitivity to subjet color charges. We demonstrate that our AM achieves performance comparable to the Particle Transformer (ParT) while requiring fewer computational resources in a comparison of top jet tagging using jets simulated at the hadronic calorimeter angular resolution scale. Furthermore, as a more constrained architecture than ParT, the AM exhibits smaller training uncertainties because of the bias-variance tradeoff. We also compare the information content of AM and ParT by decorrelating the features already learned by AM. Lastly, we briefly comment on the results of AM with finer angular resolution inputs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Enhanced Estimation of Quantum Properties with Common Randomized Measurements

We present a technique for enhancing the estimation of quantum state properties by incorporating approximate prior knowledge about the quantum state. This consists in performing randomized measurements on a quantum processor and comparing the results with those obtained from a classical computer that stores an approximation of the quantum state. We provide unbiased estimators for expectation values of multicopy observables and present performance guarantees in terms of variance bounds that depend on the prior knowledge accuracy. We demonstrate the effectiveness of our approach through experimental and numerical examples detecting mixed-state entanglement, and estimating polynomial approximations of the von Neumann entropy and state fidelities. Published by the American Physical Society 2024

Physics↗
DOE OSTI2025

Turbulence statistical analysis of the L-H transition and RMPs in KSTAR

Here, we investigate the turbulence statistics associated with low-to-high confinement (L-H) transitions and externally applied resonant magnetic perturbations (RMPs) in KSTAR. Time-series fluctuations of electron density n e , electron temperature T e , and the time derivative of the poloidal magnetic field dB θ /dt (Mirnov coils) are analysed using information-geometric measures (information rate Γ and information length $\mathcal{L}$ = ∫ Γ dt), together with kurtosis κ and variance σ 2 . In low-density upper single-null plasmas (n e ~ 1.2 x 10 19 m -3 ), a ~80 kHz magnetic mode coupling n e , T e , dB θ /dt and emerges prior to the L-H transition and persists into the edge-localised modes H-mode. Edge-localised RMPs (ERMPs) suppress this coherent mode but enhance intermittency, producing frequent bursts that abruptly reshape the time-dependent probability density functions (PDFs) and generate large spikes in Γ (with smaller changes in κ), signalling ERMP-driven departures from quasi-stationarity. The impact of ERMPs on background fluctuation levels depends on density, radial location, and the fluctuating variable itself ($\tilde{n}$, $\tilde{T}$, $\dot{B}$ θ ), whereas $\mathcal{L}$ provides a robust, regime-agnostic measure of cumulative statistical reorganisation and spatial decorrelation. In particular, at low density we observe weaker coupling between $\tilde{n}$ and $\tilde{T}$, along with a tendency toward decreased radial correlation-most clearly for $\tilde{T}$-under ERMPs. Overall, information geometry cleanly captures intermittent events, quantifies non-equilibrium PDF evolution, and offers a compact, cross-diagnostic metric for assessing resonant magnetic perturbation effects on edge transport and correlation across densities, radial locations, and confinement states.

Kim, Eun-jin [Coventry Univ. (United Kingdom); Seo↗
DOE OSTI2025

Hyperspectral imaging for real-time waste materials characterization and recovery using endmember extraction and abundance detection

Hyperspectral imaging, combined with advanced spectral unmixing techniques and artificial intelligence, offers a powerful solution for improving material identification and classification. Here, this study evaluates the effectiveness of the pixel purity index and the sequential maximum angle convex cone algorithms in extracting and validating spectral signatures from pure samples of paper components (cellulose and lignin) and plastic (polypropylene). Principal-component analysis showed that both algorithms captured nearly all relevant variance for the tested materials. Spectral signatures were compared using the spectral angle mapper, revealing high similarity in the short-wave infrared region and greater variability in the visible near-infrared range. The methodology was then applied to a disposable coffee cup to detect and quantify mixed materials, accurately estimating material abundance and object area with less than 1% error. This approach enhances material classification, supporting product verification, quality control, and automated sorting for sustainable waste management and resource recovery.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Incorporating the Effect of Large‐Scale Vertical Motion on Convection Through Convective Mass Flux Adjustment in E3SMv2

Abstract Recent observational studies suggest that the large‐scale dynamical forcing (vertical motion) plays important roles in deep convection development. In this study we propose a convective mass flux adjustment (MAdj) approach to represent the dynamical effects of large‐scale vertical motion on convection in the Department of Energy's Energy Exascale Earth System Model version 2 (E3SMv2). With MAdj, convection is enhanced (suppressed) when there is large‐scale ascending (descending) motion at the planetary boundary layer top. The coupling of convection with large‐scale circulation significantly improves the simulation of climate variability in E3SMv2 across multiple scales from the diurnal cycle, convectively coupled equatorial waves, to the Madden‐Julian Oscillation (MJO). The standard E3SMv2 tends to simulate overly weak diurnal amplitude of precipitation and overly weak variance of convectively coupled equatorial Kelvin and westward inertio‐gravity (WIG) waves. It also fails to simulate the essential characteristics of the MJO: continuous eastward propagation. With MAdj, the amplitude of diurnal cycle of precipitation is systematically increased and its probability density distribution is much closer to observations. The MAdj can also simulate more realistic eastward propagation of the MJO and much stronger convectively coupled Kelvin and WIG waves. Moreover, the MAdj approach slightly improves the climatology simulations in precipitation, cloud, radiation, circulation, temperature, and moisture fields, with overall root‐mean‐square error (RMSE) of major climatological fields reduced by about 2%. The MAdj approach suppresses excessive grid‐scale precipitation, reducing precipitation wet biases over South China Sea, Philippine Sea, Himalayas, and South Pacific Convergence Zone in western Pacific in summer.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Understanding Diverse Model Projections of Future Extreme El Niño

The majority of future projections in the Coupled Model Intercomparison Project (CMIP5) show more frequent exceedances of the 5 mm day -1 rainfall threshold in the eastern equatorial Pacific rainfall during El Niño, previously described in the literature as an increase in “extreme El Niño events”; however, these exceedance frequencies vary widely across models, and in some projections actually decrease. Here we combine single-model large ensemble simulations with phase 5 of the Coupled Model Intercomparison Project (CMIP5) to diagnose the mechanisms for these differences. The sensitivity of precipitation to local SST anomalies increases consistently across CMIP-class models, tending to amplify extreme El Niño occurrence; however, changes to the magnitude of ENSO-related SST variability can drastically influence the results, indicating that understanding changes to SST variability remains imperative. Future El Niño rainfall intensifies most in models with 1) larger historical cold SST biases in the central equatorial Pacific, which inhibit future increases in local convective cloud shading, enabling more local warming; and 2) smaller historical warm SST biases in the far eastern equatorial Pacific, which enhance future reductions in stratus cloud, enabling more local warming. Additionally, these competing mechanisms complicate efforts to determine whether CMIP5 models under- or overestimate the future impacts of climate change on El Niño rainfall and its global impacts. However, the relation between future projections and historical biases suggests the possibility of using observable metrics as “emergent constraints” on future extreme El Niño, and a proof of concept using SSTA variance, precipitation sensitivity to SST, and regional SST trends is presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Evaluating spectral cloud effective radius retrievals from the Enhanced MODIS Airborne Simulator (eMAS) during ORACLES

Satellite remote sensing retrievals of cloud effective radius (CER) are widely used for studies of aerosol–cloud interactions. Such retrievals, however, rely on forward radiative transfer (RT) calculations using simplified assumptions that can lead to retrieval errors when the real atmosphere deviates from the forward model. Here, coincident airborne remote sensing and in situ observations obtained during NASA's ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) field campaign are used to evaluate retrievals of CER for marine boundary layer stratocumulus clouds and to explore impacts of forward RT model assumptions and other confounding factors. Specifically, spectral CER retrievals from the Enhanced MODIS Airborne Simulator (eMAS) and the Research Scanning Polarimeter (RSP) are compared with polarimetric retrievals from RSP and with CER derived from droplet size distributions (DSDs) observed by the Phase Doppler Interferometer (PDI) and a combination of the Cloud and Aerosol Spectrometer (CAS) and the Two-Dimensional Stereo Probe (2D-S). The sensitivities of the eMAS and RSP spectral retrievals to assumptions about the DSD effective variance (CEV) and liquid water complex index of refraction are explored. CER and CEV inferred from eMAS spectral reflectance observations of the backscatter glory provide additional context for the spectral CER retrievals. The spectral and polarimetric CER retrieval agreement is case dependent, and updating the retrieval RT assumptions, including using RSP polarimetric CEV retrievals as a constraint, yields mixed results that are tied to differing sensitivities to vertical heterogeneity. Moreover, the in situ cloud probes, often used as the benchmark for remote sensing CER retrieval assessments, themselves do not agree, with PDI DSDs yielding CER values 1.3–1.6 µm larger than CAS and with CEV roughly 50 %–60 % smaller than CAS. Implications for the interpretation of spectral and polarimetric CER retrievals and their agreement are discussed.

Meyer, Kerry [NASA Goddard Space Flight Center (GS↗
DOE OSTI2023

A bi-level data-driven framework for fault-detection and diagnosis of HVAC systems

Long-term operation of heating, ventilation, and air conditioning (HVAC) systems will eventually lead to a range of HVAC system failures, resulting in excessive energy consumption and maintenance costs. Here, to avoid HVAC malfunctioning, fault detection diagnostic (FDD) is utilized as a common practice. Machine learning methods have lately received considerable interest for FDD analysis of HVAC systems due to their high detection accuracy. Meanwhile, HVAC malfunctions are regarded as rare occurrences, hence normal operating data samples are much more accessible than data samples in faulty and malfunctioning conditions. The dominating frequency of normal operation in HVAC datasets has also led to heavily biased classification algorithms within the literature. Moreover, the focus of previous literature has been on increasing the accuracy of the models which leads to a high number of false positives (misleading alarms) in the system. In order to enhance the performance of diagnostic procedures and fill the mentioned gaps, this study proposes a novel data-driven framework. A bi-level machine learning framework is developed for diagnosing faults in air handling units (AHUs) and rooftop units (RTUs) based on principal component analysis (PCA), time series anomaly detection, and random forest (RF). It is shown that PCA can reduce the dataset dimension with one principal component accounting for 95% of data variance. Also, the random forest could classify the faults with 89% precision for single-zone AHU, 85% precision for RTU, and 79% for multi-zone AHU. By proposing this framework, three persistent challenges are addressed: (I) minimizing false positives; (II) accounting for data imbalance; and (III) normal condition monitoring of equipment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Distributionally robust facility location problem under decision-dependent stochastic demand

While the traditional facility location problem considers exogenous demand, in some applications, locations of facilities could affect the willingness of customers to use certain types of services, e.g., carsharing, and therefore they also affect realizations of random demand. Moreover, a decision maker may not know the exact distribution of such endogenous demand and how it is affected by location choices. In this paper, we consider a distributionally robust facility location problem, in which we interpret the moments of stochastic demand as functions of facility-location decisions. We reformulate a two-stage decision-dependent distributionally robust optimization model as a monolithic formulation, and then derive exact mixed-integer linear programming reformulation as well as valid inequalities when the means and variances of demand are piecewise linear functions of location solutions. We conduct extensive computational studies, in which we compare our model with a decision-dependent deterministic model, as well as stochastic programming and distributionally robust models without the decision-dependent assumption. Here, the results show superior performance of our approach with remarkable improvement in profit and quality of service under various settings, in addition to computational speed-ups given by formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Weak-Form Latent Space Dynamics Identification

This software showcases the enhanced capabilities of the Latent Space Dynamics Identification (LaSDI) algorithm through the application of the weak form, resulting in WLaSDI. WLaSDI first compresses the data, then projects it onto test functions, and subsequently learns the local latent space models. Notably, WLaSDI demonstrates significantly improved robustness to noise. Using weak-form equation learning techniques, WLaSDI achieves local latent space modeling. Compared to the standard sparse identification of nonlinear dynamics (SINDy) used in LaSDI, the variance reduction of the weak form ensures robust and precise latent space recovery, enabling fast, robust, and accurate simulations. We demonstrate the efficacy of WLaSDI against LaSDI using several common benchmark examples, including viscid and inviscid Burgers', radial advection, and heat conduction. For instance, in 1D inviscid Burgers' simulations with up to 100% Gaussian white noise, WLaSDI maintains relative errors consistently below 6%, whereas LaSDI errors can exceed 10,000%. Similarly, in radial advection simulations, WLaSDI keeps relative errors below 16%, compared to potential errors of up to 10,000% with LaSDI. Additionally, WLaSDI achieves significant speedups, such as a 140X speedup in 1D Burgers' simulations compared to the corresponding full order model.

Choi, Youngsoo↗
DOE OSTI2026

Machine Learning–Augmented Laser-Induced Breakdown Spectroscopy for Spectral Discrimination of Iron Oxalates

Enhanced characterization and phase identification of post-PUREX Pu Oxalates (PuOXA) are pivotal for nonproliferation and pre-detonation nuclear forensics. Despite significant advances in the characterization of PuO 2 samples, little is known about the impact of both the chemical structure and oxidation states of PuOXA (i.e., Pu(III) and Pu(IV)) have on optical emission signatures. Here, we demonstrate the analytical capabilities of laser-induced breakdown spectroscopy (LIBS) applied to Fe(II) and Fe(III) oxalate samples as surrogates for PuOXA, highlighting the discriminating features in the LIBS emission spectra arising from differences in the oxidation states within mixed FeOXA samples. We report the enhancement of spectral feature selection using Principal Component Analysis (PCA), which enables the analytical superiority of machine learning algorithms such as Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), Partial Least Squares Regression (PLSR), Support Vector Regression (SVR), and Random Forest Regression (RFR) over conventional univariate techniques for phase discrimination and chemometric analysis. Cluster analysis revealed how both matrix effects and laser ablation influence cluster separability by introducing spectral artifacts that misdirect the maximization of variance. PCA-selected emission lines were used in the regression models, demonstrating that both univariate and multivariate linear regression models (i.e., PLSR and SVR) can achieve acceptable performance, with machine learning models outperforming conventional calibration regressions. Furthermore, the application of non-linearly activated PCA-selected emission lines illustrates how simplifying the data while retaining captured variance enables the use of less complex and more computationally efficient models. Furthermore, this is particularly evident in the underperformance of RFR, which suffers from increased computational costs and overfitting owing to its high complexity.

Oxalates↗
DOE OSTI2024

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Abstract A major challenge in the inversion of subsurface parameters is the ill‐posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In this study, we investigate the effect of model complexity on fracture aperture inversion and thermal performance prediction in a field‐scale EGS model. Principal component analysis was used to map the aperture field to a low‐dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble‐based inversion method, and the inferred aperture field was used to predict thermal performance. With an over‐simplified aperture model, ensemble collapse occurred. The inverted aperture models failed to resolve necessary flow and transport features, leading to a biased thermal performance prediction. A complex aperture model involved excessive features and was prone to overinterpreting the inversion data. Both the tracer/pressure/flow rate data reproduction and thermal prediction showed significant uncertainties, making it difficult to properly estimate long‐term thermal performance. Fortunately, our results indicate that there exists an appropriate model complexity which can simultaneously match inversion data and predict thermal performance with an acceptable uncertainty. The quality of the fit of tracer data appears to be a useful indicator of such an appropriate model complexity.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Measuring stomatal and guard cell metrics for plant physiology and growth using StoManager1

Abstract Automated guard cell detection and measurement are vital for understanding plant physiological performance and ecological functioning in global water and carbon cycles. Most current methods for measuring guard cells and stomata are laborious, time-consuming, prone to bias, and limited in scale. We developed StoManager1, a high-throughput tool utilizing geometrical, mathematical algorithms, and convolutional neural networks to automatically detect, count, and measure over 30 guard cell and stomatal metrics, including guard cell and stomatal area, length, width, stomatal aperture area/guard cell area, orientation, stomatal evenness, divergence, and aggregation index. Combined with leaf functional traits, some of these StoManager1-measured guard cell and stomatal metrics explained 90% and 82% of tree biomass and intrinsic water use efficiency (iWUE) variances in hardwoods, making them substantial factors in leaf physiology and tree growth. StoManager1 demonstrated exceptional precision and recall (mAP@0.5 over 0.96), effectively capturing diverse stomatal properties across over 100 species. StoManager1 facilitates the automation of measuring leaf stomatal and guard cells, enabling broader exploration of stomatal control in plant growth and adaptation to environmental stress and climate change. This has implications for global gross primary productivity (GPP) modeling and estimation, as integrating stomatal metrics can enhance predictions of plant growth and resource usage worldwide. Easily accessible open-source code and standalone Windows executable applications are available on a GitHub repository (https://github.com/JiaxinWang123/StoManager1) and Zenodo (https://doi.org/10.5281/zenodo.7686022).

Wang, Jiaxin (ORCID:0000000348085085)↗
DOE OSTI2023

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

Couchman, Miles M. P. (ORCID:0000000246676829)↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗