The Bias–Variance–Correlation tradeoff and its Implications for ML in science
A discussion of the phenomenon of bias-variance-correlation tradeoff in machine learning.
SEARCH · Search NASA
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.
A discussion of the phenomenon of bias-variance-correlation tradeoff in machine learning.
This paper is a discussion of machine learning theory on empirically learning classification rules. The paper proposes six myths in the machine learning community that address issues of bias, learning as search, computational learning theory, Occam's razor, 'universal' learning algorithms, and interactive learnings. Some of the problems raised are also addressed from a Bayesian perspective. The paper concludes by suggesting questions that machine learning researchers should be addressing both theoretically and experimentally.
The bias-variance tradeoff is a well-recognized phenomenon in statistics and machine learning. In this talk, I will discuss an extension, dubbed the bias-variance-correlation tradeoff. Roughly speaking, as the flexibility of a model decreases, the correlations in the outputs of a trained model for different inputs increases. Such correlations have implications for several applications of machine learning in high energy physics, e.g., the use generative models for event generation. In particular, I will argue that claims in the literature of data amplification by generative models stem from ignoring important correlations between the model's outputs for different inputs.
Parameterizations in Earth System Models (ESMs) are subject to biases and uncertainties arising from subjective empirical assumptions and incomplete understanding of the underlying physical processes. Recently, the growing representational capability of machine learning (ML) in solving complex problems has spawned immense interests in climate science applications. Specifically, ML-based parameterizations have been developed to represent convection, radiation and microphysics processes in ESMs by learning from observations or high-resolution simulations, which have the potential to improve the accuracies and alleviate the uncertainties. Previous works have developed some surrogate models for these processes using ML. These surrogate models need to be coupled with the dynamical core of ESMs to investigate the effectiveness and their performance in a coupled system. In this study, we present a novel Fortran-Python interface designed to seamlessly integrate ML parameterizations into ESMs. This interface showcases high versatility by supporting popular ML frameworks like PyTorch, TensorFlow, and Scikit-learn. We demonstrate the interface's modularity and reusability through two cases: a ML trigger function for convection parameterization and a ML wildfire model. We conduct a comprehensive evaluation of memory usage and computational overhead resulting from the integration of Python codes into the Fortran ESMs. By leveraging this flexible interface, ML parameterizations can be effectively developed, tested, and integrated into ESMs.
Sulfur dioxide (SO2) is a criteria air pollutant due to its contributions to aerosol formation, rainfall acidification, and harm to human health. The placement of air quality monitoring sites is typically biased towards urban areas, leaving large areas with very limited monitoring data. The Ozone Monitoring Instrument (OMI) has been used to provide estimates of SO2 vertical column densities (VCDs) globally at spatial resolution of 10s of kms once per day. OMI SO2 VCDs have been previously used to estimate surface SO2 concentrations using chemical transport model (CTM) simulations. The CTMs use estimated emissions and assimilated meteorological data, and simulate the chemical and physical processes that determine the vertical profile of SO2, which can be used to derive a ratio between the surface concentrations and VCDs. These models are complex, computationally expensive, and have large uncertainties in the simulated surface-to-VCD ratio due to biases in emissions and relatively coarse resolution. Machine learning techniques are comparatively easier to use, much less computationally expensive to use after training, and can produce more accurate estimations of surface concentrations than the CTM-based method. The interpretation of machine learning models often poses challenges, and in some cases, non-physical variables unrelated to SO2 are used as predictors. In this work, we create an artificial neural network (ANN) to relate OMI retrievals and archived GEOS-FP boundary layer heights to surface SO2 concentrations from the ChinaHighAirPollutants ChinaHighSO2 dataset (CHAP; Wei et al., 2023) on a seasonal average timescale from 2013-2018. Our model only utilizes five variables that are directly relevant to the satellite retrieval, lifetime, and spatial distribution of SO2. The model was trained on 16 seasons (four of each) with independent validation (one of each season) and testing datasets (one of each season) to avoid overfitting. Our ANN generates surface SO2 concentrations that are sensitive (slope = 0.51) and consistent (r = 0.74) with the CHAP data, but are underpredicted by an average of 1.2 ppbv with a mean absolute error of 2.2 ppbv. These results are better than recent studies utilizing the CTM method. To our knowledge, this is the best performing machine learning model that only uses physical variables to predict surface SO2. Our work demonstrates that a carefully constructed, simple ML model can accurately estimate surface-based SO2 concentrations from satellite VCD measurements, and this technique has future promise to expend to newer, higher resolution satellites and other air pollutants.
Abstract. Parameterizations in earth system models (ESMs) are subject to biases and uncertainties arising from subjective empirical assumptions and incomplete understanding of the underlying physical processes. Recently, the growing representational capability of machine learning (ML) in solving complex problems has spawned immense interests in climate science applications. Specifically, ML-based parameterizations have been developed to represent convection, radiation, and microphysics processes in ESMs by learning from observations or high-resolution simulations, which have the potential to improve the accuracies and alleviate the uncertainties. Previous works have developed some surrogate models for these processes using ML. These surrogate models need to be coupled with the dynamical core of ESMs to investigate the effectiveness and their performance in a coupled system. In this study, we present a novel Fortran–Python interface designed to seamlessly integrate ML parameterizations into ESMs. This interface showcases high versatility by supporting popular ML frameworks like PyTorch, TensorFlow, and scikit-learn. We demonstrate the interface's modularity and reusability through two cases: an ML trigger function for convection parameterization and an ML wildfire model. We conduct a comprehensive evaluation of memory usage and computational overhead resulting from the integration of Python codes into the Fortran ESMs. By leveraging this flexible interface, ML parameterizations can be effectively developed, tested, and integrated into ESMs.
Constructing a chemically diverse dataset while avoiding sampling bias is critical to training efficient and generalizable force fields. However, in computational chemistry and materials science, many common dataset generation techniques are prone to oversampling regions of the potential energy surface. Furthermore, these regions can be difficult to identify and isolate from each other or may not align well with human intuition, making it challenging to systematically remove bias in the dataset. While traditional clustering and pruning (down-sampling) approaches can be useful for this, they can often lead to information loss or a failure to properly identify distinct regions of the potential energy surface due to difficulties associated with the high dimensionality of atomic descriptors. In this work, we introduce the Multi-kernel Edge Attention-based Graph Autoencoder (MEAGraph) model, an unsupervised approach for analyzing atomic datasets. MEAGraph combines multiple linear kernel transformations with attention-based message passing to capture geometric sensitivity and enable effective dataset pruning without relying on labels or extensive training. Demonstrated applications on niobium, tantalum, and iron datasets show that MEAGraph efficiently groups similar atomic environments, allowing for the use of basic pruning techniques for removing sampling bias. This approach provides an effective method for representation learning and clustering that can be used for data analysis, outlier detection, and dataset optimization.
The AIACHNE (AI/ML Informed cAlifornium CHi Nuclear data Experiment) project aims at designing an experiment for the 252 Cf Prompt Fission Neutron Spectrum (PFNS) that explores systematic biases in an experimental database retrieved from the EXFOR databases. To that end, machine learning (ML) methods were applied to pint-point measurement features likely related to bia. From that information, we selected a feature that should be explored by the AIACHNE experiment. Measurement features are metadata encapsulating all pertinent information about the physical measurement and analysis techniques. Examples are, for instance, what neutron and fission detectors were used for the physical metadata, and what background reduction techniques were employed for analysis techniques. Such metadata were retrieved both from EXFOR entries as well as the literature of data sets described in detail in Ref. [2]. The prerequisite for applying machine learning techniques is casting the metadata into a format that can be parsed by the algorithm. This step might seem trivial but requires to find a unique language where metadata that carry the same physics meaning across several experiments must have the same identifier. One example is, for instance, the neutron detector. As seen in Figure 1, the machine learning code identified the use of 6 Li detectors as being related to bias in some datasets of the AIACHNE 252 Cf PFNS experimental database. In fact, here are several experiments that used neutron detectors containing 6Li in the database, for instance for the example below. EXFOR format has a unique keywords describing detectors such as “SCIN” or “GLASD”. One may think that these keywords are already sufficient descriptors for ML to uniquely find an issue. However, “SCIN” (used for [3, 4]) and “GLASD” (used for [5]) fail to inform the algorithm what is the active material in the detector. And, the key common issue leading to bias in 252 Cf related to neutron detectors is not whether it is a glass detector or a scintillator. No, the issue is that 6 Li was within both detector types and that even small mistakes in the detector response functions around approximately 200 keV are amplified by the 6 Li(n,α) resonance there leading to bias in data as highlighted in Fig. 1 and Ref. [1]. Hence, the features describing the neutron detector must call out the active material in the detector, rather than the existing EXFOR detector keyword, that the ML algorithm can find physically meaningful features related to bias. The AIACHNE team used a precursor of the WPEC (Working Party on International Nuclear Data Evaluation Co-operation) SG(Subgroup)-50 format to store the metadata for the ML analysis.
NASA's highly successful Kepler Mission has revolutionized our understanding of the Galaxy. We now know that planets, even Earth-size planets in the habitable zone, are common. With the end of the Kepler Mission we now look to the future with the Transiting Exoplanet Survey Satellite (TESS) which will discover thousands of exoplanets in orbit around the brightest stars in the sky. In a two-year survey, TESS will perform an all-sky search of more than 200,000 stars for temporary drops in brightness caused by planetary transits. With Kepler and TESS, humanity is finally at the verge of studying the masses, sizes, densities, orbits, and atmospheres of a large cohort of small planets, including a sample of rocky worlds in the habitable zones of their host stars which may prove to host life. The massive data sets generated by Kepler and TESS must be meticulously combed for the weakest planetary signals every month. While a daunting and error-prone task for humans, this is an exciting opportunity for the breakthroughs recently seen in machine learning. Specifically, traditional methods for identifying planet transits require extensive data processing pipelines followed by extensive human vetting. This manual process risks loss of information due to the data processing and to inconsistency and biases due to individual human vetters. The latest advancements in machine learning will allow an objective classifier to minimize the losses of information and greatly lessen the burden on the human vetters, in addition to providing assessment of quality and score to each planet candidate, freeing the humans to concentrate on border cases and other more interesting investigations.
The AIACHNE (AI/ML Informed cAlifornium CHi Nuclear data Experiment) project aims at designing an experiment for the 252 Cf Prompt Fission Neutron Spectrum (PFNS) that explores systematic biases in an experimental database retrieved from the EXFOR databases. To that end, machine learning (ML) methods were applied to pint-point measurement features likely related to bias. From that information, we selected a feature that should be explored by the AIACHNE experiment. Measurement features are metadata encapsulating all pertinent information about the physical measurement and analysis techniques. Examples are, for instance, what neutron and fission detectors were used for the physical metadata, and what background reduction techniques were employed for analysis techniques. Such metadata were retrieved both from EXFOR entries as well as the literature of data sets described in detail in Reference 2 (at the end of the article).
The oxygen evolution reaction (OER) is a key anodic half-cell reaction that accompanies several critical electrochemical reduction reactions of interest to a variety of applications. Despite steady advances in understanding and qualitatively predicting OER activity and selectivity trends, a comprehensive description or prediction of material aqueous (in)stability and degradation mechanisms remains elusive, even though these processes critically influence device lifetime and economic feasibility. In this work, we investigate the interplay, or lack thereof, between OER activity and material aqueous stability across rutile oxides, with a particular focus on iridium oxide (IrO 2 ). By applying a Born–Haber cycle, we calculate the thermodynamic driving force for metal dissolution as a function of the applied bias and electrolyte conditions. We apply interpretable machine learning techniques, including principal component analysis and symbolic regression, to analyze trends across rutile oxides and find that key thermodynamic descriptors for OER activity and surface stability are only very weakly correlated. Instead, the local atomic environment─especially electronic structure signatures for interactions between the active site and its neighbors─plays a more important role in predicting material stability. Leveraging these insights, we investigate the impact of doping IrO 2 with a range of transition metals and show that the stability of Ir active sites can be tuned largely independently of its predicted OER activity. These insights lay the foundation for material design to improve stability with respect to corrosion, with the ultimate aim to enhance long-term stability without sacrificing catalytic performance in the OER.
Physical entropy sources that remain stable under extreme temperatures are essential for cryptography in emerging technological frontiers in deep space exploration, geothermal energy harvesting, and nuclear energy. However, conventional semiconductor platforms fail to generate stable and reliable cryptographic keys above 200 degrees C due to performance degradation. Here, we report a diamond-based cryptographic primitive that exploits the defect-rich sp 2 -bonded grain boundary network in nitrogen-incorporated ultrananocrystalline diamond (n-UNCD) film as a robust entropy source to generate cryptographic keys that remain operationally stable even after enduring extreme temperatures of 700 degrees C for 54 h while also surviving thermal cycling between room temperature and 700 degrees C for 48 h. The strength of the generated keys is assessed through several cryptographic metrics such as bit uniformity, entropy, hamming distances, and correlation coefficients, all of which are found to be near their respective ideal values. Moreover, the generated keys pass the NIST SP 800 and SP 800-90B tests and are also resilient to supply bias variations and a regression-based machine learning attack model based on the Fourier series. The robustness of the keys is attributed to the better thermal stability and chemical inertness of the n-UNCD film. This is supported by high-resolution energy-dispersive X-ray spectroscopy (EDS), which shows no significant lateral diffusion of metal atoms into the n-UNCD layer, and by Raman spectroscopy, which reveals no significant changes in the bonding configuration of the n-UNCD structure. Our findings highlight the remarkable potential of n-UNCD film for extreme environment cryptography by expanding the operational limits of conventional hardware security platforms.
Detecting large-scale flux ropes (FRs) embedded in interplanetary coronal mass ejections (ICMEs) and assessing their geoeffectiveness are essential, since they can drive severe space weather. At 1 au, these FRs have an average duration of 1 day. Their most common magnetic features are large, smoothly rotating magnetic fields. Their manual detection has become a relatively common practice over decades, although visual detection can be time-consuming and subject to observer bias. Our study proposes a pipeline that utilizes two supervised binary classification machine-learning models trained with solar wind magnetic properties to automatically detect large-scale FRs and additionally determine their geoeffectiveness. The first model is used to generate a list of autodetected FRs. Using the properties of the southward magnetic field, the second model determines the geoeffectiveness of FRs. Our method identifies 88.6% and 80% of large-scale ICMEs (duration 1day) observed at 1au by the Wind and the Solar TErrestrial RElations Observatory missions, respectively. While testing with continuous solar wind data obtained from Wind, our pipeline detected 56 of the 64 large-scale ICMEs during the 2008–2014 period (recall = 0.875), but also many false positives (precision = 0.56), as we do not take into account any additional solar wind properties other than the magnetic properties. We find an accuracy of 0.88 when estimating the geoeffectiveness of the autodetected FRs using our method. Thus, in space-weather nowcasting and forecasting at L1 or any planetary missions, our pipeline can be utilized to offer a first-order detection of large-scale FRs and their geoeffectiveness.
This data package includes data and scripts from the manuscript “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”.The study addressed common challenges faced in environmental sensing and modeling, including uncertain input data, missing sensor observations, and high-dimensional datasets with interrelated but redundant variables. Point-scaled meteorological and soil sensor observations were perturbed with noises and missing values, and denoising autoencoder (DAE) neural networks were developed to reconstruct the perturbed data and further predict evapotranspiration. This study concluded that (1) the reconstruction quality of each variable depends on its cross-correlation and alignment to the underlying data structure, (2) uncertainties from the models were overall stronger than those from the data corruption, and (3) there was a tradeoff between reducing bias and reducing variance when evaluating the uncertainty of the machine learning models.This package includes:(1) Four ipython scripts (.ipynb): “DAE_train.ipynb” trains and evaluates DAE neural networks, “DAE_predict.ipynb” makes predictions from the trained DAE models, “ET_train.ipynb” trains and evaluates ET prediction neural networks, and “ET_predict.ipynb” makes predictions from trained ET models.(2) One python file (.py): “methods.py” includes all user-defined functions and python codes used in the ipython scripts.(3) A “sub_models” folder that includes five trained DAE neural networks (in pytorch format, .pt), which could be used to ingest input data before being fed to the downstream ET models in ‘ET_train.ipynb” or ‘ET_predict.ipynb’.(4) Two data files (.csv). Daily meteorological, vegetation, and soil data is in “df_data.csv”, where “df_meta.csv” contains the location and time information of “df_data.csv”. Each row (index) in “df_meta.csv” corresponds to each row in “df_data.csv”. These data files are formatted to follow the data structure requirements and be directly used in the ipython scripts, and they have been shuffled chronologically to train machine learning models. The meteorological and soil data was collected using point sensors between 2019-2023 at(4.a) Three shrub-dominated field sites in East River, Colorado (named “ph1”, “ph2” and “sg5” in “df_meta.csv”, where “ph1” and “ph2” were located at PumpHouse Hillslopes, and “sg5” was at Snodgrass Mountain meadow) and(4.b) One outdoor, mesoscale, and herbaceous-dominated experiment in Berkeley, California (named “tb” in “df_meta.csv”, short for Smartsoils Testbed at Lawrence Berkeley National Lab).- See "df_data_dd.csv" and "df_meta_dd.csv" for variable descriptions and the Methods section for additional data processing steps. See "flmd.csv" and "README.txt" for brief file descriptions.- All ipython scripts and python files are written in and require PYTHON language software.
The Goddard Earth Observing System composition forecast (GEOS-CF) system is a high-resolution (0.25 degree) global constituent prediction system from NASA’s Global Modeling and Assimilation Office (GMAO). GEOS-CF offers a new tool for atmospheric chemistry research, with the goal to supplement NASA’s broad range of space-based and in-situ observation sand to support flight campaign planning, support of satellite observations, and air quality research. GEOS-CF expands on the GEOS weather and aerosol modeling system by introducing the GEOS-Chem chemistry module to provide analyses and 5-day forecasts of atmospheric constituents including ozone (O3), carbon monoxide (CO), nitrogen dioxide (NO2), and fine particulate matter (PM2.5). The chemistry module integrated in GEOS-CF is identical to the offline GEOS-Chem model and readily benefits from the innovations provided by the GEOS-Chem community.Evaluation of GEOS-CF against satellite, ozone sonde and surface observations show realistic simulated concentrations of O3, NO2, and CO, with normalized mean biases of -0.1 to -0.3, normalized root mean square errors (NRMSE) between 0.1-0.4, and correlations between 0.3-0.8. Comparisons against surface observations highlight the successful representation of air pollutants under a variety of meteorological conditions, yet also highlight current limitations, such as an over prediction of summertime ozone over the Southeast United States. GEOS-CFv1.0 generally overestimates aerosols by 20-50% due to known issues in GEOS-Chem v12.0.1 that have been addressed in later versions.The 5-day hourly forecasts have skill scores comparable to the analysis. Model skills can be improved significantly by applying a bias-correction to the surface model output using a machine-learning approach.
Inaccurate prediction of aircraft trajectory by ground-based decision support tools (DST) is a major concern in air traffic management (ATM). Aircraft trajectory prediction tools rely on a simplified point-mass aircraft performance model (APM) to make their predictions. Even though the performance coefficients and weight of an aircraft are a vital part of the APM’s predictions and accuracy, these coefficients are proprietary in nature and therefore, unavailable to DSTs. Current ATM research focuses on improving the estimate of some APM parameters by freezing all other coefficients. This simplified approach introduces unwanted sources of bias and negatively impacts the accuracy of the performance model. In this paper, we apply machine learning (ML) techniques for the simultaneous prediction of three key APM parameters (two drag coefficients and the initial aircraft weight). To accomplish this, we employ an ordinary differential equation (ODE) fitting approach to generate optimized APM parameter labels customized to each individual flight record. Subsequently, we train ML models to capture the relationship between the historical data and the optimized APM parameters. Two different ML model solutions are applied and APM coefficients are predicted for unseen flights. The results indicate that the ML models are able to capture the relationship between APM parameters and flight-related features with good accuracy.
TAE Technologies’ fifth-generation fusion device, C-2W (also called ‘Norman’), is the world’s largest compact-toroid device and has made significant progress in field-reversed configuration (FRC) plasma performance. C-2W produces record breaking, macroscopically stable, high-temperature advanced beam-driven FRC plasmas, dominated by injected fast particles and sustained in steady state, which is primarily limited by neutral-beam (NB) pulse duration. The NB power supply system has recently been upgraded to extend the pulse length from 30 ms to 40 ms, which allows for a longer plasma lifetime and thus better characterization and further enhancement of FRC performance. An active plasma control system is routinely used in C-2W to produce consistent FRC performance as well as for reliable machine operations using magnet coils, edge-biasing electrodes, gas injection and tunable-energy NBs. Google’s machine learning framework for experimental optimization has also been routinely used to enhance plasma performance. D
Rapid and accurate prediction of the physicochemical properties of molecules given their structures remains a key challenge in cheminformatics. Machine learning approaches offer high-throughput options, but the optimality of inductive biases and data representations are up for debate. For example, BERT-based masked language models (MLMs) can be trained in a self-supervised way on hundreds of millions to billions of readily available SMILES strings. Another option is graph neural networks (GNNs), which can operate directly on molecular structures. Yet, generating accurate molecular geometry is computationally expensive, leading to a relative scarcity in data compared to SMILES strings. It is attractive to combine these two paradigms by pre-training an LM on a large corpus of SMILES strings and embedding these representation into a geometric graph neural network. Despite the promise of such an approach, and contrary to previous studies, we find mixed results with the combination of the LMs and GNNs on several molecule datasets. In particular, we found evidence for improvement on the FreeSolv and QM7 benchmarks, but degraded performance on the ESOL, LIPO and QM9 datasets compared to a GNN baseline.