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Bingo: A Customizable Framework for Symbolic Regression with Genetic Programming

In this paper, we introduce Bingo, a flexible and customizable yet performant Python framework for symbolic regression with genetic programming. Bingo maintains a modular code structure for simple abstraction and easily swappable components. Fitness functions, selection methods, and constant optimization methods allow for easy problem-specific customization. Bingo also maintains several features for increased efficiency such as parallelism, equation simplification, and a C++ backend. We compare Bingo’s performance to other genetic programming for symbolic regression (GPSR) methods to show that it is both competitive and flexible.

David Randall↗
DOE OSTI2016

Symbolic Regression with DEAP

SoRa is a tool for fitting multi-dimensional data with any kind of mathematical function. The fit is not restricted to a particular form, any mathematical function may be included in the search.

Leek, Jim↗
DOE OSTI2020

TBASS: A Robust Adaptation of Bayesian Adaptive Spline Surfaces

The R package TBASS is an extension of the BASS package created by Francom and Sansó (2019). The package is used to fit a Bayesian multivariate adaptive spline to a dataset that either follows a Student’s t-distribution or has outliers. Much of the framework for TBASS is adapted from the concepts of Bayesian Multivariate Adaptive Regression Splines (BMARS), specifically the work done by Denison, Mallick, and Smith (1998). The spline function is fit using a Reversible-Jump Markov Chain Monte Carlo algorithm,. By including this more robust generalization, a dataset with outliers can be accurately fit using the BMARS model, without the possibility of overfitting or variance inflation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Machine learning the spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called t-t'-t''-J model, where the determination of the parameter t' in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the t-t'-t''-J model using two machine-learning techniques: K-nearest neighbor regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about 1.3 x 10 5 spectral functions. Here we show that, for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing, e.g., rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density of states. Our results suggest that it may be possible to use deep-learning methods to predict materials parameters from experimentally measured spectral functions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Social support and cognitive function in Chinese older adults who experienced depressive symptoms: is there an age difference?

Objective This study examined the moderating effect of overall social support and the different types of social support on cognitive functioning in depressed older adults. We also investigated whether the moderating effect varied according to age. Methods A total of 2,500 older adults (≥60 years old) from Shanghai, China were enrolled using a multistage cluster sampling method. Weighted linear regression and multiple linear regression was utilized to analyze the moderating effect of social support on the relationship between depressive symptoms and cognitive function and to explore its differences in those aged 60–69, 70–79, and 80 years and above. Results After adjusting for covariates, the results indicated that overall social support (β = 0.091, p = 0.043) and support utilization (β = 0.213, p < 0.001) moderated the relationship between depressive symptoms and cognitive function. Support utilization reduced the possibility of the cognitive decline in depressed older adults aged 60–69 years (β = 0.310, p < 0.001) and 80 years and above (β = 0.199, p < 0.001), while objective support increased the possibility of cognitive decline in depressed older people aged 70–79 years (β = −0.189, p < 0.001). Conclusion Our findings highlight the buffering effects of support utilization on cognitive decline in depressed older adults. We suggest that age-specific measures should be taken when providing social support to depressed older adults in order to reduce the deterioration of cognitive function.

Jing, Yurong↗
DOE OSTI2022

Impact of acute temperature and air pollution exposures on adult lung function: A panel study of asthmatics

Background Individuals with respiratory conditions, such as asthma, are particularly susceptible to adverse health effects associated with higher levels of ambient air pollution and temperature. This study evaluates whether hourly levels of fine particulate matter (PM 2.5 ) and dry bulb globe temperature (DBGT) are associated with the lung function of adult participants with asthma. Methods and findings Global positioning system (GPS) location, respiratory function (measured as forced expiratory volume at 1 second (FEV 1 )), and self-reports of asthma medication usage and symptoms were collected as part of the Exposure, Location, and Lung Function (ELF) study. Hourly ambient PM 2.5 and DBGT exposures were estimated by integrating air quality and temperature public records with time-activity patterns using GPS coordinates for each participant (n = 35). The relationships between acute PM 2.5 , DBGT, rescue bronchodilator use, and lung function collected in one week periods and over two seasons (summer/winter) were analyzed by multivariate regression, using different exposure time frames. In separate models, increasing levels in PM 2.5 , but not DBGT, were associated with rescue bronchodilator use. Conversely DBGT, but not PM 2.5 , had a significant association with FEV 1 . When DBGT and PM 2.5 exposures were placed in the same model, the strongest association between cumulative PM 2.5 exposures and the use of rescue bronchodilator was identified at the 0–24 hours (OR = 1.030; 95% CI = 1.012–1.049; p-value = 0.001) and 0–48 hours (OR = 1.030; 95% CI = 1.013–1.057; p-value = 0.001) prior to lung function measure. Conversely, DBGT exposure at 0 hours (β = 3.257; SE = 0.879; p-value>0.001) and 0–6 hours (β = 2.885; SE = 0.903; p-value = 0.001) hours before a reading were associated with FEV 1 . No significant interactions between DBGT and PM 2.5 were observed for rescue bronchodilator use or FEV 1 . Conclusions Short-term increases in PM 2.5 were associated with increased rescue bronchodilator use, while DBGT was associated with higher lung function (i.e. FEV 1 ). Further studies are needed to continue to elucidate the mechanisms of acute exposure to PM 2.5 and DBGT on lung function in asthmatics.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

MABAL: a Novel Deep-Learning Architecture for Machine-Assisted Bone Age Labeling

Bone age assessment (BAA) is a commonly performed diagnostic study in pediatric radiology to assess skeletal maturity. The most commonly utilized method for assessment of BAA is the Greulich and Pyle method (Pediatr Radiol 46.9:1269–1274, 2016; Arch Dis Child 81.2:172–173, 1999) atlas. The evaluation of BAA can be a tedious and time-consuming process for the radiologist. As such, several computer-assisted detection/diagnosis (CAD) methods have been proposed for automation of BAA. Classical CAD tools have traditionally relied on hard-coded algorithmic features for BAA which suffer from a variety of drawbacks. Recently, the advent and proliferation of convolutional neural networks (CNNs) has shown promise in a variety of medical imaging applications. There have been at least two published applications of using deep learning for evaluation of bone age (Med Image Anal 36:41–51, 2017; JDI 1–5, 2017). However, current implementations are limited by a combination of both architecture design and relatively small datasets. The purpose of this study is to demonstrate the benefits of a customized neural network algorithm carefully calibrated to the evaluation of bone age utilizing a relatively large institutional dataset. In doing so, this study will aim to show that advanced architectures can be successfully trained from scratch in the medical imaging domain and can generate results that outperform any existing proposed algorithm. The training data consisted of 10,289 images of different skeletal age examinations, 8909 from the hospital Picture Archiving and Communication System at our institution and 1383 from the public Digital Hand Atlas Database. The data was separated into four cohorts, one each for male and female children above the age of 8, and one each for male and female children below the age of 10. The testing set consisted of 20 radiographs of each 1-year-age cohort from 0 to 1 years to 14–15+ years, half male and half female. The testing set included left-hand radiographs done for bone age assessment, trauma evaluation without significant findings, and skeletal surveys. A 14 hidden layer-customized neural network was designed for this study. The network included several state of the art techniques including residual-style connections, inception layers, and spatial transformer layers. Data augmentation was applied to the network inputs to prevent overfitting. A linear regression output was utilized. Mean square error was used as the network loss function and mean absolute error (MAE) was utilized as the primary performance metric. MAE accuracies on the validation and test sets for young females were 0.654 and 0.561 respectively. For older females, validation and test accuracies were 0.662 and 0.497 respectively. For young males, validation and test accuracies were 0.649 and 0.585 respectively. Finally, for older males, validation and test set accuracies were 0.581 and 0.501 respectively. The female cohorts were trained for 900 epochs each and the male cohorts were trained for 600 epochs. An eightfold cross-validation set was employed for hyperparameter tuning. Test error was obtained after training on a full data set with the selected hyperparameters. Using our proposed customized neural network architecture on our large available data, we achieved an aggregate validation and test set mean absolute errors of 0.637 and 0.536 respectively. To date, this is the best published performance on utilizing deep learning for bone age assessment. Our results support our initial hypothesis that customized, purpose-built neural networks provide improved performance over networks derived from pre-trained imaging data sets. We build on that initial work by showing that the addition of state-of-the-art techniques such as residual connections and inception architecture further improves prediction accuracy. This is important because the current assumption for use of residual and/or inception architectures is that a large pre-trained network is required for successful implementation given the relatively small datasets in medical imaging. Instead we show that a small, customized architecture incorporating advanced CNN strategies can indeed be trained from scratch, yielding significant improvements in algorithm accuracy. It should be noted that for all four cohorts, testing error outperformed validation error. One reason for this is that our ground truth for our test set was obtained by averaging two pediatric radiologist reads compared to our training data for which only a single read was used. This suggests that despite relatively noisy training data, the algorithm could successfully model the variation between observers and generate estimates that are close to the expected ground truth.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2019

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

Presently the training of neural networks relies on data of comparable accuracy but in real applications only a very small set of high-fidelity data is available while inexpensive lower fidelity data may be plentiful. We propose a new composite neural network (NN) that can be trained based on multi-fidelity data. It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data. We first demonstrate the accuracy of the new multi-fidelity NN for approximating some standard benchmark functions but also a 20-dimensional function that is not easy to approximate with other methods, e.g. Gaussian process regression. Subsequently, we extend the recently developed physics-informed neural networks (PINNs) to be trained with multi-fidelity data sets (MPINNs). MPINNs contain four fully-connected neural networks, where the first one approximates the low-fidelity data, while the second and third construct the correlation between the low- and high-fidelity data and produce the multi-fidelity approximation, which is then used in the last NN that encodes the partial differential equations (PDEs). Specifically, by decomposing the correlation into a linear and nonlinear part, the present model is capable of learning both the linear and complex nonlinear correlations between the low- and high-fidelity data adaptively. By training the MPINNs, we can: (1) obtain the correlation between the low- and high-fidelity data, (2) infer the quantities of interest based on a few scattered data, and (3) identify the unknown parameters in the PDEs. In particular, we employ the MPINNs to learn the hydraulic conductivity field for unsaturated flows as well as the reactive models for reactive transport. The results demonstrate that MPINNs can achieve relatively high accuracy based on a very small set of high-fidelity data. Despite the relatively low dimension and limited number of fidelities (two-fidelity levels) for the benchmark problems in the present study, the proposed model can be readily extended to very high-dimensional regression and classification problems involving multi-fidelity data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Prediction and uncertainty quantification of shale well performance using multifidelity Monte Carlo

Uncertainty quantification is an integral component of reservoir management, especially considering the inherent uncertainty in subsurface systems. While a standard practice to estimate the uncertainty, Monte Carlo (MC) simulation is computationally intense when the sampling population comprises high-fidelity simulations. Alternatively, the Multi-fidelity Monte Carlo (MFMC) simulation overcomes this computational intensity by integrating low- and high-fidelity simulations. Our goal is to minimize the number of expensive high-fidelity simulations while maintaining accuracy and using numerous fast and cheap low-fidelity simulations to efficiently sample to input parameter space of interest. We selected gas production from unconventional wells to demonstrate the potential speedups and accuracy of the MFMC approach. The model fidelity usually determines the trade-off between accuracy and efficiency. While the high-fidelity model is more accurate, the low-fidelity model is more efficient. Our high-fidelity simulation includes reservoir simulations of a hydraulically fractured well. On the other hand, our low-fidelity model comprises the parallel-plate flow model. We used differential programming to efficiently solve the 1D flow model, where automatic differentiation is used to efficiently compute the gradients. We matched the production profile of high-fidelity simulations with our low-fidelity simulations. Then, we used a support vector regression to map the high- and low-fidelity input parameters. The mapping function is essential to tune the low-dimensional parameter space of the low-fidelity model to the high-dimensional parameter space of the high-fidelity model. We found that we can use a combination of 9 high fidelity and 10,000 low fidelity simulations to efficiently and accurately simulate pressure management. This method is at least two orders of magnitude faster than only using high-fidelity simulations. Finally, from a broader perspective, MFMC could efficiently estimate the uncertainty of various systems and models, integrating low- and high-fidelity models.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2021

Measuring Plant Metabolite Abundance in Spearmint ( Mentha spicata L.) with Raman Spectra to Determine Optimal Harvest Time

A fast field-deployable method utilizing Raman spectroscopy to determine the optimal harvest time of plants to extract the highest abundance of target metabolites is presented. Rosmarinic acid is a metabolite extracted from spearmint (Mentha spicata L.). Leaves from commercial “Native” and proprietary clonal line “KI110” spearmint were measured as a function of cell type and age to determine rosmarinic acid abundance. A linear regression model with leave-one-out cross-validation (R 2 CV = 0.61, RMSECV = 11.1 mg/g) was developed between selected Raman peak areas and rosmarinic acid concentrations determined by high-performance liquid chromatography (HPLC). A principal component analysis (PCA) model was also developed to determine rosmarinic acid abundance. The method may be suited to the analysis of many agriculturally relevant plant species and metabolites with distinct Raman peaks.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Mathematical modelling for the drying method and smoothing drying rate using cubic spline for seaweed Kappaphycus Striatum variety Durian in a solar dryer

The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Discovery of structure–property relations for molecules via hypothesis-driven active learning over the chemical space

The discovery of the molecular candidates for application in drug targets, biomolecular systems, catalysts, photovoltaics, organic electronics, and batteries necessitates the development of machine learning algorithms capable of rapid exploration of chemical spaces targeting the desired functionalities. Here, we introduce a novel approach for active learning over the chemical spaces based on hypothesis learning. We construct the hypotheses on the possible relationships between structures and functionalities of interest based on a small subset of data followed by introducing them as (probabilistic) mean functions for the Gaussian process. This approach combines the elements from the symbolic regression methods, such as SISSO and active learning, into a single framework. The primary focus of constructing this framework is to approximate physical laws in an active learning regime toward a more robust predictive performance, as traditional evaluation on hold-out sets in machine learning does not account for out-of-distribution effects which may lead to a complete failure on unseen chemical space. Here, we demonstrate it for the QM9 dataset, but it can be applied more broadly to datasets from both domains of molecular and solid-state materials sciences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗
DOE OSTI2013

Effect of low and high storage temperatures on head space gas concentrations and physical properties of wood pellets

Headspace gas concentrations and wood pellet properties were studied in sealed glass canisters at 5–40 degrees C storage temperatures. CO2 and CO concentrations at 5, 10, 20 and 40 degrees C at the end of 23–28 days of storage were 1600 and 200, 4700 and 1200, and 31 200 and 15 800 parts per million by volume (ppmv) respectively. Corresponding O2 concentration was about 19•49, 19•20, 18•0 and 2•07% respectively. Non-linear regression equations adequately described the gas concentrations in the storage container as a function of time. Safe level estimation functions developed were linear for O2 and logarithmic for CO and CO2 concentrations. Measured pellet properties moisture, length, diameter, unit, bulk and tapped density, durability, calorific value, ash content and per cent fines were in the range of 4•6–5•02%, 14–15 mm, 6•4–6•5 mm, 1125–1175 kg m-3, 750–770 kg m-3, 825–840 kg m-3, 73–74%, 18•32–18•78 MJ kg-1, 0•65–0•74% and 0•13–0•15%. Durability values of pellets decreased by 13% at 40 degrees C storage temperature and other properties changed marginally.

09 BIOMASS FUELS↗
NASA NTRS1971

Transfer of thermal microwaves in the atmosphere, volume 1

The Mie theory is used to determine the absorption and scattering properties of liquid hydrometeors at 27 microwave frequencies from 500 MHz to 60 GHz. Based on the Marshall-Palmer distribution of drop sizes, regression equations are developed for the volume absorption coefficient of rain as a function of its temperature and content of liquid water.

Paris, J. F.↗
NASA NTRS1976

Feasibility demonstration of a variable frequency driver-microwave transient regression rate measurement system

The feasibility of a system capable of rapidly and directly measuring the low-frequency (motor characteristics length bulk mode) combustion response characteristics of solid propellants has been investigated. The system consists of a variable frequency oscillatory driver device coupled with an improved version of the JPL microwave propellant regression rate measurement system. The ratio of the normalized regression rate and pressure amplitudes and their relative phase are measured as a function of varying pressure level and frequency. Test results with a well-characterized PBAN-AP propellant formulation were found to compare favorably with the results of more conventional stability measurement techniques.

Strand, L. D.↗
NASA NTRS2002

Optical properties of intact leaves for estimating chlorophyll concentration

Changes in leaf chlorophyll content can serve as relative indicators of plant vigor and environmental quality. This study identified reflectance, transmittance, and absorptance wavebands and band ratios within the 400- to 850-nm range for intact leaves that could be used to estimate extracted leaf chlorophyll per unit leaf area (areal concentration) with minimal error. Leaf optical properties along with chlorophyll a, b, and a + b concentrations were measured for the planar-leaved sweetgum (Liquidambar styraciflua L.), red maple (Acer rubrum L.), wild grape (Vitis rotundifolia Michx.), and switchcane [Arundinaria gigantea (Walter) Muhl.], and for needles of longleaf pine (Pinus palustris Miller). Generally, reflectance, transmittance, and absorptance corresponded most precisely with chlorophyll concentrations at wavelengths near 700 nm, although regressions were also strong in the 550- to 625-nm range. A power function was superior to a simple linear function in yielding low standard deviations of the estimate (s). When data were combined among the planar-leaved species, s values were low at approximately 50 mumol/m2 out of a 940 mumol/m2 range in chlorophyll a + b at best-fit wavelengths of 707 to 709 nm. Minimal s values for chlorophyll a + b ranged from 32 to 62 mumol/m2 across species when band ratios having numerator wavelengths of 693 to 720 nm were used with the application of a power function. Optimal denominator wavelengths for the band ratios were 850 nm for reflectance and transmittance and 400 nm for absorptance. This information can be applied in designing field portable chlorophyll meters and in the landscape-scale remote sensing of plant responses to the environment.

Chlorophyll/analysis↗
NASA NTRS2016

Lidar-Based Estimates of Above-Ground Biomass in the Continental US and Mexico Using Ground, Airborne, and Satellite Observations

Existing national forest inventory plots, an airborne lidar scanning (ALS) system, and a space profiling lidar system (ICESat-GLAS) are used to generate circa 2005 estimates of total aboveground dry biomass (AGB) in forest strata, by state, in the continental United States (CONUS) and Mexico. The airborne lidar is used to link ground observations of AGB to space lidar measurements. Two sets of models are generated, the first relating ground estimates of AGB to airborne laser scanning (ALS) measurements and the second set relating ALS estimates of AGB (generated using the first model set) to GLAS measurements. GLAS then, is used as a sampling tool within a hybrid estimation framework to generate stratum-, state-, and national-level AGB estimates. A two-phase variance estimator is employed to quantify GLAS sampling variability and, additively, ALS-GLAS model variability in this current, three-phase (ground-ALS-space lidar) study. The model variance component characterizes the variability of the regression coefficients used to predict ALS-based estimates of biomass as a function of GLAS measurements. Three different types of predictive models are considered in CONUS to determine which produced biomass totals closest to ground-based national forest inventory estimates - (1) linear (LIN), (2) linear-no-intercept (LNI), and (3) log-linear. For CONUS at the national level, the GLAS LNI model estimate (23.95 +/- 0.45 Gt AGB), agreed most closely with the US national forest inventory ground estimate, 24.17 +/- 0.06 Gt, i.e., within 1%. The national biomass total based on linear ground-ALS and ALS-GLAS models (25.87 +/- 0.49 Gt) overestimated the national ground-based estimate by 7.5%. The comparable log-linear model result (63.29 +/-1.36 Gt) overestimated ground results by 261%. All three national biomass GLAS estimates, LIN, LNI, and log-linear, are based on 241,718 pulses collected on 230 orbits. The US national forest inventory (ground) estimates are based on 119,414 ground plots. At the US state level, the average absolute value of the deviation of LNI GLAS estimates from the comparable ground estimate of total biomass was 18.8% (range: Oregon,−40.8% to North Dakota, 128.6%). Log-linear models produced gross overestimates in the continental US, i.e., N2.6x, and the use of this model to predict regional biomass using GLAS data in temperate, western hemisphere forests is not appropriate. The best model form, LNI, is used to produce biomass estimates in Mexico. The average biomass density in Mexican forests is 53.10 +/- 0.88 t/ha, and the total biomass for the country, given a total forest area of 688,096 sq km, is 3.65 +/- 0.06 Gt. In Mexico, our GLAS biomass total underestimated a 2005 FAO estimate (4.152 Gt) by 12% and overestimated a 2007/8 radar study's figure (3.06 Gt) by 19%.

Hybrid 3-Phase sampling↗