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DOE OSTI2024

Advanced Cross Section Library Generation using Reduced Order Models

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which consist of databases of tabulated values, used to calculate the neutron cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of microscopic cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. In order to address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multigroup cross section data across isotopes, reaction types, and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs have been trained for all isotopes in this work and systematic Griffin testing is ongoing to ensure the feasibility of this ROM technique for predicting cross section and reducing memory requirements without a significant sacrifice in computational performance.

42 - ENGINEERING↗

DOE OSTI2024

Reduce-Order Modeling of Multigroup Neutron Cross Sections for High-Temperature Gas-cooled Reactors

Deterministic neutronics calculations rely on multigroup neutron cross section libraries, which usually consists of a database of tabulated values, used to calculate the cross sections through multivariate linear interpolation. However, interpolation of the multidimensional cross section data becomes memory inefficient and time consuming as the number of tabulations increases, significantly slowing down the neutronics calculation, especially in the case of micro cross section libraries where every isotope (on the order of hundreds) has its own set of specific reactions and cross sections. To address this challenge, this work constructs efficient and robust reduced-order models (ROMs) of the multi-group cross sections to support the Griffin simulation of high-temperature gas-cooled reactors (HTGRs). The first part of the study investigates the linearity of the multi-group cross section data across isotopes, reaction types and energy groups on pre-generated datasets for the purpose of dimensionality reduction. Secondly, a down-selection of ROM techniques is presented on representative classical machine learning (ML) techniques, including variants of linear regression, kernel-based methods, tree-based algorithms, and artificial neural networks. The selection criteria jointly consider the memory efficiency, predictive accuracy, prediction speed, and scalability in comparison to the multidimensional interpolation. Among all the ML techniques, deep neural networks (DNNs) have proven to be the best selection with sufficient accuracy, high robustness, good memory efficiency, great scalability, and superior flexibility. DNNs for have been trained for all isotopes in this work and systematic Griffin testing is ongoing at this moment to ensure the feasibility of this ROM technique for cross section predictions.

42 - ENGINEERING↗

DOE OSTI2024

Using an Isotope Enabled Mass Balance to Evaluate Existing Land Surface Models

Abstract Land surface models (LSMs) play a crucial role in elucidating water and carbon cycles by simulating processes such as plant transpiration and evaporation from bare soil, yet calibration often relies on comparing LSM outputs of landscape total evapotranspiration ( ET ) and discharge with measured bulk fluxes. Discrepancies in partitioning into component fluxes predicted by various LSMs have been noted, prompting the need for improved evaluation methods. Stable water isotopes serve as effective tracers of component hydrologic fluxes, but data and model integration challenges have hindered their widespread application. Leveraging National Ecological Observation Network measurements of water isotope ratios at 16 US sites over 3 years combined with LSM‐modeled fluxes, we employed an isotope‐enabled mass balance framework to simulate ET isotope values ( δET ) within three operational LSMs (Mosaic, Noah, and VIC) to evaluate their partitioning. Models simulating δET values consistent with observations were deemed more reflective of water cycling in these ecosystems. Mosaic exhibited the best overall performance (Kling‐Gupta Efficiency of 0.28). For both Mosaic and Noah there were robust correlations between bare soil evaporation fraction and error (negative) as well as transpiration fraction and error (positive). We found the point at which errors are smallest ( x ‐intercept of the multi‐site regression) is at a higher transpiration fraction than is currently specified in the models. Which means that transpiration fraction is underestimated on average. Stable isotope tracers offer an additional tool for model evaluation and identifying areas for improvement, potentially enhancing LSM simulations and our understanding of land‐surface hydrologic processes.

58 GEOSCIENCES↗

NASA NTRS2007

[Space Weather Impact on the Electricity Market]

Forbes & St. Cyr (2004, hereafter "FISC") have provided evidence that the electricity market can be impacted by space weather. Our analysis indicated that the estimated market impact for PJM was 3.7 % or approximately $500 million dollars over the 19 month sample period. Kappenman has taken exception to this estimate and contends that we have exaggerated the magnitude of the problem that space weather poses to PJM. There are four specific issues: (1) he claims that we have ignored relevant literature; (2) he asserts that Dst is not an appropriate proxy for GICs in PJM; (3) he charges that our findings are inconsistent with the impact of the 17 September 2000 storm; and (4) he alleges that our discussion of October 2003 storms is misleading. In our article, we have explained our methodology, multivariate regression analysis, with a particular focus on how it compares to correlation analysis. We have also explained the limitations of our analysis. We noted that "...While the Dstlprice relationship was found to be robust, the precise estimate should be treated with a relatively high degree of caution given that econometric modeling is not an exact science as well as the fact that the measure of space weather may be a poor proxy for GICs" (paragraph 96). We have also noted that additional research using local magnetometer data are needed (paragraph 97). We did not claim that that our findings for PJM are representative of the impact of space weather on other power grids. On the contrary, we noted that ... "Only analysis of other power grids will tell. " (paragraph 97). Kappenman inaccurately asserts that we have indicated that our findings . . . "imply much higher total costs are likely across the US and elsewhere in the world." He also inaccurately asserts that we have claimed that " . . . Dst is the most suited proxy for GIC in the PJM grid.. ." Moreover, he inaccurately refers to our analysis as a correlation study that uses Dst as quasi-binary indicator.

SaintCyr, O. Chris↗

NASA NTRSDate not supplied

Evaluation of Correction Methods for NASA GeneLab Transcriptomic Datasets

Conducting space biology experiments aboard the International Space Station, particularly those utilizing complex model organisms like mice, is expensive and difficult due to limited crew availability, hardware, and space. As a result, sample numbers from these studies are low, reducing the statistical power of any one experiment. Aggregating spaceflight datasets serves as a method to increase sample numbers, allowing for novel insights through bioinformatic analysis of ‘omics data from merged datasets. However, aggregating datasets can introduce unwanted variation including 1) differences in sample handling, processing, and sequencing platforms between datasets (technical variation) as well as 2) differences in experimental design between datasets such as sex or age of the model organism used. In the present study, NASA GeneLab-hosted RNAseq datasets from rodent liver tissues were used to evaluate several statistical methods to correct for this unwanted variation through two approaches, reference-based and standard. The following correction algorithms were applied with (reference-based) and/or without (standard) considering Universal Mouse RNA Reference samples: ComBat and ComBat_seq from the SVA package, median polish, empirical Bayes, and ANOVA-based algorithms from the MBatch package, and negative binomial regression normalization in the DESeq2 package. For each approach, after the correction algorithm was applied, differential gene expression (DGE) analysis of flight and ground control samples was performed with the combined data. The robustness of each tool was evaluated using BatchQC, to determine statistical differences between datasets before and after correction, Principal Component Analysis, to evaluate global gene expression in samples before and after correction, and by comparing DGE analysis of individual datasets and combined datasets before and after correction. The results showed that the reference-based approach introduced several additional (and likely artificial) DEGs when compared with the standard approach. Thus, the most robust standard correction will be implemented in the GeneLab Visualization 2.0 platform when datasets are combined.

GeneLab, RNA-seq, Batch Correction↗

NASA NTRSDate not supplied

Evaluation of Correction Methods for NASA GeneLab Transcriptomic Datasets

Conducting space biology experiments aboard the International Space Station, particularly those utilizing complex model organisms like mice, is expensive and difficult due to limited crew availability, hardware, and space. As a result, sample numbers from these studies are low, reducing the statistical power of any one experiment. Aggregating spaceflight datasets serves as a method to increase sample numbers, allowing for novel insights through bioinformatic analysis of ‘omics data from merged datasets. However, aggregating datasets can introduce unwanted variation including 1) differences in sample handling, processing, and sequencing platforms between datasets (technical variation) as well as 2) differences in experimental design between datasets. In the present study, NASA GeneLab-hosted RNAseq datasets from mouse liver tissues were used to evaluate several statistical methods to correct for this unwanted variation through two approaches, reference-based and standard. The following correction algorithms were applied with (reference-based) and/or without (standard) considering Universal Mouse RNA Reference samples: ComBat and ComBat_seq from the SVA package, median polish, empirical Bayes, and ANOVA-based algorithms from the MBatch package, and negative binomial regression normalization in the DESeq2 package. For each approach, after the correction algorithm was applied, differential gene expression (DGE) analysis of flight and ground control samples was performed with the combined data. The robustness of each tool was evaluated using BatchQC to determine statistical differences between datasets before and after correction, Principal Component Analysis to evaluate global gene expression in samples before and after correction, and by comparing DGE analysis of individual datasets and combined datasets before and after correction. The results showed that the reference-based approach introduced several additional (and likely artificial) DEGs when compared with the respective standard approach. Of the methods tested, standard ComBat and DESeq2 were identified as the most robust correction methods for combining spaceflight mouse liver RNAseq datasets hosted on GeneLab.

GeneLab↗

NASA NTRSDate not supplied

Combining RNA-SEQ Datasets from NASA GENELAB: An Evaluation of Correction Methods

Background: Conducting space biology experiments aboard the International Space Station, particularly those utilizing complex model organisms like mice, is expensive and difficult due to limited crew availability, hardware, and space. As a result, sample numbers from these studies are low, reducing the statistical power of any one experiment. Aggregating spaceflight datasets serves as a method to increase sample numbers, allowing for novel insights through bioinformatic analysis of ‘omics data from merged datasets. However, aggregating datasets can introduce unwanted variation including 1) differences in sample handling, processing, and sequencing platforms between datasets (technical variation) as well as 2) differences in experimental design between datasets. Methods: In the present study, NASA GeneLab-hosted RNAseq datasets from mouse liver tissues were used to evaluate several statistical methods to correct for this unwanted variation through two approaches, reference-based and standard. The following correction algorithms were applied with (reference-based) and/or without (standard) considering Universal Mouse RNA Reference samples: ComBat and ComBat_seq from the SVA package, the median polish, empirical Bayes, and ANOVA-based algorithms from the MBatch package, and negative binomial regression normalization in the DESeq2 package. For each approach, after the correction algorithm was applied, differential gene expression (DGE) analysis of flight and ground control samples was performed with the combined data. The robustness of each tool was evaluated using BatchQC to determine statistical differences between datasets before and after correction, Principal Component Analysis to evaluate global gene expression in samples before and after correction, and by comparing DGE analysis of individual datasets and combined datasets before and after correction. Results: The results showed that the reference-based approach introduced several additional (and likely artificial) differentially expressed genes when compared with the respective standard approach. Conclusions: Of the methods tested, standard ComBat_seq and DESeq2 were identified as the most robust correction methods for combining spaceflight mouse liver RNAseq datasets hosted on GeneLab.

Finsam Samson↗

NASA NTRS1990

Framework for a space shuttle main engine health monitoring system

A framework developed for a health management system (HMS) which is directed at improving the safety of operation of the Space Shuttle Main Engine (SSME) is summarized. An emphasis was placed on near term technology through requirements to use existing SSME instrumentation and to demonstrate the HMS during SSME ground tests within five years. The HMS framework was developed through an analysis of SSME failure modes, fault detection algorithms, sensor technologies, and hardware architectures. A key feature of the HMS framework design is that a clear path from the ground test system to a flight HMS was maintained. Fault detection techniques based on time series, nonlinear regression, and clustering algorithms were developed and demonstrated on data from SSME ground test failures. The fault detection algorithms exhibited 100 percent detection of faults, had an extremely low false alarm rate, and were robust to sensor loss. These algorithms were incorporated into a hierarchical decision making strategy for overall assessment of SSME health. A preliminary design for a hardware architecture capable of supporting real time operation of the HMS functions was developed. Utilizing modular, commercial off-the-shelf components produced a reliable low cost design with the flexibility to incorporate advances in algorithm and sensor technology as they become available.

Hawman, Michael W.↗

NASA NTRS2022

Evaluating Approaches Relating Ecosystem Productivity with Desis Spectral Information

Data from the DLR Earth Sensing Imaging Spectrometer (DESIS), mounted on the International Space Station (ISS), were used to develop and test algorithms for remotely retrieving ecosystem productivity. Twenty DESIS images were used from three widely separated forested study sites representing deciduous and conifer forests. Gross primary production (GPP) values from eddy covariance flux towers at the sites were matched with DESIS spectral reflectances collected on the same days. Multiple algorithms were successful relating spectral reflectance with GPP, including: spectral vegetation indices (SVI) sensitive to chlorophyll content, SVI used in a photosynthetic light-use efficiency model framework, spectral shape characteristics through spectral derivatives and absorption feature analysis, and statistical models leading to multiband hyperspectral indices from partial least squares regression. Successful algorithms were able to achieve R2 better than 0.7 using a diverse set of observations combining data from different sites from multiple years and at multiple times during the year. The demonstrated robustness of the algorithms provides some confidence in using DESIS imagery to map spatial patterns of GPP.

K F Huemmrich↗

NASA NTRS2022

Evaluating Approaches Relating Ecosystem Productivity with DESIS Spectral Information

Gross Primary Productivity (GPP)↗

NASA NTRS1988

Angle of attack estimation using an inertial reference platform

This paper presents the mathematical development and flight test results of an angle of attack estimation system based on inertial navigation system inputs. The estimator uses these inputs to determine the coefficient of lift required at any instant inflight. Angle of attack is then modeled through a regression analysis based on coefficient of lift, altitude and Mach. Overall correlation of the estimator as tested was generally within 0.5 degrees through 17 degrees angle of attack on an F-15A aircraft. A robustness analysis indicates that the system can be used adequately in maneuvering flight.

Zeis, Joseph E., Jr.↗

NASA NTRS2002

Comparison of Total Solar Irradiance with NASA/NSO Spectromagnetograph Data in Solar Cycles 22 and 23

An earlier study compared NASA/NSO Spectromagnetograph (SPM) data with spacecraft measurements of total solar irradiance (TSI) variations over a 1.5 year period in the declining phase of solar cycle 22. This paper extends the analysis to an eight-year period which also spans the rising and early maximum phases of cycle 23. The conclusions of the earlier work appear to be robust: three factors (sunspots, strong unipolar regions, and strong mixed polarity regions) describe most of the variation in the SPM record, but only the first two are associated with TSI. Additionally, the residuals of a linear multiple regression of TSI against SPM observations over the entire eight-year period show an unexplained, increasing, linear time variation with a rate of about 0.05 W m(exp -2) per year. Separate regressions for the periods before and after 1996 January 01 show no unexplained trends but differ substantially in regression parameters. This behavior may reflect a solar source of TSI variations beyond sunspots and faculae but more plausibly results from uncompensated non-solar effects in one or both of the TSI and SPM data sets.

Jones, Harrison P.↗

NASA NTRSDate not supplied

Statistical Classification of Biosignature Information using Multiple Instrument Observations

The accurate identification of biosignatures (indications of life) from data taken from remote or in situ planetary exploration is one of the most important challenges in astrobiology, the interdisciplinary field examining habitability and the potential for extraterrestrial life. This study employs machine learning algorithms to optimize the identification of biosignatures, with an emphasis on those which are agnostic to a specific biochemical basis. We exploit the wealth of terrestrial data available from biogenic and abiogenic systems to enhance efficient feature prioritization. Our dataset, pulled from public databases and laboratory recorded measurements, includes elemental abundance, isotopic fractionation, and VNIR/Raman spectra The data curation process included standardization for detection limits and ranges. Subsequent feature extraction yielded detailed inputs for machine learning, including combinations of elemental content, isotopic ratios, and parameters of spectral peaks and troughs. Feature significance was evaluated across diverse machine learning methodologies, such as k-nearest neighbors, logistic regression, Random Forest, support vector machines, and Gaussian Naïve Bayes, along with a combined voting classifier. We utilized Receiver Operating Characteristic Area Under the Curve (ROC AUC) across 2,000 50% test-train splits as a robust metric of model performance. Results revealed a promising ROC AUC of 0.853 for the combined voting classifier. Removing elemental abundance data notably reduced model accuracy (13% decrease in AUC), highlighting its critical role in biosignature detection. Several other individual data features exhibited significance within their respective data types, offering additional granularity. This research fortifies the relevance of machine learning to astrobiology, potentially enhancing life detection missions by allowing algorithmic prioritization of high-interest samples for further investigation. Future work will refine data standardization, expand the dataset to include more terrestrial systems, and incorporate convolutional neural networks for spectral feature extraction. The potential for public data sharing is also under exploration, reinforcing our commitment to collective scientific advancement.

Statistical↗

NASA NTRS2013

Integrating Solar Induced Fluorescence and the Photochemical Reflectance Index for Estimating Gross Primary Production in a Cornfield

The utilization of remotely sensed observations for light use efficiency (LUE) and tower-based gross primary production (GPP) estimates was studied in a USDA cornfield. Nadir hyperspectral reflectance measurements were acquired at canopy level during a collaborative field campaign conducted in four growing seasons. The Photochemical Reflectance Index (PRI) and solar induced chlorophyll fluorescence (SIF), were derived. SIF retrievals were accomplished in the two telluric atmospheric oxygen absorption features centered at 688 nm (O2-B) and 760 nm (O2-A). The PRI and SIF were examined in conjunction with GPP and LUE determined by flux tower-based measurements. All of these fluxes, environmental variables, and the PRI and SIF exhibited diurnal as well as day-to-day dynamics across the four growing seasons. Consistent with previous studies, the PRI was shown to be related to LUE (r2 = 0.54 with a logarithm fit), but the relationship varied each year. By combining the PRI and SIF in a linear regression model, stronger performances for GPP estimation were obtained. The strongest relationship (r2 = 0.80, RMSE = 0.186 mg CO2/m2/s) was achieved when using the PRI and SIF retrievals at 688 nm. Cross-validation approaches were utilized to demonstrate the robustness and consistency of the performance. This study highlights a GPP retrieval method based entirely on hyperspectral remote sensing observations.

cornfield↗

NASA NTRS1990

Health monitoring system for the SSME - Program overview

This paper considers the design of a health management system (HMS) program for enhancement of the safety of SSME operations during ground tests and space missions. The fault detection techniques based on time series, nonlinear regression, and clustering algorithms were developed and were demonstrated based on data from SSME ground test failures. The fault detection algorithms of the HMS system exhibited 100 percent detection of faults and an extremely low fault alarm rate, and were robust to sensor loss. A preliminary design of hardware architecture capable of supporting real-time operation of the HMS functions is described.

Hawman, Michael W.↗

NASA NTRSDate not supplied

Towards an Aviation Large Language Model by Fine-tuning and Evaluating Transformers

In the aviation domain, there are many applications for machine learning and artificial intelligence tools that utilize natural language. For example, there is a desire to know the commonalities in written safety reports such as voluntary post incidents reports or aerial wildfire operations reports to better understand the risks present. Another use-case is the possibility of extracting airspace procedures and constraints currently written in documents such as Letters of Agreement. These applications can benefit from the use of state-of-the-art natural language processing techniques when adapted to the language/phraseology specific to the aviation domain. This paper evaluates the viability of adaptation of NLP tools to the aviation domain by fine-tuning transformer based models using aviation data sets. In 2018, a novel language model based on neural units (also called transformers) was created and became known as “Bidirectional Encoder Representations from Transformers” or BERT. This architecture combined with large amounts of English training data and innovative semi-supervised training tasks set the standard for what would later emerge as Large Language Models. The performance of these models was further improved by hyperparameter tuning and refinement of the semi-supervised training task and resulted in “Robustly Optimized BERT Pre-training Approach through hyperparameter tuning” or RoBERTa models. These pre-trained Large Language Models proved to be useful for a wide variety of natural language processing tasks such as text classification and question answering through a process called fine-tuning. The transformer architecture with pre-trained weights served as the basis with the last few layers replaced with layers fine-tuned to perform a new task e.g., a layer that provides a label for the entire input text. This process of fine-tuning can also be used to adapt the models to new domains; e.g., BioBERT started with the pre-trained BERT model and was completed by additional fine-tuning and training on biomedical documents. Transformer-based architectures can also be used to create rich representations of text called embeddings which can serve as the input to other machine learning models. This allows simpler algorithms such as logistic regression to use context-rich representations of the text while still remaining quick to train and evaluate. In the world of aviation, there is a growing demand for natural language processing and understanding but the domain presents unique challenges. Due to the technical content (and specialized language) of most aviation documents, fine-tuning pre-trained Large Language Models to specific tasks has not met the benchmark on natural language processing tasks set by simpler models trained from scratch on the data. To address this deficiency, this paper evaluates the improvements from fine-tuning a Large Language Model on a large set of aviation documents using the original semi-supervised training tasks before performing specific natural language tasks. In fine-tuning, a domain-specific dataset is used on the original training task but with the pre-trained Large Language Model instead of starting from a random initialization. This approach allows the model to be adapted to the specific domain language without discarding the information gained from training on general English data. This paper utilized two major dataset types to train and assess the RoBERTa fine-tuning performance. The first are 7,057 Letters of Agreement which are Federal Aviation Administration (FAA) documents that formalize airspace operations across the national airspace system. They contain many examples of ‘aviation English’ using domain specific terminology and phrasing which serves as a representative basis to perform the semi-supervised fine-tuning. The second type is the 494 document classification labels to be used for evaluation. This down-stream evaluation aims to show the performance of the fine-tuned model, better understand how much data is needed for an effective fine-tuning, and how fine-tuning can be adapted for different applications in-the domain. After semi-supervised training, evaluation begins by encoding the documents for classification using the fine-tuned RoBERTa model. Then a logistic regression classifier is trained to label the document type and compared against our ground truth labels. This currently leads to a 82.8% accuracy on 10-fold cross validation showing improvement over baseline RoBERTa which achieved 81.0%. We plan to measure the improvements on additional tasks and it is expected that these improvements will lead to more robust models that can tackle the natural language processing challenges present in aviation datasets.

ATM↗

DOE OSTI2025

Deep learning model for fast, science-based forecasting of fluid migration along faults in geologic carbon storage scenarios

Effective long-term geologic storage depends on robust site selection and credible, science-based forecasting of subsurface behavior to ensure storage integrity. For this work, we develop a deep learning–based reduced-order model (ROM) to quantify potential carbon dioxide (CO₂) and brine migration through geological faults. The ROM combines a Transformer model for binary classification and a Stacked Ensemble for regression, trained on a comprehensive dataset generated from 1400 physics-based reservoir simulations. Key geologic and operational parameters—including fault geometry, reservoir structure, and injection conditions—were systematically varied to capture a wide range of fluid migration scenarios. The ROM accurately predicts the onset of migration, cumulative migration volumes of both CO₂ and brine, and associated migration rates, as compared to an independent set of validation simulations, while significantly reducing computational cost compared to traditional simulation methods. Model performance was evaluated across diverse fault configurations, revealing that shallow reservoir geometry and fault angle are among the most influential factors governing migration behavior. Sensitivity analysis using SHapley Additive exPlanations (SHAP) provided interpretability, revealing distinct patterns in how geological and operational features drive transient versus cumulative migration outcomes. The ROM’s ability to rapidly simulate fault migration scenarios enables efficient sensitivity analyses, scenario evaluations, and decision support for site selection and monitoring design. This approach enhances the safety, scalability, and long-term operational performance of geologic carbon storage (GCS) systems by providing a robust, interpretable tool for predicting subsurface fluid migration and assessing fault-related migration potential.

42 ENGINEERING↗

NASA NTRSDate not supplied

Bayesian Model Selection for Reducing Bloat and Overfitting in Genetic Programming for Symbolic Regression

When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.

Uncertainty quantification↗