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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Dynamic data-driven multiscale modeling for predicting the degradation of a 316L stainless steel nuclear cladding material

Here, we have developed a long short-term memory stacked ensemble (LSTM-SE) surrogate modeling approach that can provide rapid predictions of microstructural evolution and the resultant mechanical properties of American Iron and Steel Institute (AISI) 316L series stainless steel (316LSS) fuel cladding under conditions of varying temperature and radiation dose rate. To acquire training data, we developed and implemented a kinetic Monte Carlo (KMC) model to simulate precipitation kinetics of M 23 C 6 , γ', and G phases within SS316L cladding. Experimentally reported precipitation kinetics of SS316L in literature were linked to the kinetic parameters of the simulated precipitation in our KMC model. The model was then used to simulate microstructure evolution under synthetically generated treatments of varying temperature and radiation dose rate, for periods of up to 3000 hours. Changes in volume fraction, number density, and particle size of precipitates were recorded, and particle area fractions were correlated using statistical methods to develop the surrogate model. Simultaneously, the mechanical properties of the simulated microstructures were evaluated using microstructure-based finite element method (FEM) analysis to determine the elastic modulus, yield stress, ultimate tensile strength, and elongation to failure of the aged microstructures. Using this approach, our surrogate model can predict precipitation behavior within 0.25% volume fraction and mechanical properties within 6% relative error from the values predicted by the KMC and FEM models using 50 training simulations as input. The trained recurrent neural network-based model can return estimations of precipitation kinetics and mechanical properties ~1000 times faster than the physics-based codes. This work demonstrates, as a proof of concept, that reactor material service lifetimes under variable service conditions can be predicted for a statistics-based model from a practicably obtainable dataset.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Hierarchical Testing of a Hybrid Machine Learning‐Physics Global Atmosphere Model

Machine learning (ML)-based models have demonstrated high skill and computational efficiency, often outperforming conventional physics-based models in weather and subseasonal predictions. While prior studies have assessed their fidelity in capturing synoptic-scale atmospheric dynamics, their performance across timescales and under out-of-distribution forcing, such as +3K or +4K uniform-warming forcings, and the sources of biases remain elusive, to establish the model's reliability for Earth science. Here, we design three sets of experiments targeting synoptic-scale phenomena, interannual variability, and out-of-distribution uniform-warming forcings. We evaluate the Neural General Circulation Model (NeuralGCM), a hybrid model integrating a dynamical core with ML-based component, against observations and physics-based Earth system models (ESMs). At the synoptic scale, NeuralGCM captures the evolution and propagation of extratropical cyclones with performance comparable to ESMs. At the interannual scale, when forced by El Niño-Southern Oscillation sea surface temperature (SST) anomalies, NeuralGCM successfully reproduces associated teleconnection patterns but exhibits deficiencies in capturing nonlinear response. Under out-of-distribution uniform-warming forcings, NeuralGCM simulates similar responses in global-average temperature and precipitation and reproduces large-scale tropospheric circulation features similar to those in ESMs. Notable weaknesses include overestimating the tracks and spatial extent of extratropical cyclones, biases in the teleconnected wave train triggered by tropical SST anomalies, and differences in upper-level warming and stratospheric circulation responses to SST warming compared to physics-based ESMs. The causes of these weaknesses were explored. Despite the noted weaknesses, NeuralGCM reproduces responses across experiments reasonably and performs comparably to ESMs. By integrating a dynamical core with ML, NeuralGCM shows potential for developing ML-based ESMs.

global warming↗
DOE OSTI2026

Crowdsourcing the Frontier: Advancing Hybrid Physics‐ML Climate Simulation via a $\$$50,000 Kaggle Competition

Subgrid machine-learning (machine learning [ML]) parameterizations have the potential to introduce a new generation of climate models that incorporate the effects of higher-resolution physics without incurring the prohibitive computational cost associated with more explicit physics-based simulations. However, important issues, ranging from online instability to inconsistent online performance, have limited their operational use for long-term climate projections. To more rapidly drive progress in solving these issues, domain scientists and ML researchers opened up the offline aspect of this problem to the broader ML and data science community with the release of ClimSim, a NeurIPS Data sets and Benchmarks publication, and an associated Kaggle competition. This paper reports on the downstream results of the Kaggle competition by coupling emulators inspired by the winning teams' architectures to an interactive climate model (including full cloud microphysics, a regime historically prone to online instability) and systematically evaluating their online performance. Our results demonstrate that online stability in the low-resolution real-geography setting is reproducible across multiple diverse architectures, which we consider a key milestone. All tested architectures exhibit strikingly similar offline and online biases, though their responses to architecture-agnostic design choices (e.g., expanding the list of input variables) can differ significantly. Multiple Kaggle-inspired architectures achieve state-of-the-art results on certain metrics such as zonal mean bias patterns and global Root Mean Squared Error, indicating that crowdsourcing the essence of the offline problem is one path to improving online performance in hybrid physics-AI climate simulation.

Environmental sciences↗
DOE OSTI2025

Molecular property prediction for very large databases with natural language processing: a case study in ionic liquid design

The prospect of using artificial intelligence (AI) to accurately screen very large databases of compounds for multiple properties has yet to be realized. Here, we explore this possibility using ionic liquids (ILs) which offer unique physicochemical properties and excellent tunability, making them highly versatile solvents for various research applications. Screening millions of potential ILs for the best perfomance for use in specific tasks with experimental methods alone however, is impractical. Further, traditional’ physics-based computational chemistry is hindered by high computational cost. To address this challenge, we leverage a natural language processing (NLP)-based molecular embedding technique with advanced machine learning (ML) models to predict seven key IL properties: viscosity, density, ionic conductivity, surface tension, melting temperature, toxicity, and water solubility. Comprehensive datasets for these properties are obtained, then NLP featurization with Mol2vec is compared with other featurization techniques such as 2D Morgan fingerprints, and 3D quantum chemistry-derived sigma profiles. NLP-based featurization exhibited the best predictive performance, achieving the highest R 2 and lowest RMSE values for all the studied IL properties. Further, we present case studies of how ILs might be screened using combined property criteria for practical cases – lignocellulosic biomass processing, CO 2 capture, and optimal electrolytes for batteries – screening a novel database of ∼10.6 million generated feasible ILs. The results introduce NLP as a powerful tool for engineering many designer solvents with desirable properties for task specific applications.

Mohan, Mood [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2025

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Impact of various DIII-D diagnostics on the accuracy of neural network surrogates for kinetic EFIT reconstructions

Abstract Kinetic equilibrium reconstructions make use of profile information such as particle density and temperature measurements in addition to magnetics data to compute a self-consistent equilibrium. They are used in a multitude of physics-based modeling. This work develops a multi-layer perceptron (MLP) neural network (NN) model as a surrogate for kinetic Equilibrium Fitting (EFITs) and trains on the 2019 DIII-D discharge campaign database of kinetic equilibrium reconstructions. We investigate the impact of including various diagnostic data and machine actuator controls as input into the NN. When giving various categories of data as input into NN models that have been trained using those same categories of data, the predictions on multiple equilibrium reconstruction solutions (poloidal magnetic flux, global scalars, pressure profile, current profile) are highly accurate. When comparing different models with different diagnostics as input, the magnetics-only model outputs accurate kinetic profiles and the inclusion of additional data does not significantly impact the accuracy. When the NN is tasked with inferring only a single target such as the EFIT pressure profile or EFIT current profile, we see a large increase in the accuracy of the prediction of the kinetic profiles as more data is included. These results indicate that certain MLP NN configurations can be reasonably robust to different burning-plasma-relevant diagnostics depending on the accuracy requirements for equilibrium reconstruction tasks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Introducing a multiscale feature integration network for inpainting with applications to enhanced CMB map reconstruction

We introduce a novel neural network, SkyReconNet, which combines the expanded receptive fields of dilated convolutional layers along with standard convolutions, to capture both the global and local features for reconstructing the missing information in an image. We implement our network to inpaint the masked regions in a full-sky cosmic microwave background (CMB) map. Inpainting CMB maps is a particularly formidable challenge when dealing with extensive and irregular masks, such as galactic masks which can obscure substantial fractions of the sky. The hybrid design of SkyReconNet leverages the strengths of standard and dilated convolutions to accurately predict CMB fluctuations in the masked regions by effectively utilizing the information from surrounding unmasked areas. During training, the network optimizes its weights by minimizing a composite loss function that combines the structural similarity index measure (SSIM) and mean squared error (MSE). SSIM preserves the essential structural features of the CMB, ensuring an accurate and coherent reconstruction of the missing CMB fluctuations, while MSE minimizes the pixelwise deviations, thus enhancing the overall accuracy of the predictions. The predicted CMB maps and their corresponding angular power spectra align closely with the targets, achieving the performance limited only by the fundamental uncertainty of cosmic variance. The network’s generic architecture enables application to other physics-based challenges involving data with missing or defective pixels, systematic artifacts, etc. In conclusion, our results demonstrate its effectiveness in addressing the challenges posed by large irregular masks, offering a significant inpainting tool not only for CMB analyses but also for image-based experiments across disciplines where such data imperfections are prevalent.

Cosmic microwave background↗
DOE OSTI2024

Communication Network Layer State Estimation Measurement Model for a Cyber-Secure Smart Grid

Network communication has been proven to be a very important tool and a key factor in the recent development and progress of the power grid operation. It is also considered as the foundation for the smart grid because information and communication are integrated into electricity distribution to achieve reliable and accurate knowledge of the power grid. In previous years, absorbing energy from substations and delivering it to customers was the only type of interaction we knew between utility companies and customers. Presently, the growing connections of small distributed generation units caused by the cost reduction of most of the technologies used in generation and storage of electrical energy, along with the potential benefits of renewable energy have pushed many researchers to look into the improvement of information and communication technologies (ICT) in order to ensure a bidirectional flow of power and data. Moreover, the evolution of information and communication technologies and its applications to smart grid have converted the smart grid into a cyber-physical system where vulnerabilities and additional security challenges such as cyber-threats and cyber-attacks have emerged. Previously, we have demonstrated that using machine learning-based processing on data gathered from communication networks and the power grid was a promising solution for detecting cyber threats by implementing a co-simulation of cyber-security for cross-layer strategy. Since the majority of the challenges observed can only be solved in the network communication layer, we present in this work a physics-based state estimation model of the communication network system towards enhanced cyber-physical security of the smart grid. Information integration with the previously developed machine learning model is developed, providing a enhanced cyber-physical security application for the smart grid. Easy-to-implement model, without hard-to-derive parameters, highlight potential aspects of the model for real-life applications.

Mathieu, Reynold↗
DOE OSTI2024

Efficient mapping between void shapes and stress fields using Deep Convolutional Neural Networks with sparse data

Establishing fast and accurate structure-to-property relationships is an important component in the design and discovery of advanced materials. Physics-based simulation models like the finite element method (FEM) are often used to predict deformation, stress, and strain fields as a function of material microstructure in material and structural systems. Such models may be computationally expensive and time intensive if the underlying physics of the system is complex. This limits their application to solve inverse design problems and identify structures that maximize performance. In such scenarios, surrogate models are employed to make the forward mapping computationally efficient to evaluate. However, the high dimensionality of the input microstructure and the output field of interest often renders such surrogate models inefficient, especially when dealing with sparse data. Deep convolutional neural network (CNN) based surrogate models have shown great promise in handling such high-dimensional problems. In this paper, a single ellipsoidal void structure under a uniaxial tensile load represented by a linear elastic, high-dimensional and expensive-to-query, FEM model. We consider two deep CNN architectures, a modified convolutional autoencoder framework with a fully connected bottleneck and a UNet CNN, and compare their accuracy in predicting the von Mises stress field for any given input void shape in the FEM model. Additionally, a sensitivity analysis study is performed using the two approaches, where the variation in the prediction accuracy on unseen test data is studied through numerical experiments by varying the number of training samples from 20 to 100.

surrogate modeling; convolutional neural networks;↗
DOE OSTI2024

Decision-making based on Markov decision process in integrated artificial reasoning framework—Part I: Theory

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

Markov decision process↗
DOE OSTI2025

Deep Learning–Assisted Multiobjective Optimization of Geological CO 2 Storage Performance under Geomechanical Risks

In geological CO 2 storage, designing the optimal well control strategy for CO 2 injection to maximize CO 2 storage while minimizing the associated geomechanical risks is not trivial. This challenge arises due to pressure buildup, CO 2 plume migration, the highly nonlinear nature of geomechanical responses to rock-fluid interaction, and the high computational cost associated with coupled flow and geomechanics simulations. In this paper, we introduce a novel optimization framework to address these challenges. The optimization problem is formulated as follows: maximize total CO 2 storage while minimizing geomechanical risks by adjusting the injection schedules within bounded constraints. The geomechanical risks are primarily driven by injection-induced pressure build-up, which is characterized by ground displacement and the induced microseismicity. We used the Fourier neural operator (FNO)-based deep learning model to construct surrogate models, replacing the time-consuming coupled flow and geomechanics simulations for evaluating the aforementioned objective functions. The developed surrogate models have been incorporated into a multiobjective optimization framework through a genetic algorithm to reduce the computational burden. The proposed optimization framework reduces the computational cost from approximately 2,400 hours, when using objective function evaluations based on physics-based simulations, to around 20 minutes. A set of Pareto-optimal solutions of the proposed workflow yields nontrivial optimal decisions, reducing the microseismicity potential and the vertical displacement. This Pareto front highlights the optimal trade-offs between CO 2 storage amount, safety, and ground displacement, emphasizing the need for careful optimization and management of injection strategies to achieve a balanced outcome. The novelty of this work is twofold. First, we demonstrate the importance of incorporating the minimization of the geomechanical risks as objective functions into the CO 2 storage optimization workflow to mitigate the potential risk of induced microseismicity and ground displacement. Second, we leverage the FNO-based surrogate models to optimize a real-field CO 2 storage operation.

42 ENGINEERING↗
DOE OSTI2024

Physics-based modeling and data analytics [Slides]

This presentation contains a summary of ongoing work within the physics-based modeling and data analytics work package within the Nuclear Materials Discovery and Qualification initiative (NMDQi). Topics include work on MOOSE-based crystal plasticity, molecular dynamics modeling of recombination in metals and alloys, the MOOSE Stochastic Tools Module, and machine learning and atomistic modeling to predict thermo-kinetic properties of nuclear structural materials.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Expanding the representation of aerosol, cloud, and precipitation processes with graph network-based simulators

We explored a novel framework for simulating the small-scale processes that drive the evolution of aerosol, cloud, and precipitation particles, which are a critical gap in the predictive understanding of weather and climate. Particle-based methods have emerged as an effective tool for modeling aerosol-cloud-precipitation interactions, but existing particle-based models are computationally too expensive to simulate the large domains relevant for the atmosphere or to represent the full suite of relevant processes. The lack of a comprehensive and efficient reference model is a critical bottleneck in our understanding of cloud and precipitation processes and our ability to parameterize these processes for regional- and global-scale simulations. To address this need, we explored an approach to accelerate and expand particle-based models using a new machine learning approach, graph network-based simulators (GNS). Rather than modeling the evolution of the system by numerically integrating continuity equations, the GNS represents dynamics through learned message passing. Our aim was to develop fast and accurate surrogate models for particle-based simulations. We explored applying GNS to simulate cloud droplet transport, growth, and evaporation under turbulent conditions, but we found the GNS over-smoothed the simulations. We then applied the GNS to simulate aerosol dynamics through gas condensation and found the GNS was able to reproduce the benchmark, physics-based simulation with high accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Improving the Freight Productivity of a Heavy-Duty, Battery Electric Truck by Intelligent Energy Management

This project aimed to enhance the range and reduce the operating costs of battery electric Class 8 trucks traveling over 250 miles daily. This was achieved through the development and implementation of an intelligent-Energy Management System (i-EMS) that leverages vehicle and operations data, physics-aware machine learning algorithms, and vehicle-to-cloud (V2C) connectivity. The project hypothesized that advanced machine learning algorithms and real-time data analytics could significantly improve the energy efficiency and range of these trucks. Key objectives included developing a physics-aware machine learning algorithm, implementing an i-EMS with V2C connectivity and physics-aware spatial data analytics (PSDA), and validating the system’s effectiveness with fleet partners HEB Companies and Murphy Logistics. Extensive data collection from vehicle operations, including vehicle characteristics, road conditions, and payload, was conducted. A machine learning algorithm was developed to predict energy consumption and enable proactive decision-making. The i-EMS was implemented on two Volvo VNR BEVs, with operators receiving charging and routing recommendations. Charging stations were installed at depot locations in Texas and Minnesota, with an additional on-route charger in Minnesota. Significant findings included a 14% range improvement for Murphy Logistics on a highway-driving eco-route and a 22% range improvement for HEB Companies on a city-driving eco-route. The i-EMS utilized rule-based methods and physics-based algorithms to predict and reduce energy consumption, with real-time monitoring and analysis through V2C connectivity enabling proactive decision-making. The project demonstrated the feasibility and economic viability of battery electric Class 8 trucks for long-haul operations, showcasing the potential of physics-aware machine learning in optimizing energy management. The successful implementation of the i-EMS in real-world scenarios validates its practical application and effectiveness, paving the way for the widespread adoption of battery electric vehicles in the freight transportation industry.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Physics-Informed Machine Learning Model for Ceramic Matrix Composite Creep

A physics-informed recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear, time-dependent constitutive behavior of ceramic matrix composites (CMCs) driven by matrix damage and constituent creep at the microscale. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the high-fidelity generalized method of cells (HFGMC) approach which calls appropriate creep and damage models for each of the constituents. This coupling permits simulating the nonlinear behavior of CMCs based on constituent response at the microscale along with microstructural features such as fiber and porosity volume fraction and fiber radius. The microscale repeating unit cell is loaded under creep fatigue conditions to replicate the material loading experienced in a turbine engine. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input stress sequence, temperature, and microstructural features, the resulting strain history response while satisfying physical constraints related to creep rate, isochoric inelastic deformation, and strain energy density. The trained surrogate model is shown to effectively match the strain history over quantified distributions of microstructural features and relevant loading regimes and temperatures. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore, the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex microstructures, nonlinear time-dependent material response, and under non-monotonic loading conditions.

ceramic matrix composites↗
DOE OSTI2024

Anomaly detection for cyber-physical systems

An anomaly detector is configured to construct cyber and/or physical features comprising information configured to characterize the cyber and/or physical state of a cyber-physical system. The physical features may be based on physical and/or physics-based relationships between a plurality of physical state attributes. A health of the cyber-physical system may be based on an error between estimates of one or more of the physical state attributes and measurements of the one or more physical state attributes. The relationships may be incorporated into machine learning membership functions used to classify cyber and/or physical behavior of the system.

Rieger, Craig G.↗