Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Sparse regression”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Quantifying spatial and vertical variations in soil C:N relationships in permafrost-affected landscapes

Permafrost regions are experiencing rapid changes that affect carbon (C) and nitrogen (N) cycles, with implications for vegetation dynamics and gas exchanges with the atmosphere. Soil C:N ratio is a key indicator of organic matter quality, yet spatial estimates of N stocks and C:N ratios lag behind those for C. We used quantile regression forests to compare direct and indirect digital soil mapping approaches for predicting soil C:N ratios at 0–30, 30–60, and 60–100 cm depths across a latitudinal transect in Alaska. The indirect approach – deriving C:N from separately predicted C and N stocks – outperformed direct mapping for the surface layer (0–30 cm), while direct mapping was marginally better at greater depths. However, prediction accuracy decreased with depth for both methods. Temperature and topography were the most important predictors. Both approaches overestimated low and underestimated high C:N ratios, with direct mapping showing greater bias. Our results underscore the challenges of modeling C:N ratios in heterogeneous, data-sparse permafrost soils, but also suggest that indirect mapping holds promise if supported by more extensive datasets.

54 ENVIRONMENTAL SCIENCES↗

An ℓ 0 ℓ 2 -norm regularized regression model for construction of robust cluster expansions in multicomponent systems

In this work we introduce ℓ 0 ℓ 2 -norm regularization and hierarchy constraints into linear regression for the construction of cluster expansions to describe configurational disorder in materials. The approach is implemented through mixed integer quadratic programming (MIQP). The ℓ 2 -norm regularization is used to suppress intrinsic data noise, while the ℓ 0 -norm is used to penalize the number of nonzero elements in the solution. The hierarchy relation between clusters imposes relevant physics and is naturally included by the MIQP paradigm. As such, sparseness and cluster hierarchy can be well optimized to obtain a robust, converged set of effective cluster interactions with improved physical meaning. We demonstrate the effectiveness of ℓ 0 ℓ 2 -norm regularization in two high-component disordered rocksalt cathode material systems, where we compare the cross-validation, convergence speed, and the reproduction of phase diagrams, voltage profiles, and Li-occupancy energies with those of the conventional ℓ 1 -norm regularized cluster expansion models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Features of Point Clouds Synthesized from Multi-View ALOS/PRISM Data and Comparisons with LiDAR Data in Forested Areas

LiDAR waveform data from airborne LiDAR scanners (ALS) e.g. the Land Vegetation and Ice Sensor (LVIS) havebeen successfully used for estimation of forest height and biomass at local scales and have become the preferredremote sensing dataset. However, regional and global applications are limited by the cost of the airborne LiDARdata acquisition and there are no available spaceborne LiDAR systems. Some researchers have demonstrated thepotential for mapping forest height using aerial or spaceborne stereo imagery with very high spatial resolutions.For stereo imageswith global coverage but coarse resolution newanalysis methods need to be used. Unlike mostresearch based on digital surface models, this study concentrated on analyzing the features of point cloud datagenerated from stereo imagery. The synthesizing of point cloud data from multi-view stereo imagery increasedthe point density of the data. The point cloud data over forested areas were analyzed and compared to small footprintLiDAR data and large-footprint LiDAR waveform data. The results showed that the synthesized point clouddata from ALOSPRISM triplets produce vertical distributions similar to LiDAR data and detected the verticalstructure of sparse and non-closed forests at 30mresolution. For dense forest canopies, the canopy could be capturedbut the ground surface could not be seen, so surface elevations from other sourceswould be needed to calculatethe height of the canopy. A canopy height map with 30 m pixels was produced by subtracting nationalelevation dataset (NED) fromthe averaged elevation of synthesized point clouds,which exhibited spatial featuresof roads, forest edges and patches. The linear regression showed that the canopy height map had a good correlationwith RH50 of LVIS data with a slope of 1.04 and R2 of 0.74 indicating that the canopy height derived fromPRISM triplets can be used to estimate forest biomass at 30 m resolution.

LiDARD↗

Mapping tree canopy cover and canopy height with L-band SAR using LiDAR data and Random Forests

Light detection and ranging (LiDAR) data can provide direct measurements of vegetation structures but are limited by the sparse spatial coverage. Polarimetric synthetic aperture radar (SAR) can perform large-scale high-resolution mapping without weather constraints but the information about vegetation and ground subsurface are mixed in the backscatter data. In this paper, we adopted the Random Forests algorithm to train an upscaling function using tree canopy cover (TCC) and canopy height model (CHM) derived from Goddard’s LiDAR, Hyperspectral and Thermal Imager (G-LiHT) data. The regression model is then applied to the L-band Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) data acquired during the 2017 Arctic-Boreal Vulnerability Experiment (ABoVE) airborne campaign to map the TCC and CHM over the Delta Junction area in interior Alaska.

Moghaddam, Mahta↗

Generation of Data-Driven Expected Energy Models for Photovoltaic Systems

Although unique expected energy models can be generated for a given photovoltaic (PV) site, a standardized model is also needed to facilitate performance comparisons across fleets. Current standardized expected energy models for PV work well with sparse data, but they have demonstrated significant over-estimations, which impacts accurate diagnoses of field operations and maintenance issues. This research addresses this issue by using machine learning to develop a data-driven expected energy model that can more accurately generate inferences for energy production of PV systems. Irradiance and system capacity information was used from 172 sites across the United States to train a series of models using Lasso linear regression. The trained models generally perform better than the commonly used expected energy model from international standard (IEC 61724-1), with the two highest performing models ranging in model complexity from a third-order polynomial with 10 parameters (Radj2 = 0.994) to a simpler, second-order polynomial with 4 parameters (Radj2=0.993), the latter of which is subject to further evaluation. Subsequently, the trained models provide a more robust basis for identifying potential energy anomalies for operations and maintenance activities as well as informing planning-related financial assessments. We conclude with directions for future research, such as using splines to improve model continuity and better capture systems with low (≤1000 kW DC) capacity.

14 SOLAR ENERGY↗

Anomaly Detection for Online Monitoring of Thermocouple Sensors in the Advanced Test Reactor

This study explores data-driven anomaly detection methods to analyze sensor fail- ures in the Advanced Gas Reactor (AGR) nuclear fuel irradiation experiments. Specifically, we examine failures of thermocouples (TCs), which are critical for mon- itoring and controlling in-reactor temperatures during operation. Failures were pri- marily observed during abrupt power transitions and manifested as sensor drop-outs, drifts, or unexplained behavior. We applied three time-series analysis techniques— rolling mean smoothing, matrix profile, and vector auto-regression (VAR)—to de- tect anomalies in TC data prior to failure events. The rolling mean method effec- tively highlighted deviations aligned with reported failures, while the matrix profile provided partial early warning but sometimes flagged normal fluctuations during power-down periods. VAR shows potential in capturing multivariate dependencies but requires further calibration. A rare case of TC drift was also documented, which did not result in failure, underscoring the challenge of building predictive models with sparse positive examples. Our findings demonstrate that traditional statistical tools can aid anomaly detection but have limited predictive power without richer training data. We propose future directions including synthetic data generation, real- time surrogate modeling, and multi-modal feature integration. This work provides a foundation for applying robust anomaly detection frameworks to mission-critical sensor systems in experimental settings.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Classification of Dust Days by Satellite Remotely Sensed Aerosol Products

Considerable progress in satellite remote sensing (SRS) of dust particles has been seen in the last decade. From an environmental health perspective, such an event detection, after linking it to ground particulate matter (PM) concentrations, can proxy acute exposure to respirable particles of certain properties (i.e. size, composition, and toxicity). Being affected considerably by atmospheric dust, previous studies in the Eastern Mediterranean, and in Israel in particular, have focused on mechanistic and synoptic prediction, classification, and characterization of dust events. In particular, a scheme for identifying dust days (DD) in Israel based on ground PM10 (particulate matter of size smaller than 10 nm) measurements has been suggested, which has been validated by compositional analysis. This scheme requires information regarding ground PM10 levels, which is naturally limited in places with sparse ground-monitoring coverage. In such cases, SRS may be an efficient and cost-effective alternative to ground measurements. This work demonstrates a new model for identifying DD and non-DD (NDD) over Israel based on an integration of aerosol products from different satellite platforms (Moderate Resolution Imaging Spectroradiometer (MODIS) and Ozone Monitoring Instrument (OMI)). Analysis of ground-monitoring data from 2007 to 2008 in southern Israel revealed 67 DD, with more than 88 percent occurring during winter and spring. A Classification and Regression Tree (CART) model that was applied to a database containing ground monitoring (the dependent variable) and SRS aerosol product (the independent variables) records revealed an optimal set of binary variables for the identification of DD. These variables are combinations of the following primary variables: the calendar month, ground-level relative humidity (RH), the aerosol optical depth (AOD) from MODIS, and the aerosol absorbing index (AAI) from OMI. A logistic regression that uses these variables, coded as binary variables, demonstrated 93.2 percent correct classifications of DD and NDD. Evaluation of the combined CART-logistic regression scheme in an adjacent geographical region (Gush Dan) demonstrated good results. Using SRS aerosol products for DD and NDD, identification may enable us to distinguish between health, ecological, and environmental effects that result from exposure to these distinct particle populations.

satellite remote sensing↗

Probabilistic Machine Learning Estimation of Ocean Mixed Layer Depth from Dense Satellite and Sparse In-Situ Observations

The ocean mixed layer plays an important role in the coupling between the upper ocean and atmosphere across a wide range of time scales. Estimation of the variability of the ocean mixed layer is therefore important for atmosphere-ocean prediction and analysis. The increasing coverage of in situ Argo profile data allows for an increasingly accurate analysis of the mixed layer depth (MLD) variability associated with deviations from the seasonal climatology. However, sampling rates are not sufficient to fully resolve subseasonal (<90 day) MLD variability. Yet, many multivariate observations-based analyses include implicit modeled subseasonal MLD variability. One analysis method is optimal interpolation of in situ data, but the interior analysis can be improved by leveraging surface data with regression or variational approaches. Here, we demonstrate how machine learning methods and satellite sea surface temperature, salinity, and height facilitate MLD estimation in a pilot study of two regions: the mid-latitude southern Indian and the eastern equatorial Pacific Oceans. We construct multiple machine learning architectures to produce weekly 1/2° gridded MLD anomaly fields (relative to a monthly climatology) with uncertainty estimates. We test multiple traditional and probabilistic machine learning techniques to compare both accuracy and probabilistic calibration. We validate our methodology by applying it to ocean model simulations. We find that incorporating sea surface data through a machine learning model improves the performance of spatiotemporal MLD variability estimation compared to optimal interpolation of Argo observations alone. These preliminary results are a promising first step for the application of machine learning to MLD prediction.

Machine Learning↗

Comparing Ice Jam Hindcasting Models with Tree Scar Data

Hindcasting models can use historic ice jam observations and hydroclimatic data to identify conditions that form ice jams.However, historic ice jam records are often sparse or incomplete. New sources of historic ice jam data could improve hindcasting models, leading to better ice jam forecasting and flood warning systems. Because ice jams damage riparian trees, marker rings associated with historic scars include information about ice jam frequency and severity. This study examined marker rings from 56 trees along the Muskegon River to supplement the historic ice jam data on this system. The study team compared tree ring data to results from hindcasting models, which were independently validated with newspaper reports on 1,500 separate days. Logistic regression converted the marker ring data into annual ice jam probabilities. Ice jam dates from the dendrochronology data were too noisy to train or validate a hindcasting model. However, the marker ring data did confirm that ice jams on the Muskegon are nonstationary. Ice jams are significantly more likely now than they were before 1966.The marker rings also helped to distinguish between false-negatives and nondetects in the hindcasting model.

Stanford Gibson↗

Bayesian Geostatistical Modelling of PM10 and PM2.5 Surface Level Concentrations in Europe Using High-Resolution Satellite-Derived Products

Air quality monitoring across Europe is mainly based on in situ ground stations which are too sparse to accurately assess the exposure effects of air pollution for the entire continent. The demand for precise predictive modelsthat estimate gridded geophysical parameters of ambient air at high spatial resolution has rapidly grown. Here, we investigate the potential of satellite derived products to improve particulate matter (PM) estimates. Bayesiangeostatistical models addressing confounding between the spatial distribution of pollutants and remotely sensed predictors were developed to estimate yearly averages of both, fine (PM2.5) and coarse (PM10) surface PM concentrations at 1 sq.km spatial resolution over 46 European countries and were compared to geostatistical, geographically weighted and land-use regression formulations. Rigorous model selection identified the Earth observation data which contribute most to pollutants' estimation. Geostatistical models outperformed the predictive ability of the frequently employed land-use regression. The resulting estimates of PM10 and PM2.5, which represent the main air quality indicators for the urban Sustainable Development Goal, indicate that in 2016, 66.2% of the European population was breathing air above the WHO Air Quality Guidelines thresholds. Our estimates are readily available to policy makers and scientists assessing the effects of long-term exposure to pollution on human and ecosystem health.

Beloconi, Anton↗

Population genomic response to geographic gradients by widespread and endemic fishes of the Arabian Peninsula

Genetic structure within marine species may be driven by local adaptation to their environment, or alternatively by historical processes, such as geographic isolation. The gulfs and seas bordering the Arabian Peninsula offer an ideal setting to examine connectivity patterns in coral reef fishes with respect to environmental gradients and vicariance. The Red Sea is characterized by a unique marine fauna, historical periods of desiccation and isolation, as well as environmental gradients in salinity, temperature, and primary productivity that vary both by latitude and by season. The adjacent Arabian Sea is characterized by a sharper environmental gradient, ranging from extensive coral cover and warm temperatures in the southwest, to sparse coral cover, cooler temperatures, and seasonal upwelling in the northeast. Reef fish, however, are not confined to these seas, with some Red Sea fishes extending varying distances into the northern Arabian Sea, while their pelagic larvae are presumably capable of much greater dispersal. These species must therefore cope with a diversity of conditions that invoke the possibility of steep clines in natural selection. Here, we test for genetic structure in two widespread reef fish species (a butterflyfish and surgeonfish) and eight range-restricted butterflyfishes across the Red Sea and Arabian Sea using genome-wide single nucleotide polymorphisms. We performed multiple matrix regression with randomization analyses on genetic distances for all species, as well as reconstructed scenarios for population subdivision in the species with signatures of isolation. We found that (a) widespread species displayed more genetic subdivision than regional endemics and (b) this genetic structure was not correlated with contemporary environmental parameters but instead may reflect historical events. We propose that the endemic species may be adapted to a diversity of local conditions, but the widespread species are instead subject to ecological filtering where different combinations of genotypes persist under divergent ecological regimes.

59 BASIC BIOLOGICAL SCIENCES↗

Effects of Dose Error and Sample Size on Sonic Boom Dose-response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

Effects of Dose Error and Sample Size on Sonic Boom Dose-Response Curves

NASA will soon be collecting noise-annoyance community survey data as the X-59 aircraft flies supersonically over several communities in the USA. Sparse measurements of the X-59 sonic thumps will be used together with physics-based simulations to estimate noise doses at survey participant locations. These dose estimates have associated error that affects the accuracy of modeled dose-response curves, which can result in misestimation of annoyance. The precision in dose-response curves is also a consideration in selecting the number of survey participants. To enable pretest studies of dose error and precision, simulated dose-response data were generated based on NASA’s Quiet Supersonic Flights 2018 test. The data included various degrees of dose error and sample size. Frequentist multilevel logistic regression models were fit to the true and perturbed dose-response data. Simple proportional relationships were identified between the model parameters and the perturbation standard deviation. The summary dose-response curves illustrate the impact on accuracy if dose error is not accounted for in the model. The precision in the dose-response curves is also shown as the number of participants and degree of participation is varied. Finally, sampling variability is illustrated by showing the dose-response curves for several replicates with random draws of participants and errors.

X-59↗

Gaussian Process Regression Method for Costing SmallSat Bus Capabilities

NASA is responding to the growing interest in, andcapabilities of, small satellites for science applications with an increasingnumber and frequency of Announcements of Opportunityfor small satellite space missions. Estimating the probabilitythat these mission concepts will fit within the small cost capsof these opportunities is largely driven by the probability thatone of the burgeoning number of small satellite providers will beable to meet the payload’s accommodation requirements withinthe budget for the spacecraft. JPL has collected a databasecontaining technical specifications and cost of commerciallyavailable Smallsat buses across various vendors. The primarypurpose of the database is for use in JPL’s Team X architecturestudies to inform cost estimates of a spacecraft bus which fitsthe customer’s technical requirements for their payload andmission. Customer needs are often unique and don’t alignperfectly with an off-the-shelf commercial spacecraft bus, whichmotivates the need to develop a cost model across the continuoustechnical parameter space.Al’s Bus Cost Distribution Estimator (ABCDE) uses Gaussianprocess regression (GPR) to predict commercial Smallsat spacecraftbus cost based on a subset of a customer’s technicalrequirements (payload mass, payload power, delta V, pointingcontrol, and downlink rate). GPR is implemented in ABCDE asa Bayesian method which fits an implied multivariate regressionon the technical parameters and uses kriging to intentionally“overfit” the residuals. Overfitting the residuals allows costestimates to collapse in uncertainty closer to the data pointswhile maintaining larger uncertainty intervals in regions of parameterspace with fewer data records. The data used to fit thismodel is sensitive and represents cost estimates for off-the-shelfcommercial buses. GPR simultaneously protects the sensitivityof the database and uses the sparse nature of the database toaccount for uncertainty in cost in a useful way. For a givenset of customer technical requirements, the tool provides a costestimate distribution, the percentiles of which can be interpretedas a confidence level of finding a commercial bus under a specifiedcost cap. ABCDE dramatically pushes the boundaries ofspacecraft cost estimation models due to its Bayesian methodology(accounting for the maximum uncertainty in the underlyingregression), the mathematically advanced kriging methodology,and the novelty of its application in Team X architecture tradestudies.

Austin, Alex↗

Improved Rainfall Data in the Philippines through Concurrent Use of GPM IMERG and Ground-Based Measurements

The availability of accurate and reliable rainfall data that are applicable to various phenomenological, climatological, and modeling studies is important, especially in the Philippines, which is considered to be highly vulnerable to natural hazards and a changing climate. The presented strategy involved constructing a dataset consisting of synoptic data, automatic rain gauge (ARG) measurements, and satellite data that are co-registered, consistent, and formatted in the same manner. Although sparse in number, the synoptic stations provide the most accurate rainfall information and were used as the baseline for creating the dataset. The ARGs that are within a distance of 1 km to the synoptic stations were used to determine the correction factors needed to make the synoptic and ARG data consistent. Subsequently, the corrected ARGs were used to make the satellite IMERG data consistent with both ARG and synoptic data. In case of the latter, only IMERG pixels with at least 10 ARGs within the relatively large footprint of the satellite sensor were used in estimating the required correction parameters derived from a combination of a power transform and linear regression correction techniques. The final results show good agreement of synoptic and corrected ARG data with correlation coefficients of 0.94 and 0.97 for the 10 day and monthly data, respectively, and improvement in the linear regression slope from 0.67 to 0.90 for 10 day data, and 0.70 to 0.94 for monthly data. In addition, the corrected ARG data agree well with the corrected IMERG data, with correlation coefficients of 0.88 and 0.93 for the 10 day and monthly data, respectively, and an improvement in slope from 0.66 to 0.87 for 10 day data, and 0.74 to 0.99 for monthly data. The merit of using a combined dataset is illustrated through comparative analyses of the IMERG data and spatially interpolated synoptic and ARG data. The results show general agreements in spatial patterns of rainfall across the datasets, especially in areas where in situ measurements are recorded. The observed discrepancy when ground data is limited emphasizes the need for satellite IMERG data to obtain the true spatial patterns of rainfall distribution.

rainfall↗

Machine Learning for Mapping Multipactor Susceptibility in RF Systems: Capabilities and Generalization Constraints

Multipactor is a surface-driven electron avalanche phenomenon that degrades the performance and reliability of radio-frequency (RF) systems in particle accelerator and vacuum electronics applications. Multipactor behavior in a given device structure is conventionally assessed through susceptibility charts, which provide a parameter-space characterization of the instability. In this work, we assess the capabilities of machine-learning (ML) models to learn and predict such susceptibility charts and analyze the constraints governing their generalization across materials. Using a simulation-derived dataset spanning six distinct secondary-electron-yield material profiles in a canonical two-surface planar geometry, we train supervised regression models and artificial neural networks to predict the time-averaged electron growth rate, δavg, across the relevant parameter space. Model performance is evaluated using metrics that explicitly probe the structure of susceptibility charts, including Intersection over Union, Structural Similarity Index, and correlation analysis. Tree-based ensemble models outperform neural-network models in reconstructing susceptibility regions and in generalizing across material domains. Principal-component analysis reveals disjoint material feature distributions, indicating that the piecewise mode structure of multipactor susceptibility is difficult to represent with a single global model and that generalization is constrained by data coverage rather than by model complexity. An exhaustive reduced-coverage study further shows that sparse material-space coverage can yield mean performance in the same general range but producing large variability in the susceptibility-region overlap. These results clarify the capabilities of ML-based surrogate models for parameter-space characterization of multipactor discharge. They also provide guidance for their appropriate use in RF system design.

43 PARTICLE ACCELERATORS↗

Ensemble Estimation of Historical Evapotranspiration for the Conterminous U.S.

Abstract Evapotranspiration (ET) is the largest component of the water budget, accounting for the majority of the water available from precipitation. ET is challenging to quantify because of the uncertainties associated with the many ET equations currently in use, and because observations of ET are uncertain and sparse. In this study, we combine information provided by available ET data and equations to produce a new monthly data set for ET for the conterminous U.S. (CONUS). These maps are produced from 1895 to 2018 at an 800 m spatial scale, marking a finer resolution than currently available products over this time period. In our approach, the relative performance of a suite of ET equations is assessed using water balance, flux tower, and remotely sensed ET estimates. At the observation locations, we use error distributions to quantify relative weights for the equations and use these in a modified Bayesian model averaging weighted ensemble approach. The relative weights are spatially generalized using a random forest regression, which is applied to wall‐to‐wall explanatory variable maps to generate CONUS‐wide relative weight maps and ensemble estimates. We assess the performance of the ensemble using a reserved subset of the observations and compare this performance against other national‐scale map products for historical to modern ET. The ensemble ET maps are shown to provide an improved accuracy over the alternative comparison products. These ET maps could be useful for a variety of hydrologic modeling and assessment applications that benefit from a long record, such as the study of periods of water scarcity through time.

Environmental Sciences & Ecology↗

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗