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72 records · Page 4

Data exploration systems for databases

Data exploration systems apply machine learning techniques, multivariate statistical methods, information theory, and database theory to databases to identify significant relationships among the data and summarize information. The result of applying data exploration systems should be a better understanding of the structure of the data and a perspective of the data enabling an analyst to form hypotheses for interpreting the data. This paper argues that data exploration systems need a minimum amount of domain knowledge to guide both the statistical strategy and the interpretation of the resulting patterns discovered by these systems.

Greene, Richard J.↗

Feature Selection in High-Dimensional Space with Applications to Gene Expression Data

Recent years have seen rapid growth in high-dimensional datasets. Most existing machine learning (ML) algorithms fail in high-dimensional settings where many features could be redundant. A critical process of feature selection is thus applied in such a setting that helps in identifying the most relevant features while removing redundant ones. With the increase in high dimensionality, one is also faced with problems of efficiency and interpretation in performing such selection methods. Therefore, this paper proposes a “novel” feature selection framework that uses an ensemble of interpretable ML algorithms to perform feature selection and the ranking of final features. Finally, this framework is applied to a gene expression dataset obtained through collaboration with the National Aeronautics and Space Administration (NASA)’s Biological and Physical Sciences (BPS) team and helps identify important and relevant genes contributing to specific target attributes through classification tasks.

Nishan Pantha↗

Blindness in designing intelligent systems

New investigations of the foundations of artificial intelligence are challenging the hypothesis that problem solving is the cornerstone of intelligence. New distinctions among three domains of concern for humans--description, action, and commitment--have revealed that the design process for programmable machines, such as expert systems, is based on descriptions of actions and induces blindness to nonanalytic action and commitment. Design processes focusing in the domain of description are likely to yield programs like burearcracies: rigid, obtuse, impersonal, and unable to adapt to changing circumstances. Systems that learn from their past actions, and systems that organize information for interpretation by human experts, are more likely to be successful in areas where expert systems have failed.

Denning, Peter J.↗

A Science-Focused Artificial Intelligence (AI) Responding in Real-Time to New Information: Capability Demonstration for Ocean World Missions

Introduction: Artificial intelligence (AI) has long been considered a potential mechanism to explore increasingly challenging environments, including those with extreme temperatures and pressures, limited communication capabilities, or those with demanding terrain. We posit that missions in extreme environments could deploy an onboard AI focused on science observations and goals in order to augment a traditional concept(s) of operations (ConOps). An onboard AI capability could perform functions such as data analysis in order to make high-level decisions, including prioritized data transmission for analysis by ground-based teams or autonomously-guided follow-on analyses that maximize science return. Such a capability would empower missions to respond to scientific data of interest in real-time; a mission could make observations and perform a preliminary analysis to alert ground-based scientists to an observation of interest, enabling an informed, rapid response from Earth-based teams. Enceladus Case Study for Onboard AI: We are developing an onboard AI capability for real-time telemetry response that formulates and carries-out informed decisions in service to established mission goals, enabling increased science return of a mission. We focus our AI development for use on a constellation of SmallSats orbiting Enceladus. Our Enceladus case study tests autonomous decision-making capabilities in scenarios with complex orbital dynamics, plume ejecta, extreme cold environments, power restrictions, and a requirement to maximize science return for a potential positive detection of life, while critically evaluating the potential for false positives. Telemetry includes simulated scientific data, spacecraft onboard operational data (e.g., position, velocity, and rotation), and engineering hardware performance data. Enceladus SmallSat Constellation. Our constellation includes eight SmallSat spacecraft in an 8:35 resonant orbit-based formation, leveraging Saturn’s gravitational forces to maintain stable orbits with global coverage around Enceladus. To our knowledge, we simulate the first stable configuration of multiple spacecraft in closed orbits around Enceladus, using a full ephemeris force model (Russell and Lara, 2009). Each spacecraft’s orbit will precess, causing an eastward ground track shift (from an orbiter’s perspective) of each spacecraft for each orbit. However, all spacecraft return to their original positions relative to Enceladus after eight Enceladus revolutions around Saturn. We model communication pathways between SmallSats to understand how information would need to be transmitted across the constellation to enable AI-driven decision-making and resource allocation across the fleet. Capability Demonstration. Our simulated capability demonstration inputs position, velocity, and rotation telemetry from our Enceladus-focused constellation simulations, and mass spectrometry data collected from abiotic and biotic laboratory-analog ocean world experiments (Theiling et al., 2018; Theiling, 2021; Da Poian et al., 2023). Data from these experiments are used to simulate MS measurements and different scenarios of science observations for onboard analysis performed on each of the eight spacecraft. For these demonstrations, we integrate 24 machine learning (ML) algorithms into an onboard intelligence as a ‘knowledge base’, including algorithms evaluating data quality and those predicting (with % confidence) gas composition, ocean aqueous chemistry, and whether the sample was influenced by microbial life. The onboard AI capability is designed to use the knowledge base to come to a consensus-based decision in the interpretation of the observed data in order to request additional action outside of a pre-defined ConOps. Requested actions could include e.g., prioritized downlink to Earth (for analysis by ground-based teams) or follow-on analyses performed across the constellation. The spacecraft’s intelligent onboard planner must then determine whether sufficient resources (e.g., time, power, etc.) are available and weigh the request with mission priorities. In our simulation, the constellation is able to identify potential biosignatures using onboard ML algorithms, evaluate the confidence of that prediction, and perform follow-on analyses across the fleet to confirm the detection, in order to best prepare a transmission of these data to Earth-based teams.

astrobiology↗

Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.

Corbetta, Matteo↗

Development and Application of NASA SPoRT’s DustTracker-AI Model for Real-Time Identification and Tracking of Dust in Geostationary Satellite Imagery

The NASA Short-term Prediction Research and Transition (SPoRT) Center developed the DustTracker-AI model for identifying and tracking dust in NASA/NOAA Geostationary Operational Environmental Satellite (GOES) imagery in a real-time framework. A training dataset consisting of day and night dust cases was gathered over the southwestern consisting of 115 distinct images and over a million dust pixels and 256 million no dust pixels. The dataset was separated into training (60%), testing (20%), and validation (20%). A simple random forest machine learning model was developed originally to overcome the problem of night-time dust detection and has been expanded to a comprehensive day/night model for dust identification and tracking. This physically-based machine-learning approach uses NASA/NOAA GOES-16 Advanced Baseline Imager infrared imagery as inputs to the model. The model probability of dust output achieves an Area-Under-Curve (AUC) of 0.97 with a standard deviation of 0.04 for dust cases. For images with dust present, the model correctly labels 85% of dust pixels for all dust images in the validation data set. In conjunction with developing the machine-learning model, the NASA Short-term Prediction Research and Transition Center (SPoRT) partnered with NOAA National Weather Service forecast offices to evaluate the model for utility in weather forecasting operations during the 2021 and 2023 late winter-spring seasons. Preliminary evaluation has indicated the majority of forecasters described the DustTracker-AI probabilities as having added confidence to interpreting the Dust RGB and other satellite products to objectively assess the dust extent and trends and increased the amount of time the dust plume could be tracked into the night as compared to use of the Dust RGB. More recently, SPoRT tested small scale events associated with thunderstorm outflow and burn scars to determine the model’s ability to capture local events. This presentation highlights design of the model, validation/evaluation of model performance, and example cases collected during end user product assessments.

Connor H Welch↗

Advancing Methodologies for Applying Machine Learning and Evaluating Spatiotemporal Models of Fine Particulate Matter (PM 2.5 ) Using Satellite Data Over Large Regions

Reconstructing the distribution of fine particulate matter (PM 2.5 ) in space and time, even far from ground monitoring sites, is an important exposure science contribution to epidemiologic analyses of PM 2.5 health impacts. Flexible statistical methods for prediction have demonstrated the integration of satellite observations with other predictors, yet these algorithms are susceptible to overfitting the spatiotemporal structure of the training datasets. We present a new approach for predicting PM 2.5 using machine-learning methods and evaluating prediction models for the goal of making predictions where they were not previously available. We apply extreme gradient boosting (XGBoost) modeling to predict daily PM 2.5 on a 1 x 1 km 2 resolution for a 13 state region in the Northeastern USA for the years 2000–2015 using satellite-derived aerosol optical depth and implement a recursive feature selection to develop a parsimonious model. We demonstrate excellent predictions of withheld observations but also contrast an RMSE of 3.11 μg/m 3 in our spatial cross-validation withholding nearby sites versus an overfit RMSE of 2.10 μg/m 3 using a more conventional random ten-fold splitting of the dataset. As the field of exposure science moves forward with the use of advanced machine-learning approaches for spatiotemporal modeling of air pollutants, our results show the importance of addressing data leakage in training, overfitting to spatiotemporal structure, and the impact of the predominance of ground monitoring sites in dense urban sub-networks on model evaluation. The strengths of our resultant modeling approach for exposure in epidemiologic studies of PM 2.5 include improved efficiency, parsimony, and interpretability with robust validation while still accommodating complex spatiotemporal relationships.

air pollution↗

A Low-Power High-Speed Smart Sensor Design for Space Exploration Missions

A low-power high-speed smart sensor system based on a large format active pixel sensor (APS) integrated with a programmable neural processor for space exploration missions is presented. The concept of building an advanced smart sensing system is demonstrated by a system-level microchip design that is composed with an APS sensor, a programmable neural processor, and an embedded microprocessor in a SOI CMOS technology. This ultra-fast smart sensor system-on-a-chip design mimics what is inherent in biological vision systems. Moreover, it is programmable and capable of performing ultra-fast machine vision processing in all levels such as image acquisition, image fusion, image analysis, scene interpretation, and control functions. The system provides about one tera-operation-per-second computing power which is a two order-of-magnitude increase over that of state-of-the-art microcomputers. Its high performance is due to massively parallel computing structures, high data throughput rates, fast learning capabilities, and advanced VLSI system-on-a-chip implementation.

Fang, Wai-Chi↗

Evaluating the Efficacy of Conditional Variational Autoencoders in Generating Synthetic Single Nuclei RNA-Seq Data for Space Biology Research

Astronauts are subject to unique stressors during spaceflight, leading to changes in their cellular function. However, neither astronauts nor model organisms respond the same to spaceflight, and research implicates a contribution of omics components in differential responses. Understanding how gene expression affects astronaut health is critical for the success of long-term space missions, prompting interest in developing personalized predictive models leveraging artificial intelligence (AI) and machine learning (ML) techniques. Developing such models requires extensive data, which is challenging to obtain and share. This study explores the use of conditional variational autoencoders (CVAEs) to synthetically generate single-nuclei RNA-seq (snRNA-seq) data. CVAEs build on standard variational autoencoders (VAEs) by conditioning data generation on covariates like sample identity and mission parameters, enhancing the relevance of generated data for specific contexts. For our work, we built two CVAEs with varying degrees of sparsity to optimize both interpretability and generative power. We train and validate models on existing snRNA-seq data collected from the brain tissue of mice subjected to spaceflight conditions and their ground control counterparts. We evaluate model performance using statistical tests and visualizations to compare synthetic data to real data. We aim to demonstrate that these prototype CVAE architectures could be used in future space biology work and that this is a method worth further exploring.

Sarah Golts↗

Multi-Mission Automated Task Invocation Subsystem

Multi-Mission Automated Task Invocation Subsystem (MATIS) is software that establishes a distributed data-processing framework for automated generation of instrument data products from a spacecraft mission. Each mission may set up a set of MATIS servers for processing its data products. MATIS embodies lessons learned in experience with prior instrument- data-product-generation software. MATIS is an event-driven workflow manager that interprets project-specific, user-defined rules for managing processes. It executes programs in response to specific events under specific conditions according to the rules. Because requirements of different missions are too diverse to be satisfied by one program, MATIS accommodates plug-in programs. MATIS is flexible in that users can control such processing parameters as how many pipelines to run and on which computing machines to run them. MATIS has a fail-safe capability. At each step, MATIS captures and retains pertinent information needed to complete the step and start the next step. In the event of a restart, this information is retrieved so that processing can be resumed appropriately. At this writing, it is planned to develop a graphical user interface (GUI) for monitoring and controlling a product generation engine in MATIS. The GUI would enable users to schedule multiple processes and manage the data products produced in the processes. Although MATIS was initially designed for instrument data product generation,

Cheng, Cecilia S.↗

Automating sky object classification in astronomical survey images

We describe the application of machine classification techniques to the development of an automated tool for the reduction of a large scientific data set. The 2nd Palomer Observatory Sky Survey is nearly completed. This survey provides comprehensive coverage of the northern celestial hemisphere in the form of photographic plates. The plates are being transformed into digitized images whose quality will probably not be surpassed in the next ten to twenty years. The images are expected to contain on the order of 10(exp 7) galaxies and 10(exp 8) stars. Astronomers wish to determine which of these sky objects belong to various classes of galaxies and stars. The size of this data set precludes manual analysis. Our approach is to develop a software system which integrates the functions of independently developed techniques for image processing and data classification. Digitized sky images are passed through image processing routines to identify sky objects and to extract a set of features for each object. These routines are used to help select a useful set of attributes for classifying sky objects. Then GID3* and O-BTree, two inductive learning techniques, learn classification decision trees from examples. These classifiers will be used to process the rest of the data. This paper gives an overview of the machine learning techniques used, describes the details of our specific application, and reports the initial encouraging results. The results indicate that our approach is well-suited to the problem. The primary benefits of the approach are increased data reduction throughput and consistency of classification. The classification rules which are the product of the inductive learning techniques will form an object, examinable basis for classifying sky objects. A final, not to be underestimated benefit is that astronomers will be freed from the tedium of an intensely visual task to pursue more challenging analysis and interpretation problems based on automatically cataloged data.

Fayyad, Usama M.↗

Greenland Geothermal Heat Flow Database and Map (Version 1)

We compile and analyze all available geothermal heat flow measurements collected in and around Greenland into a new database of 419 sites and generate an accompanying spatial map. This database includes 290 sites previously reported by the International Heat Flow Commission (IHFC), for which we now standardize measurement and metadata quality. This database also includes 129 new sites, which have not been previously reported by the IHFC. These new sites consist of 88 offshore measurements and 41 onshore measurements, of which 24 are subglacial. We employ machine learning to synthesize these in situ measurements into a gridded geothermal heat flow model that is consistent across both continental and marine areas in and around Greenland. This model has a native horizontal resolution of 55 km. In comparison to five existing Greenland geothermal heat flow models, our model has the lowest mean geothermal heat flow for Greenland onshore areas. Our modeled heat flow in central North Greenland is highly sensitive to whether the NGRIP (North GReenland Ice core Project) elevated heat flow anomaly is included in the training dataset. Our model's most distinctive spatial feature is pronounced low geothermal heat flow (< 40 mW m−2) across the North Atlantic Craton of southern Greenland. Crucially, our model does not show an area of elevated heat flow that might be interpreted as remnant from the Icelandic plume track. Finally, we discuss the substantial influence of paleoclimatic and other corrections on geothermal heat flow measurements in Greenland. The in situ measurement database and gridded heat flow model, as well as other supporting materials, are freely available from the GEUS Dataverse (https://doi.org/10.22008/FK2/F9P03L; Colgan and Wansing, 2021).

William Colgan↗

Coevolution of Machine Learning and Process-Based Modelling to Revolutionize Earth and Environmental Sciences: A Perspective

Machine learning (ML) applications in Earth and environmental sciences (EES) have gained incredible momentum in recent years. However, these ML applications have largely evolved in ‘isolation’ from the mechanistic, process-based modelling (PBM) paradigms, which have historically been the cornerstone of scientific discovery and policy support. In this perspective, we assert that the cultural barriers between the ML and PBM communities limit the potential of ML, and even its ‘hybridization’ with PBM, for EES applications. Fundamental, but often ignored, differences between ML and PBM are discussed as well as their strengths and weaknesses in light of three overarching modelling objectives in EES, (1) nowcasting and prediction, (2) scenario analysis, and (3) diagnostic learning. The paper ponders over a ‘coevolutionary’ approach to model building, shifting away from a borrowing to a co-creation culture, to develop a generation of models that leverage the unique strengths of ML such as scalability to big data and high-dimensional mapping, while remaining faithful to process-based knowledge base and principles of model explainability and interpretability, and therefore, falsifiability.

Saman Razavi↗

Discriminative Methodology using the Unscented Transform in Special Euclidean Group SE(3) for Autonomous GN&C

Kalman filtering techniques usually compare a known dynamic model with some process noise to an updated, noisy measurement. Both sources of noise are generally assumed to be Gaussian and are filtered to obtain a more accurate estimate of the state of the system of interest. However, these methods assume that a relatively accurate dynamical model already exists. By including discriminative methodology to interpret differences in the predictive model and the measured states over time, an incorrect model can be corrected overtime, allowing a spacecraft to learn about its environment and adapt to changing conditions. In this paper, a discriminative unscented Kalman filter (DUKF) is introduced on the special Euclidean group SE(3) formulation framework. A spacecraft is initialized near a small body with no knowledge of its parameters, and using several consecutive conditional models the environment is studied and the filter is updated. The case study of a spacecraft in a slightly elliptical, inclined, relatively tight orbit around the irregular moon Phobos is simulated and discussed. The accuracy of this approach is quantifying the differences between the true state, the UKF with a poor model, and the DUKF.

GN&C↗

SPHINX: An SEP Model Validation Infrastructure developed through Community Challenges and the SEP Scoreboards

Solar Energetic Particle (SEP) events are interesting from a scientific perspective as they are the product of a broad set of physical processes from the corona out through the extent of the heliosphere, and provide insight into processes of particle acceleration and transport that are widely applicable in astrophysics. From the operations perspective, SEP events pose a radiation hazard for aviation, electronics in space, and human space exploration, in particular for missions outside of the Earth’s protective magnetosphere including to the Moon and Mars (Whitman et al 2022). For these reasons, SEP modelers have developed a rich and diverse set of models with a wide variety of aims. Some models probe the basic physics at the heart of particle acceleration and transport. Others produce fast statistical forecasts or employ disruptive new techniques like Machine Learning with the goal to assist end users in making operational decisions. To enable a consistent and quantitative understanding of SEP model performance, a generalized, automated validation infrastructure, called SPHINX, is being developed at NASA SRAG in close collaboration with NASA CCMC, NASA M2M, NOAA SWPC, and BIRA-IASB. This infrastructure has been built up through a multi-year community challenge. Starting in 2018 at the SHINE workshop, an effort was launched through SHINE, ISWAT, and ESWW to encourage quantitative, comprehensive, and consistent validation of SEP models. This effort has defined a set of challenge SEP events with the aim of generating quantitative comparisons between forecasts and observations and a set of challenge “non-events” to assess false alarms. In 2023, these challenge lists have been extended to statistically significant numbers with a prescribed set of rules for producing forecasts and supported through the dedicated SEPVAL working meetings. The participation of the research community has allowed the infrastructure to validate all the types of outputs being produced by SEP models. In parallel, the SPHINX code is being applied to real time forecasts submitted to the SEP Scoreboards, ensuring that the validation infrastructure can interpret forecasts produced in an operational scenario and provide metrics meaningful for operations. Upon completion, SPHINX and its interactive user interface, SPHINX-Web, will be made available for public use.

space weather↗

Using machine learning techniques to automate sky survey catalog generation

We describe the application of machine classification techniques to the development of an automated tool for the reduction of a large scientific data set. The 2nd Palomar Observatory Sky Survey provides comprehensive photographic coverage of the northern celestial hemisphere. The photographic plates are being digitized into images containing on the order of 10(exp 7) galaxies and 10(exp 8) stars. Since the size of this data set precludes manual analysis and classification of objects, our approach is to develop a software system which integrates independently developed techniques for image processing and data classification. Image processing routines are applied to identify and measure features of sky objects. Selected features are used to determine the classification of each object. GID3* and O-BTree, two inductive learning techniques, are used to automatically learn classification decision trees from examples. We describe the techniques used, the details of our specific application, and the initial encouraging results which indicate that our approach is well-suited to the problem. The benefits of the approach are increased data reduction throughput, consistency of classification, and the automated derivation of classification rules that will form an objective, examinable basis for classifying sky objects. Furthermore, astronomers will be freed from the tedium of an intensely visual task to pursue more challenging analysis and interpretation problems given automatically cataloged data.

Fayyad, Usama M.↗

Identifying Human Errors and Error Mechanisms From Accident Reports Using Large Language Models

Emerging operational concepts for aviation hinge on novel paradigms for human machine interaction. Critical to their safe operation is early consideration of human error into the design process. Existing methods for consideration of human error require significant expert input, which is challenging both in early design and in novel systems for which there is little existing safety expertise. In this research, we propose a methodology for identifying human error, error producing factors, and mechanisms in early design from historical incident reports. Additionally, we hypothesize that cross-domain sharing of lessons learned can aid with early design human considerations in circumstances where data is not relevant or incomplete. This is addressed by identifying causes of human error in aviation and railway domains through applying state-of-the art natural language processing techniques to historical incident reports. Using this method, it is possible to extract extensive reports on human error from past incidents. Using the proposed approach, we identify nine human errors from railway reports and fourteen from aviation reports, with three errors common to both domains. There is at least one error producing conditions for each human error while a majority of the errors have more than one error mechanism. We also found that a majority of the human errors, error producing factors, and error mechanisms (even if they are not common between the domains) can be used to inform safe operations across domains as long as the errors are not domain specific and are interpreted and contextualized using engineering judgement.

Human Errors↗

Reliability of Maximal Strength Testing in Novice Weightlifters

The one repetition maximum (1RM) is a criterion measure of muscle strength. However, the reliability of 1RM testing in novice subjects has received little attention. Understanding this information is crucial to accurately interpret changes in muscle strength. To evaluate the test-retest reliability of a squat (SQ), heel raise (HR), and deadlift (DL) 1RM in novice subjects. Twenty healthy males (31 plus or minus 5 y, 179.1 plus or minus 6.1 cm, 81.4 plus or minus 10.6 kg) with no weight training experience in the previous six months participated in four 1RM testing sessions, with each session separated by 5-7 days. SQ and HR 1RM were conducted using a smith machine; DL 1RM was assessed using free weights. Session 1 was considered a familiarization and was not included in the statistical analyses. Repeated measures analysis of variance with Tukey fs post-hoc tests were used to detect between-session differences in 1RM (p.0.05). Test-retest reliability was evaluated by intraclass correlation coefficients (ICC). During Session 2, the SQ and DL 1RM (SQ: 90.2 }4.3, DL: 75.9 }3.3 kg) were less than Session 3 (SQ: 95.3 }4.1, DL: 81.5 plus or minus 3.5 kg) and Session 4 (SQ: 96.6 }4.0, DL: 82.4 }3.9 kg), but there were no differences between Session 3 and Session 4. HR 1RM measured during Session 2 (150.1 }3.7 kg) and Session 3 (152.5 }3.9 kg) were not different from one another, but both were less than Session 4 (157.5 }3.8 kg). The reliability (ICC) of 1RM measures for Sessions 2-4 were 0.88, 0.83, and 0.87, for SQ, HR, and DL, respectively. When considering only Sessions 3 and 4, the reliability was 0.93, 0.91, and 0.86 for SQ, HR, and DL, respectively. One familiarization session and 2 test sessions (for SQ and DL) were required to obtain excellent reliability (ICC greater than or equal to 0.90) in 1RM values with novice subjects. We were unable to attain this level of reliability following 3 HR testing sessions therefore additional sessions may be required to obtain an ICC of greater than or equal to 0.90. Future resistive exercise studies should consider the reliability of specific measures to ensure that changes in strength with training are attributable to training and not learning effects associated with 1RM testing.

Loehr, James A.↗