Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Operator learning”

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.

At least 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Safety-Related Instrumentation and Control Pilot Upgrade (Initial Scoping Phase Implementation Report)

This research report (1) describes the process followed and products developed during the SR I&C Pilot Project Initial Scoping Phase, and (2) captures lessons learned. Exelon Generation and LWRS collaborated to develop a Digital Transformation Strategy as part of a larger Advanced Concept of Operations. The proposed SR I&C Pilot Upgrade provides a foundation stone for this Digital Transformation that will improve plant safety, reliability, and operational performance while lowering plant Total Cost of Ownership (TCO). Initial Scoping Phase activities for this Pilot Project have been performed in accordance with industry processes that have been adapted to better support digital upgrades. These processes include IP-ENG-001, Standard Design Process (SDP), NISP-EN-04, Standard Digital Engineering Process (SDEP), and Electric Power Research Institute (EPRI) Report 3002011816, Digital Engineering Guide (DEG). Completing Initial Scoping Phase Engineering and Operations, Licensing, and Project Management Activities was necessary to sufficiently bound the scope, schedule, and estimated cost of the Project to enable utility management to authorize moving into the Conceptual Design Phase. A significant finding of the Business Case Analysis (BCA) methodology developed and applied as part of this effort was that the growth rate of material costs for sustaining the operation of obsolete SR I&C equipment is accelerating. This directly contributed to the Project Economic Analysis created to justify continuing the Project. Project Initial Scoping Phase lessons learned have also been captured to assist the larger industry in understanding the Digital Transformation Strategy and SR I&C Pilot Project Initial Scoping Phase efforts. This is in keeping with the public/private partnership that has been established between the Department of Energy (DOE) and Exelon for this effort with engagement from the NRC. By addressing first-of-a-kind (FOAK) risks and capturing lessons learned, the SR I&C Pilot Upgrade Project addresses technical, regulatory, and business risks to enable subsequent implementers of similar upgrade.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Safety-Related Instrumentation & Control Pilot Upgrade Initiation Phase Implementation Report

This research report (1) describes the process followed and products developed during the SR I&C Pilot Project Initial Scoping Phase, and (2) captures lessons learned. Exelon Generation and LWRS collaborated to develop a Digital Transformation Strategy as part of a larger Advanced Concept of Operations. The proposed SR I&C Pilot Upgrade provides a foundation stone for this Digital Transformation that will improve plant safety, reliability, and operational performance while lowering plant Total Cost of Ownership (TCO). Initial Scoping Phase activities for this Pilot Project have been performed in accordance with industry processes that have been adapted to better support digital upgrades. These processes include IP-ENG-001, Standard Design Process (SDP) [Reference 2], NISP-EN-04, Standard Digital Engineering Process (SDEP) [Reference 3], and Electric Power Research Institute (EPRI) Report 3002011816, Digital Engineering Guide (DEG). Completing Initial Scoping Phase Engineering and Operations, Licensing, and Project Management Activities was necessary to sufficiently bound the scope, schedule, and estimated cost of the Project to enable utility management to authorize moving into the Conceptual Design Phase. A significant finding of the Business Case Analysis (BCA) methodology developed and applied as part of this effort was that the growth rate of material costs for sustaining the operation of obsolete SR I&C equipment is accelerating. This directly contributed to the Project Economic Analysis created to justify continuing the Project. Project Initial Scoping Phase lessons learned have also been captured to assist the larger industry in understanding the Digital Transformation Strategy and SR I&C Pilot Project Initial Scoping Phase efforts. This is in keeping with the public/private partnership that has been established between the Department of Energy (DOE) and Exelon for this effort with engagement from the NRC. By addressing first-of-a-kind (FOAK) risks and capturing lessons learned, the SR I&C Pilot Upgrade Project addresses technical, regulatory, and business risks to enable subsequent implementers of similar upgrades.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Generalization of Deep-Learning Models for Classification of Local Distance Earthquakes and Explosions across Various Geologic Settings

Although accurately classifying signals from earthquakes and explosions at local distance (<250 km) remains an important task for seismic network operations, the growing volume of available seismic data presents a challenge for analysts using traditional source discrimination techniques. In recent years, deep-learning models have proven effective at discriminating between low-magnitude earthquakes and explosions measured at local distances, but it is not clear how well these models are capable of generalizing across different geological settings. To address the issue of generalization between regions, we train deep-learning models (convolutional neural networks [CNNs]) on time–frequency representations (scalograms) of three-component earthquake and explosion signals from eight different regions in the continental United States. We explore scenarios where models are trained on data from all regions, individual regions, or all but one region. We find that although CNN models trained on individual regions do not necessarily generalize well across different settings, models trained on multiple regions that include diverse path coverage generalize to new regions, with station-level accuracy of up to 90% or more for data sets from unseen regions. In general, CNN-based discrimination models significantly outperform models based on uncorrected P/S ratio (measured in the 10–18 Hz frequency band), even when CNN models are tested on data from entirely unseen regions.

58 GEOSCIENCES↗
DOE OSTI2016

The DOE Unreviewed Safety Question Process, Addressing New Information For Credible Nuclear Accidents

The Department of Energy (DOE) Unreviewed Safety Question (USQ) process is in use for hazardous nuclear facilities operated within the DOE nuclear complex. DOE, which is the federal nuclear safety regulator for its nuclear facilities, requires that each nuclear facility have a Documented Safety Analysis that defines the controls for each credible accident based on a detailed accident analysis. The DOE USQ process provides key mechanisms for formally identifying to the regulator potential accident analysis issues at operating nuclear facilities including those that stem from emergent or new information on hazards. The DOE USQ process provides for formal evaluation of those emergent issues and for determining the need for formal regulator (DOE) review and approval of any resulting immediate or long-term actions. Regarding the March 2011 accident at the Fukushima Daiichi Nuclear Power Station, lessons learned on the evaluation and disposition of new information have been noted by the Institute of Nuclear Power Operations (INPO) and the National Research Council. These organizations noted that: - when new information indicates the potential for conditions that could significantly reduce safety margins or exceed current design assumptions, a timely, formal, and comprehensive assessment of the potential for substantial consequences should be conducted, and - if the new information analysis results in substantial changes to the risk profile or could impact the function of important safety systems, then compensatory actions or countermeasures need to be established without delay. The objective of this paper is to raise awareness regarding the salient requirements and guidance of the DOE USQ process used at DOE's operating nuclear facilities that bear on handling of emergent or new information on hazards and that address the lessons learned noted above by INPO and the National Research Council. There is no analysis or intent to make any implications regarding how use of the DOE USQ process might have affected events at Fukushima. The DOE USQ process, when applied as intended at DOE nuclear facilities, addresses lessons learned identified by INPO and the National Research Council regarding use of emergent or new information on hazards. The DOE USQ process ensures a timely, formal, and comprehensive assessment of the potential for substantial consequences resulting from new information on hazards. When the new information analysis results in substantial changes to the risk profile or shows an impact to the function of important safety systems, the DOE USQ process calls for compensatory actions or countermeasures to be established in a timely manner. The DOE USQ process ensures a formal evaluation by the regulator and approval of the planned actions addressing the vulnerabilities made know by new information on hazards. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

Machine Learning for Power System Disturbance and Cyber-attack Discrimination

Power system disturbances are inherently complex and can be attributed to a wide range of sources, including both natural and man-made events. Currently, the power system operators are heavily relied on to make decisions regarding the causes of experienced disturbances and the appropriate course of action as a response. In the case of cyber-attacks against a power system, human judgment is less certain since there is an overt attempt to disguise the attack and deceive the operators as to the true state of the system. To enable the human decision maker, we explore the viability of machine learning as a means for discriminating types of power system disturbances, and focus specifically on detecting cyber-attacks where deception is a core tenet of the event. We evaluate various machine learning methods as disturbance discriminators and discuss the practical implications for deploying machine learning systems as an enhancement to existing power system architectures.

cyber-attack↗
DOE OSTI2020

Using Machine Learning to Predict Future Temperature Outputs in Geothermal Systems

Optimizing the power output, and economic value, of geothermal power plants over decades of operation is a major challenge in renewable energy. Optimizing the output requires the ability to predict the mass flow rates and the output temperatures of production wells based on the inputs of injection wells, as well as the time history of the system. Machine Learning (ML) that incorporates the known physics of geothermal systems is one possible solution to this challenge. In this work, we explore the ability of ML algorithms to predict future temperature outputs based on historical data. Considering the challenges with obtaining an empirical dataset from field data that is large enough to enable reliable ML, we propose an alternate approach: developing a high-fidelity reservoir model and using computational resources to build a dataset that enables ML. As a first step towards achieving this goal, we present preliminary results from applying ML to predict the temperature timeseries of simple modeled geothermal systems. We describe the application of relevant state-of-the-art ML approaches, such as the Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNN), to extract temporal structures in the model data. We assess the accuracy of the forecasts we obtain, compare the selected approaches, and share the lessons learned that would inform the process of training and utilizing ML algorithms for larger and more complex geothermal systems.

GEOTHERMAL ENERGY↗
DOE OSTI2012

Adapting Dismantling and Decommissioning Strategies to a Variety of Nuclear Fuel Cycle Facilities - 12237

AREVA has accumulated over 20 years of experience in managing and operating fuel cycle facilities Decontamination and Decommissioning (D and D) projects of many different types and a variety of scales, both as facility owner (at La Hague for example) and as prime contractor to external customers such as the French Atomic Energy Commission (at Marcoule). A specific Business Unit was created in 2008 to capitalize on this experience and to concentrate - in one division - the specific skills required to be successful and cost effective in decommissioning projects. Indeed one of the key lessons learned in the past decades is that decommissioning is a significantly different business as compared to normal operations of a nuclear facility. Almost all the functions of a project need to be viewed from a different angle, challenged and adapted consequently in order to optimize costs and schedule. Three examples follow to illustrate the point: Safety management needs to take into account the ever changing configuration of a plant under D and D (a quite new situation for the authorities). Production of waste is significantly different in term of volume, activities, conditioning and disposal path. Technology is important but technical issues are often less critical than good management and planning. Further examples and lessons learned are developed through reviewing the projects experience basis. AREVA has a long and vast experience in the cleanup and dismantling of a number of very large and complex nuclear facilities. This effort focused initially on AREVA's own plants and is expanding now to other customers. The setup of a specific Business Unit in 2008 to takeover this business allowed concentration of the skills and the lessons learned in a dedicated division so as to provide the best means to optimize safety, performance, costs and schedules. Indeed transitioning from operations to D and D of a nuclear facility is a quantum leap. The assistance from specialized teams can bring significant cost savings. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2018

Bradwell - The first UK Nuclear Site to Enter Care and Maintenance - 18152

Magnox Ltd, a Cavendish Fluor company, is currently decommissioning twelve nuclear sites on behalf of the UK Nuclear Decommissioning Authority (NDA). Ten of these sites are former Power Stations; the other two are closed Research and Development facilities. An overall strategy for decommissioning the Magnox sites has been agreed between Magnox and the NDA. For all but one of these sites the decommissioning strategy involves an extended quiescent period, known as Care and Maintenance (C and M), during which remaining radiological hazards reduce naturally through radioactive decay. After this quiescent period the sites will be restored to an agreed end state through further decommissioning and clearance work. Sites in C and M will not be permanently manned. They will be passively safe such that prompt action will not be required in response to an alarm or fault. Preparing a nuclear site for C and M involves several inter-related strands of work including definition of the intended physical configuration of the site during C and M (the C and M entry state), establishing a safety case to support that configuration, carrying out the physical works needed to deliver the C and M entry state, preparing arrangements and a team to manage the site during C and M and consolidating the knowledge and information needed to support C and M and final clearance of the site. To enter C and M there needs to be a carefully controlled transition of site, personnel and management system into the agreed C and M configuration. Bradwell, a site on the east coast of England, was selected as part of the overall decommissioning strategy for 'early' entry into C and M; Bradwell is scheduled to enter C and M in late 2018, several years in advance of the next scheduled site, with the intent of carrying learning forward from Bradwell to the subsequent sites. Bradwell is now in the final stages of preparation for C and M. Decommissioning commenced on completion of defueling in 2005. A clearly defined C and M entry state was established early in decommissioning and, through interaction with Regulators and internal and external stakeholders, developed as a shared target, thus providing certainty to the scope of the overall decommissioning project. The site has subsequently been systematically decommissioned to meet this target C and M entry state. All legacy waste has been retrieved and packaged into robust disposal containers, the reactor buildings have a new weather envelope, and much of the site is empty space with concrete hardstanding where facilities used to exist and bare rooms where plant used to operate. The remaining radiological and environmental hazards are not significant. During C and M, which is anticipated to last for 70 years, Bradwell will be managed remotely without the requirement for personnel to be present on site, with the possible exception of an ongoing security presence when the site first enters C and M. In terms of UK decommissioning, many of the projects undertaken at Bradwell were first of a kind. The company operates under a programmed organisational and delivery model, which will enable innovation and learning from Bradwell to be carried forward across the whole Magnox fleet. In addition to decommissioning tools and techniques, processes to manage decommissioning, optimise the C and M entry state to reduce the burden on the UK taxpayer and to transition a site into C and M have been developed. This, in addition to taking people from Bradwell and seeding them into Magnox and the broader UK nuclear industry, should help to provide long term cost savings and delivery efficiencies across the entire NDA estate. This paper describes the journey of Bradwell Site through decommissioning and into C and M, highlighting the innovation and challenges that have contributed to the success of delivering the first UK nuclear site into Care and Maintenance. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

An Experimental Investigation of Students’ Learning Effects When Using a Simplified Nuclear Simulator

Securing enough data has been a main challenge in human reliability analysis (HRA). Many researchers and institutes have made a lot of efforts for collecting HRA data to produce reasonable human error probabilities (HEPs) as well as reduce the uncertainty of HRA quantification. Representatively, U.S. Nuclear Regulatory Commission (U.S. NRC), Korea Atomic Energy Research Institute (KAERI) and Idaho National Laboratory (INL) have led lots of empirical research regarding the HRA data collection. The U.S. NRC and KAERI have mainly carried out full-scope simulator research collecting HRA data through experiments using full-scope simulators with actual operators. In contrast, INL has experimentally collected the data using simplified simulators and student operators. INL has proposed the Simplified Human Error Experimental Program (SHEEP) framework to complement full-scope data collection efforts by suggesting a way to infer full-scope data based on experimental data collected from students operating simplified simulators, specifically the Rancor Microworld Simulator (Rancor) and the Compact Nuclear Simulator (CNS). The aim of the SHEEP framework is to lower the entry point for collecting useful HRA data by securing large sample sizes at a reasonable amount of cost and labor while also guaranteeing a high degree of freedom when designing experiments. The authors’ previous research investigated whether data collected from the SHEEP framework could support a representative full-scope study. Besides, human performance differences between professional and student operators when using Rancor and CNS have been analyzed to understand the lack of fidelity of the simplified simulators and student operators within the SHEEP study. As a follow up research, this study experimentally investigates students’ learning effects and the performance trends over a certain period when using Rancor. This study aims to find out 1) how much training or education is required to collect HRA data from non-experts (i.e., students) when using Rancor and 2) how much differences there are in human performance measures between students and professional operators. In this study, a longitudinal experiment is developed. The four experiment trials with two weeks interval are carried out for sixteen undergraduate students majoring nuclear engineering at Chosun University. Totally four scenarios randomly selected from ten Rancor scenarios are used in each experiment trial. Four human performance measurements (i.e., workload, situation awareness, time and error) are considered in the experiment. Lastly, the trend of students’ performance is compared with operator data having been collected from the previous experiment.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2017

Integrated Multi-Scale Data Analytics and Machine Learning for the Distribution Grid and Building-to-Grid Interface

This white paper introduces the application of advanced data analytics to the modernized grid. In particular, we consider the field of machine learning and where it is both useful, and not useful, for the particular field of the distribution grid and buildings interface. While analytics, in general, is a growing field of interest, and often seen as the golden goose in the burgeoning distribution grid industry, its application is often limited by communications infrastructure, or lack of a focused technical application. Overall, the linkage of analytics to purposeful application in the grid space has been limited. In this paper we consider the field of machine learning as a subset of analytical techniques, and discuss its ability and limitations to enable the future distribution grid and the building-to-grid interface. To that end, we also consider the potential for mixing distributed and centralized analytics and the pros and cons of these approaches. Machine learning is a subfield of computer science that studies and constructs algorithms that can learn from data and make predictions and improve forecasts. Incorporation of machine learning in grid monitoring and analysis tools may have the potential to solve data and operational challenges that result from increasing penetration of distributed and behind-the-meter energy resources. There is an exponentially expanding volume of measured data being generated on the distribution grid, which, with appropriate application of analytics, may be transformed into intelligible, actionable information that can be provided to the right actors – such as grid and building operators, at the appropriate time to enhance grid or building resilience, efficiency, and operations against various metrics or goals – such as total carbon reduction or other economic benefit to customers. While some basic analysis into these data streams can provide a wealth of information, computational and human boundaries on performing the analysis are becoming significant, with more data and multi-objective concerns. Efficient applications of analysis and the machine learning field are being considered in the loop.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Detecting Masquerade Attacks in Controller Area Networks Using Graph Machine Learning

Modern vehicles rely on a myriad of electronic control units (ECUs) interconnected via controller area networks (CANs) for critical operations. Despite their ubiquitous use and reliability, CANs are susceptible to sophisticated cyberattacks, particularly masquerade attacks, which inject false data that mimic legitimate messages at the expected frequency. These attacks pose severe risks such as unintended acceleration, brake deactivation, and rogue steering. Traditional intrusion detection systems (IDS) often struggle to detect these subtle intrusions due to their seamless integration into normal traffic. This paper introduces a novel framework for detecting masquerade attacks in the CAN bus using graph machine learning (ML). We hypothesize that the integration of shallow graph embeddings with time series features derived from CAN frames enhances the detection of masquerade attacks. We show that by representing CAN bus frames as message sequence graphs (MSGs) and enriching each node with contextual statistical attributes from time series, we can enhance detection capabilities across various attack patterns compared to using graph-based features only. Our method ensures a comprehensive and dynamic analysis of CAN frame interactions, improving robustness and efficiency. Extensive experiments on the ROAD dataset validate the effectiveness of our approach, demonstrating statistically significant improvements in the detection rates of masquerade attacks compared to a baseline that uses graph-based features only as confirmed by Mann-Whitney U and Kolmogorov-Smirnov tests (p < 0.05) .

Marfo, William [Univ. of Texas, El Paso, TX (Unite↗
DOE OSTI2022

Storage Futures Study: Key Learnings for the Coming Decades

The Storage Futures Study (SFS) is a multiyear research project that explored the role and impact of energy storage in the evolution and operation of the U.S. power sector. The SFS examined the potential impact of energy storage technology advancement on the deployment of utility-scale storage and the adoption of distributed storage, and the implications for future power system infrastructure investment and operations. The research findings and supporting data were published across a series of six reports, culminating in the final, seventh publication that draws upon findings from across the study, previous work, and additional analysis to identify eight key learnings about the coming decades. This presentation is from an NREL webinar to discuss the eight key learnings.

decarbonization↗
DOE OSTI2025

Deploying and Operating CephFS for Scientific Applications at Fermilab

Fermilab has been running a Ceph cluster in production for several years to support high-throughput scientific computing. Our primary use case is CephFS, which serves interactive data analysis workloads, with growing interest in using RGW for scalable object storage of scientific datasets. In this talk, we'll share lessons learned from successfully deploying and maintaining our Ceph cluster with cephadm, including challenges faced, performance tuning, and operational practices. We'll also present custom tools we've developed to streamline monitoring and management and discuss how Ceph fits into our broader storage architecture for large-scale scientific research.

Peisker, Alison [Fermilab]↗
DOE OSTI2022

Deep reinforcement learning based optimization for a tightly coupled nuclear renewable integrated energy system

New ways to integrate energy systems to maximize efficiency are being sought to meet carbon emissions goals. Nuclear-renewable integrated energy system (NR-IES) concepts are a leading solution that couples a nuclear power plant with renewable energy, hydrogen generation plants, and energy storage systems, such that thermal and electrical power are dispatchable to fulfill grid-flexibility requirements while also producing hydrogen and maximizing revenue. Here, this paper introduces a deep reinforcement learning (DRL)-based framework to address the complex decision-making tasks for NR-IES. The objective is to maximize revenue by generating and selling hydrogen and electricity simultaneously according to their time-varying prices while keeping the energy flow in the subsystems in balance. A Python-based simulator for a NR-IES concept has been developed to integrate with OpenAI Gym and Ray/RLlib to enable an efficient and flexible computational framework for DRL research and development. Three state-of-the-art DRL algorithms have been investigated, including two-delayed deep deterministic policy gradient (TD3), soft-actor critic (SAC), proximal policy optimization (PPO), to illustrate DRL’s superiority for controlling NR-IES by comparing it with a conventional control approach, particle swarm optimization (PSO). In this effort, PPO has shown more-stable performance and also better generalization capability than SAC and TD3. Comparisons with PSO have demonstrated that, on average, PPO can achieve 13.9% more mean episode returns from the training process and 29.4% more mean episode returns from the testing process when different hydrogen-production targets are applied.

08 HYDROGEN↗
DOE OSTI2022

Scale-up of microwave-assisted, continuous flow, liquid phase reactors: Application to 5-Hydroxymethylfurfural production

Microwave (MW) technology can be powerful for the electrification and intensification of chemical manufacturing. However, very few examples of scaled MW processes exist. In this work, we build a scaled, MW-assisted, continuous flow reactor for the processing of liquid phase chemistries with specific application to 5-hydroxymethylfurfural (HMF) production. Here, we demonstrate a corresponding computational fluid dynamics model to simulate the reactor’s temperature profile and performance, both of which are in good agreement with experiments. We construct a surrogate model to relate operating parameters to performance for guiding experiments, without demanding simulations, via active learning. Heat recirculation is demonstrated in this scaled reactor, further extending its scale and reducing the energy demand. An HMF yield of ~55 % and a productivity of 0.1 kg/hr, 8x higher than any other reactor, at a flowrate >20x than prior work, are demonstrated while maintaining energy efficiency of >98 %. A basic economic analysis estimates a $1.85/kg cost of HMF from fructose and >60 % reduction in CO 2 emissions than a conventional system without considering the impact of green electricity. We demonstrate that MW technology is well-applied to systems larger than the laboratory scale, and strategies to further reduction in cost and CO 2 are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Development of a plug-and-play anti-noise module for fault diagnosis of rotating machines in nuclear power plants

The health of rotating machines is crucial to the stable operation and safety of nuclear power plants. However, research on machine learning-based fault diagnosis of rotating machines in the nuclear industry is still in its infancy. The signal noise generated in the plant may negatively affect the effectiveness of the analysis. In this paper, a plug-and-play anti-noise machine learning module is proposed to fill the knowledge and capability gap. The modules are loaded into a convolutional neural network called deep residual network (ResNet) to obtain a new model with noise reduction capability. The basic idea is that the module is able to identify noise features and include them in the subsequent analysis, effectively filtering noise at the feature level of the network. Nine variants of the new model are compared with the original ResNet as well as four classical machine learning models to test the effectiveness of the module and to examine the impact of the module's loading modes on the performance of the new model. Finally, this research helps facilitate the application of machine learning in the plant noise environment.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2015

Projected metastable Markov processes and their estimation with observable operator models

The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗