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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 1,801 records · Page 100
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Deep learning for drag force modelling in dilute, poly-dispersed particle-laden flows with irregular-shaped particles

Here, this study applies machine learning-based approaches to develop a drag force model for irregular-shaped particles in incompressible flows. The particle-laden flows are studied through an in-house particle-resolved direct numerical simulation (PR-DNS) at low-intermediate Reynolds numbers (Re). We utilize the PR-DNS to obtain drag force coefficients and flow fields of single particles. A variational auto-encoder model is used to obtain latent vectors to represent the geometrical features of the particles, and artificial neural networks (ANN) are developed to predict drag force coefficients and flow fields of the single particles. This study applies a pairwise interaction extended point-particle (PIEP) model to obtain the coefficients assuming the flow fields of neighboring particles can be linearly superposed. The PIEP method shows significant improvement on prediction for a few neighbored particles. In addition, the results reveal R2 scores of 0.56-0.62 and errors of 9.1-10.0 % for the dilute, polydispersed systems with a volume fraction of 0.5 %.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Circumventing data imbalance in magnetic ground state data for magnetic moment predictions

Abstract Magnetic materials play a crucial role in the transition to more sustainable forms of energy and electric vehicles. There is an anticipated shortage in magnetic materials in the future, and as a result there is an urgent need to discover and design new magnetic materials. Computational magnetic material design using density functional theory is daunting because of the challenge in identifying magnetic ground states from a combinatorially large set of possibilities. Machine learning offers a path forward by enabling efficient surrogate models that can more readily enumerate these states, but there is a dearth of training data available, and what is available tends to be imbalanced with too much non-magnetic data. In this work we show that the discrete and previously tackled data imbalance that exists at the level of the magnetic ordering leads to an imbalanced continuous distribution with many zeros when the data is unraveled at the atomic magnetic moment level, which subsequently leads to models with low accuracy for magnetic properties. We mitigate this by using a two-part model framework. Our scheme is able to classify atoms into magnetic and non-magnetic with an F1 score and Matthew’s correlation coefficient (MCC) of ~91% and then to provide an implicit embedding representation that maps directly onto the magnitude of the magnetic moment with a mean absolute error of 0.1 μ B . Beyond screening for new magnetic materials, we demonstrate an additional practical use case of our scheme: the provision of good initial guesses for magnetic moments in first-principles electronic relaxations. Such initialization is shown to lead to faster convergence to configurations that lie closer to the ground state.

Computer Science↗
DOE OSTI2024

Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration

Geological carbon sequestration (GCS) involves injecting CO2 into subsurface geological formationsfor permanent storage. Numerical simulations could guide decisions in GCS projects by predictingCO 2 migration pathways and the pressure distribution in storage formation. However, these simula-tions are often computationally expensive due to highly coupled physics and large spatial-temporalsimulation domains. Surrogate modelling with data-driven machine learning has become a promis-ing alternative to accelerate physics-based simulations. Among these, the Fourier neural operator(FNO) has been applied to three-dimensional synthetic subsurface models. Despite its good accuracyin simulating CO 2 plume migration, it requires large computational resources in training and alsolacks generalizability. Here, to further improve performance, we have developed a nested Fourier-DeepONet by combining the expressiveness of the FNO with the modularity of a deep operatornetwork (DeepONet). This new framework is twice as efficient as a nested FNO for training and has atleast 80% lower GPU memory requirement due to its flexibility to treat temporal coordinates sepa-rately. These performance improvements are achieved without compromising prediction accuracy.In addition, the generalization and extrapolation ability of nested Fourier-DeepONet beyond thetraining range has been thoroughly evaluated. Nested Fourier-DeepONet outperformed the nestedFNO for extrapolation in time with more than 50% reduced error. It also exhibited good extrapolationaccuracy beyond the training range in terms of reservoir properties, number of wells, and injectionrate.

Lee, Jonathan E. [Department of Chemical and Envir↗
DOE OSTI2023

CCSI Toolset 3.19 Release

CCSI Toolset 3.19 Release Highlights A gradient generation tool was developed to support GENN models in FOQUS. Certain machine learning tools train gradient-enhanced neural network (GENN) models which can be more accurate for complex datasets given a priori knowledge of model derivatives. However, the derivatives must be known beforehand and are not often available for process data. This tool automatically predicts the gradients for a training dataset in a form usable by common GENN trainers, such as Surrogate Modeling Toolbox. Support was added for Surrogate Modeling Toolbox GENN models in FOQUS, including updates to the run methods, node properties, test framework, documentation and optional dependencies list. Users can train/save Surrogate Modeling Toolbox gradient-enhanced neural network (GENN) models with custom objects and produce .pkl files compatible with the Machine Learning/Artificial Intelligence Plugin in FOQUS. A simpler implementation of the ordering algorithm in the Sequential Design of Experiments (SDOE) module was included. The SDOE examples documentation was updated. The Optimality-Based Design of Experiments was updated to improve the error handling when the results are None.

AS↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗
DOE OSTI2026

Modeling the behavior of concentrated aqueous HNO 3 using machine learning interatomic potentials

We develop two multi-defect machine learning interatomic potentials (MLIPs) trained at the BLYP-D2 and PBE-D3 density functional theories using the DeepMD-kit, allowing for the investigation of structural and thermodynamic properties of nitric acid over a wide range of concentrations via molecular dynamics (MD) simulations. We directly compute the degree of dissociation, α, and pK a from MD simulations, revealing that HNO 3 behaves as a weaker acid at higher concentrations, noting that our standard-state pK a value is in excellent agreement with the experimental one. In general, good agreement is observed with experimental results such as α and density outside the training dataset, with only modest deviations at low-to-medium concentrations. We benchmark our custom multi-defect DeepMD MLIPs against foundational models MACE-MP0 and MACE-OFF23. The foundation models capture some aspects of HNO 3 /NO 3 − solvation in concentrated nitric acid but show noticeable density errors and miss subtle structural features relevant to spectroscopy, whereas the bespoke DeepMD MLIPs yield more compact solvation shells, reproduce density-concentration trends, and run ∼12–15× faster than MACE-MP0. Although classical FFs are still more efficient and match experimental densities better, they lack chemical reactivity and thus cannot predict α or pK a , underscoring the need for system-specific reactive MLIPs beyond universal MLIPs.

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗
DOE OSTI2023

A General Spatiotemporal Imputation Framework for Missing Sensor Data

Many applications from precision agriculture, environmental monitoring and transportation networks rely on data collected across space and time over a large geographic area. Missing data poses a significant challenge for any data-driven inference and control tasks. Data imputation or the estimation of missing data can help fill these gaps by utilizing inherent spatial relationships and temporal patterns. A variety of spatiotemporal imputation models have been developed to address missing data in spatiotemporal datasets. However, these classical methods rely on the assumption that the underlying data follows a smooth trend and fail to provide accurate estimates when there is a large number of missing points in the data. Even though there are machine learning driven tensor completion approaches such as convolutional neural network based tensor completion (CoSTCo) that capture the non-linear relationships in the dataset, the transductive nature makes the algorithm less scalable. Thus, existing approaches for estimating the missing information do not effectively capture all dimensions of the spatiotemporal data structure, resulting in erroneous predictions and poor performance. The main contributions of this paper are: (1) We propose a novel inductive framework (G-LSTM) for missing data imputation that integrates a graph neural network with LSTMs to effectively capture both spatial and temporal dependencies. (2) Experimental results on a traffic dataset demonstrate that the proposed GNN integrated with an LSTM framework achieves improved imputation and maintains steady performance even when there are extreme missing conditions in comparison with the state-of-the-art imputation framework (i.e, CoSTCo). (3) The simulation results on a traffic network show up to 69% reduction in mean absolute error and 61% reduction in root mean square error when compared to CoSTCo.

Tharzeen, Aabila↗
DOE OSTI2022

Implementing Spatio-Temporal 3D-Convolution Neural Networks and UAV Time Series Imagery to Better Predict Lodging Damage in Sorghum

Unmanned aerial vehicle (UAV)-based remote sensing is gaining momentum in a variety of agricultural and environmental applications. Very-high-resolution remote sensing image sets collected repeatedly throughout a crop growing season are becoming increasingly common. Analytical methods able to learn from both spatial and time dimensions of the data may allow for an improved estimation of crop traits, as well as the effects of genetics and the environment on these traits. Multispectral and geometric time series imagery was collected by UAV on 11 dates, along with ground-truth data, in a field trial of 866 genetically diverse biomass sorghum accessions. We compared the performance of Convolution Neural Network (CNN) architectures that used image data from single dates (two spatial dimensions, 2D) versus multiple dates (two spatial dimensions + temporal dimension, 3D) to estimate lodging detection and severity. Lodging was detected with 3D-CNN analysis of time series imagery with 0.88 accuracy, 0.92 Precision, and 0.83 Recall. This outperformed the best 2D-CNN on a single date with 0.85 accuracy, 0.84 Precision, and 0.76 Recall. The variation in lodging severity was estimated by the best 3D-CNN analysis with 9.4% mean absolute error (MAE), 11.9% root mean square error (RMSE), and goodness-of-fit (R2) of 0.76. This was a significant improvement over the best 2D-CNN analysis with 11.84% MAE, 14.91% RMSE, and 0.63 R2. The success of the improved 3D-CNN analysis approach depended on the inclusion of “before and after” data, i.e., images collected on dates before and after the lodging event. The integration of geometric and spectral features with 3D-CNN architecture was also key to the improved assessment of lodging severity, which is an important and difficult-to-assess phenomenon in bioenergy feedstocks such as biomass sorghum. This demonstrates that spatio-temporal CNN architectures based on UAV time series imagery have significant potential to enhance plant phenotyping capabilities in crop breeding and Precision agriculture applications.

3D-convolution neural networks↗
DOE OSTI2021

Deep potential generation scheme and simulation protocol for the Li 10 GeP 2 S 12 -type superionic conductors

We report solid-state electrolyte materials with superior lithium ionic conductivities are vital to the next-generation Li-ion batteries. Molecular dynamics could provide atomic scale information to understand the diffusion process of Li-ion in these superionic conductor materials. Here, we implement the deep potential generator to set up an efficient protocol to automatically generate interatomic potentials for Li 10 GeP 2 S 12 -type solid-state electrolyte materials (Li 10 GeP 2 S 12 , Li 10 SiP 2 S 12 , and Li 10 SnP 2 S 12 ). The reliability and accuracy of the fast interatomic potentials are validated. With the potentials, we extend the simulation of the diffusion process to a wide temperature range (300 K–1000 K) and systems with large size (~1000 atoms). Important technical aspects such as the statistical error and size effect are carefully investigated, and benchmark tests including the effect of density functional, thermal expansion, and configurational disorder are performed. The computed data that consider these factors agree well with the experimental results, and we find that the three structures show different behaviors with respect to configurational disorder. Our work paves the way for further research on computation screening of solid-state electrolyte materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Extracting Material Property Measurement Data from Scientific Articles

Machine learning-based prediction of material properties is often hampered by the lack of sufficiently large training datasets. The majority of such measurement data is embedded in scientific literature and the ability to automatically extract these data is essential to support the development of reliable property prediction methods. In this work, we describe a methodology for an automatic property extraction framework using material solubility as the target property. We create an annotated dataset containing tags for solubility-related entities using a combination of regular expressions and manual tagging. We then compare five entity recognition models leveraging both token-level and span-level architectures on the task of classifying solute names, solubility values, and solubility units. Additionally, we explore a novel pretraining approach that leverages automated chemical name and quantity extraction tools to generate large datasets that do not rely on intensive manual effort. Finally, we perform an analysis to identify the causes of classification errors.

Panapitiya, Gihan U.↗
DOE OSTI2024

A Bayesian Learning Approach to Wireless Outdoor Heatmap Construction using Deep Gaussian Process

We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian process (GP). The proposed approach employs a two-layer hierarchy which consists of two cascaded Gaussian processes that are capable of modeling more complex input-output relations than standard single-layer Gaussian processes. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead so that gradient descent-based methods can be performed to find out the optimal model parameters. Typically, inducing points are used in GPs to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may hinder the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, in the form of location-Received Signal Strength (RSS) pairs, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experiment results show that the proposed approach can achieve smaller prediction errors on various training and testing data configurations than DNN-based and GP-based methods.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Transforming microseismic clouds into near real-time visualization of the growing hydraulic fracture

SUMMARY Microseismic observations during unconventional reservoir stimulation are typically seen as a proxy for clusters of hydraulic fractures and the extent of the stimulated reservoir. Such straightforward interpretation is often misleading and fails to provide a physically reasonable image of the fracturing process. This paper demonstrates the application of a physics-based machine learning algorithm which enables a rapid and accurate fracture mapping from the microseismic data. Our training and validation data set relies on a history-matched geomechanical modelling workflow implemented in GEOS software for the Hydraulic Fracturing Test Site 1 (HFTS-1) project. For this study we augmented the simulated fracture growth through geostatistical modelling of induced seismicity, so that the synthetic microseismic catalogue matches the main statistical properties of the field observations. We formulated the problem of mapping the actual fracture in the clutter of events to parallel common video segmentation workflows: several past video frames (microseismic density snapshots) are passed through a deep convolutional network to classify whether a given voxel is associated with a fracture or intact rock. We found that for accurate fracture mapping, the network’s input and architecture must be augmented to incorporate the fluid injection parameters (pressure, rate, concentration of proppant, and location of the perforation within the cluster). The error rate for the network reached as little as 10 per cent of the fracture area, while a conventional microseismic interpretation approach yielded ∼300 per cent. Our approach also yields must faster predictions than conventional methods (minutes instead of weeks), and could enable engineers to make rapid decisions regarding engineering parameters (pumping rate, viscosity) in real time during stimulation.

58 GEOSCIENCES↗
NASA NTRS2019

Application of High-Dimensional Fuzzy K-Means Cluster Analysis to CALIOP/CALIPSO Version 4.1 Cloud-Aerosol Discrimination

This study applies fuzzy k-means (FKM) cluster analyses to a subset of the parameters reported in the CALIPSO lidar level 2 data products in order to classify the layers detected as either clouds or aerosols. The results obtained are used to assess the reliability of the cloud–aerosol discrimination (CAD) scores reported in the version 4.1 release of the CALIPSO data products. FKM is an unsupervised learning algorithm, whereas the CALIPSO operational CAD algorithm (COCA) takes a highly supervised approach. Despite these substantial computational and architectural differences, our statistical analyses show that the FKM classifications agree with the COCA classifications for more than 94 % of the cases in the troposphere. This high degree of similarity is achieved because the lidar-measured signatures of the majority of the clouds and the aerosols are naturally distinct, and hence objective methods can independently and effectively separate the two classes in most cases. Classification differences most often occur in complex scenes (e.g., evaporating water cloud filaments embedded in dense aerosol) or when observing diffuse features that occur only intermittently (e.g., volcanic ash in the tropical tropopause layer). The two methods examined in this study establish overall classification correctness boundaries due to their differing algorithm uncertainties. In addition to comparing the outputs from the two algorithms, analysis of sampling, data training, performance measurements, fuzzy linear discriminants, defuzzification, error propagation, and key parameters in feature type discrimination with the FKM method are further discussed in order to better understand the utility and limits of the application of clustering algorithms to space lidar measurements. In general, we find that both FKM and COCA classification uncertainties are only minimally affected by noise in the CALIPSO measurements, though both algorithms can be challenged by especially complex scenes containing mixtures of discrete layer types. Our analysis results show that attenuated backscatter and color ratio are the driving factors that separate water clouds from aerosols; backscatter intensity, depolarization, and mid-layer altitude are most useful in discriminating between aerosols and ice clouds; and the joint distribution of backscatter intensity and depolarization ratio is critically important for distinguishing ice clouds from water clouds.

Zeng, Shan↗
DOE OSTI2020

NEON AOP foliar trait maps, maps of model uncertainty estimates, and conifer map, East River, CO 2018

This data package contains mapped trait estimates and their uncertainties, and conifer map, for the National Ecological Observatory Network's Airborne Observation Platform survey data acquired over the Upper East River, Colorado in 2018. For full details, please see associated reference. in brief, trait models were developed independently for needle and non-needle leaf species using partial least squares regression (PLSR) using ground data from additional datasets: doi:10.15485/1618130, doi:10.15485/1618132, and doi:10.15485/1631278, merged with extracted spectral data from doi:10.15485/1618131. We separated vegetated pixels into needle and non-needle classes in order to generate a classification map based on the spectral differences between these leaf types (conifer.tif). We trained a deep learning model with custom architecture, detailed in Chadwick et al. In Press. The model performed with 0.998 true positive rate and 0.982 true negative rate, with ‘positives’ being non-needle identification. We then utilized PLSR to generate models of foliar traits for each leaf type. So that we could also map uncertainty in these predictions, we generated ten different models for needle and non-needle leaf species using different testing holdout sets of discrete sites. Each of these models was developed with a 100-fold cross validation procedure that utilized a 70% training set and 30% validation set with each fold, and then assessed based on the 10% of testing sites that were not included in that model’s development. The mean predicted value across the 10 models is used for the trait estimate in each pixel across the study area. The models are applied according to the leaf type designation in the conifer.tif map. The errors are the standard deviation across the 10 different models developed, with high error suggesting instability in model prediction and areas where values may not be reliable for ecological inference. These maps are only applied to areas with a NDVI > 0.5 to exclude non-vegetated areas. Shade masks could be applied to these data (doi:10.15485/1618131), but have not been for this data package. These data are also available on Google Earth Engine: https://code.earthengine.google.com/?asset=users/kdc/ER_NEON

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

DSCOVR/EPIC-derived global hourly and daily downward shortwave and photosynthetically active radiation data at 0.1° × 0.1° resolution

Downward shortwave radiation (SW) and photosynthetically active radiation (PAR) play crucial roles in Earth system dynamics. Spaceborne remote sensing techniques provide a unique means for mapping accurate spatiotemporally continuous SW–PAR, globally. However, any individual polar-orbiting or geostationary satellite cannot satisfy the desired high temporal resolution (sub-daily) and global coverage simultaneously, while integrating and fusing multisource data from complementary satellites/sensors is challenging because of co-registration, intercalibration, near real-time data delivery and the effects of discrepancies in orbital geometry. The Earth Polychromatic Imaging Camera (EPIC) on board the Deep Space Climate Observatory (DSCOVR), launched in February 2015, offers an unprecedented possibility to bridge the gap between high temporal resolution and global coverage and characterize the diurnal cycles of SW–PAR globally. In this study, we adopted a suite of well-validated data-driven machine-learning models to generate the first global land products of SW–PAR, from June 2015 to June 2019, based on DSCOVR/EPIC data. The derived products have high temporal resolution (hourly) and medium spatial resolution (0.1°×0.1°), and they include estimates of the direct and diffuse components of SW–PAR. We used independently widely distributed ground station data from the Baseline Surface Radiation Network (BSRN), the Surface Radiation Budget Network (SURFRAD), NOAA's Global Monitoring Division and the U.S. Department of Energy's Atmospheric System Research (ASR) program to evaluate the performance of our products, and we further analyzed and compared the spatiotemporal characteristics of the derived products with the benchmarking Clouds and the Earth's Radiant Energy System Synoptic (CERES) data. We found both the hourly and daily products to be consistent with ground-based observations (e.g., hourly and daily total SWs have low biases of -3.96 and -0.71 W m -2 and root-mean-square errors (RMSEs) of 103.50 and 35.40 W m -2 , respectively). The developed products capture the complex spatiotemporal patterns well and accurately track substantial diurnal, monthly, and seasonal variations in SW–PAR when compared to CERES data. They provide a reliable and valuable alternative for solar photovoltaic applications worldwide and can be used to improve our understanding of the diurnal and seasonal variabilities of the terrestrial water, carbon and energy fluxes at various spatial scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Efficient bifurcation and tabulation of multi-dimensional combustion manifolds using deep mixture of experts: An a priori study

This work describes and validates an approach for autonomously bifurcating turbulent combustion man-ifolds to divide regression tasks amongst specialized artificial neural networks (ANNs). This approach relies on the mixture of experts (MoE) framework, where each neural network is trained to be specialized in a given portion of the input space. The assignment of different input regions to the experts is determined by a gating network, which is a neural network classifier. In some previous studies, it has been demonstrated that bifurcation of a complex combustion manifold and fitting different ANNs for each part leads to better fits or faster inference speeds. However, the manner of bifurcation in these studies was based on heuristic approaches or clustering techniques. In contrast, the proposed technique enables automatic bifurcation using non-linear planes in high-dimensional turbulent combustion manifolds that are often associated with complex behavior due to different dominating physics in various zones. Furthermore, the proposed concept is validated using 4-dimensional (4D) and 5D flamelet tables, showing that the errors obtained with a given network size, or conversely the network size required to achieve a given accuracy, is considerably reduced. The effect of the number of experts on inference speed is also investigated, showing that by increasing the number of experts from 1 to 8, the inference time can be approximately reduced by a factor of two. Moreover, it is shown that the MoE approach divides the input manifold in a physically intuitive manner, suggesting that the MoE framework can elucidate high-dimensional datasets in a physically meaningful way.

42 ENGINEERING↗
DOE OSTI2020

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. Here we address this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

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