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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 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Predicting lake surface water phosphorus dynamics using process-guided machine learning

Phosphorus (P) loading to lakes is degrading the quality and usability of water globally. Accurate predictions of lake P dynamics are needed to understand whole-ecosystem P budgets, as well as the consequences of changing lake P concentrations for water quality. However, complex biophysical processes within lakes, along with limited observational data, challenge our capacity to reproduce short-term lake dynamics needed for water quality predictions, as well as long-term dynamics needed to understand broad scale controls over lake P. Here we use an emerging paradigm in modeling, process-guided machine learning (PGML), to produce a phosphorus budget for Lake Mendota (Wisconsin, USA) and to accurately predict epilimnetic phosphorus over a time range of days to decades. In our implementation of PGML, which we term a Process-Guided Recurrent Neural Network (PGRNN), we combine a process-based model for lake P with a recurrent neural network, and then constrain the predictions with ecological principles. We test independently the process-based model, the recurrent neural network, and the PGRNN to evaluate the overall approach. The process-based model accounted for most of the observed pattern in lake P; however it missed the long-term trend in lake P and had the worst performance in predicting winter and summer P in surface waters. The root mean square error (RMSE) for the process-based model, the recurrent neural network, and the PGRNN was 33.0 μg P L -1 , 22.7 μg P L -1 , and 20.7 μg P L -1 , respectively. All models performed better during summer, with RMSE values for the three models (same order) equal to 14.3 μg P L -1 , 10.9 μg P L -1 , and 10.7 μg P L -1 . Although the PGRNN had only marginally better RMSE during summer, it had lower bias and reproduced long-term decreases in lake P missed by the other two models. For all seasons and all years, the recurrent neural network had better predictions than process alone, with root mean square error (RMSE) of 23.8 μg P L -1 and 28.0 μg P L -1 , respectively. The output of PGRNN indicated that new processes related to water temperature, thermal stratification, and long term changes in external loads are needed to improve the process model. By using ecological knowledge, as well as the information content of complex data, PGML shows promise as a technique for accurate prediction in messy, real-world ecological dynamics, while providing valuable information that can improve our understanding of process.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Systematic modification of functionality in disordered elastic networks through free energy surface tailoring

A combined machine learning–physics–based approach is explored for molecular and materials engineering. Specifically, collective variables, akin to those used in enhanced sampled simulations, are constructed using a machine learning model trained on data gathered from a single system. Through the constructed collective variables, it becomes possible to identify critical molecular interactions in the considered system, the modulation of which enables a systematic tailoring of the system’s free energy landscape. To explore the efficacy of the proposed approach, we use it to engineer allosteric regulation and uniaxial strain fluctuations in a complex disordered elastic network. Its successful application in these two cases provides insights regarding how functionality is governed in systems characterized by extensive connectivity and points to its potential for design of complex molecular systems.

42 ENGINEERING↗
DOE OSTI2020

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows, but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long short-term memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data and the trained model can be retrained effectively due to power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging AI-friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

42 ENGINEERING↗
DOE OSTI2024

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

NASA's Biosentinel Mission: Lessons Learned and What's Next

In the last two years, two BioSentinel payloads were launched to space. The ISS mission launched in December 2021, and returned to the ground in August 2022 after successfully completing eight biological experiments while validating the different instruments. On the other hand, the deep space mission launched onboard Artemis I in November 2022, and is currently in a heliocentric orbit over 20 million kilometers away from the Earth. Even though all hardware subsystems were validated in deep space, the microfluidic subsystems experienced anomalies throughout the initial 6-month mission. The main goals of this presentation are (1) to present flight data from the deep space payload, including biology, fluidics, electronics, data processing, and mission operations, and (2) to discuss the lessons learned – what worked and what did not – from this unique complex mission, and how these lessons are aiding in the development of the Lunar Exploration Instrument for space biology Applications (LEIA) mission, launching to the lunar surface on a commercial lander in 2026. As of the writing of this abstract, the satellite continues to work nominally, communicating to Earth via the Deep Space Network (DSN) twice per week. Importantly, the mission received and extension to continue recording data on the deep space radiation environment on its way to solar maximum (i.e., higher probability of solar particle events). BioSentinel is supported by NASA Exploration Systems Development Mission Directorate (ESDMD).

BioSentinel↗
NASA NTRS1983

Ad Hoc modeling, expert problem solving, and R&T program evaluation

A simplified cost and time (SCAT) analysis program utilizing personal-computer technology is presented and demonstrated in the case of the NASA-Goddard end-to-end data system. The difficulties encountered in implementing complex program-selection and evaluation models in the research and technology field are outlined. The prototype SCAT system described here is designed to allow user-friendly ad hoc modeling in real time and at low cost. A worksheet constructed on the computer screen displays the critical parameters and shows how each is affected when one is altered experimentally. In the NASA case, satellite data-output and control requirements, ground-facility data-handling capabilities, and project priorities are intricately interrelated. Scenario studies of the effects of spacecraft phaseout or new spacecraft on throughput and delay parameters are shown. The use of a network of personal computers for higher-level coordination of decision-making processes is suggested, as a complement or alternative to complex large-scale modeling.

Silverman, B. G.↗
NASA NTRS2002

A Scalable, Out-of-Band Diagnostics Architecture for International Space Station Systems Support

The computational infrastructure of the International Space Station (ISS) is a dynamic system that supports multiple vehicle subsystems such as Caution and Warning, Electrical Power Systems and Command and Data Handling (C&DH), as well as scientific payloads of varying size and complexity. The dynamic nature of the ISS configuration coupled with the increased demand for payload support places a significant burden on the inherently resource constrained computational infrastructure of the ISS. Onboard system diagnostics applications are hosted on computers that are elements of the avionics network while ground-based diagnostic applications receive only a subset of available telemetry, down-linked via S-band communications. In this paper we propose a scalable, out-of-band diagnostics architecture for ISS systems support that uses a read-only connection for C&DH data acquisition, which provides a lower cost of deployment and maintenance (versus a higher criticality readwrite connection). The diagnostics processing burden is off-loaded from the avionics network to elements of the on-board LAN that have a lower overall cost of operation and increased computational capacity. A superset of diagnostic data, richer in content than the configured telemetry, is made available to Advanced Diagnostic System (ADS) clients running on wireless handheld devices, affording the crew greater mobility for troubleshooting and providing improved insight into vehicle state. The superset of diagnostic data is made available to the ground in near real-time via an out-of band downlink, providing a high level of fidelity between vehicle state and test, training and operational facilities on the ground.

Fletcher, Daryl P.↗
DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗
DOE OSTI2023

Point-particle drag, lift, and torque closure models using machine learning: Hierarchical approach and interpretability

Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest recently from the dispersed multiphase flow community. The robustness of neural models for this complex multibody problem is hindered by the availability of particle-resolved data. Here, the present work addresses this unavoidable limitation of data paucity by implementing two strategies: (1) by using a rotation and reflection equivariant neural network and (2) by pursuing a physics-based hierarchical machine learning approach. The resulting machine-learned models are observed to achieve a maximum accuracy of 85% and 96% in the prediction of neighbor-induced force and torque fluctuations, respectively, for a wide range of Reynolds number and volume fraction conditions considered. Furthermore, we pursue force and torque network architectures that provide universal prediction spanning a wide range of Reynolds number (0.25 ≤ Re ≤250) and particle volume fraction (0 ≤ φ ≤0.4). The hierarchical nature of the approach enables improved prediction of quantities such as streamwise torque, by going beyond binary interactions to include trinary interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

InversionNet3D: Efficient and Scalable Learning for 3-D Full-Waveform Inversion

Seismic full-waveform inversion (FWI) techniques aim to find a high-resolution subsurface geophysical model provided with waveform data. Some recent effort in data-driven FWI has shown some encouraging results in obtaining 2-D velocity maps. However, due to high computational complexity and large memory consumption, the reconstruction of 3-D high-resolution velocity maps via deep networks is still a great challenge. Here, in this article, we present InversionNet3D (InvNet3D), an efficient and scalable encoder–decoder network for 3-D FWI. The proposed method employs group convolution in the encoder to establish an effective hierarchy for learning information from multiple sources while cutting down unnecessary parameters and operations at the same time. The introduction of invertible layers further reduces the memory consumption of intermediate features during training and, thus, enables the development of deeper networks with more layers and higher capacity as required by different application scenarios. Experiments on the 3-D Kimberlina dataset demonstrate that InvNet3D achieves state-of-the-art reconstruction performance with lower computational cost and lower memory footprint compared to the baseline.

58 GEOSCIENCES↗
DOE OSTI2023

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Bayesian Analysis of TRISO Fuel: Quantifying Model Inadequacy, Incorporating Lower-Length-Scale Effects, and Developing Parallel Active Learning Capabilities

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel-cycle systems. This program has been providing engineering-scale support for the continued development of BISON, a high-fidelity, high-resolution fuel performance tool. Fuel behavior in nuclear reactors is governed by a complex network of mechanisms that interact with various other physics aspects in the reactor system. Any model developed to represent fuel behavior will likely be idealized, resulting in uncertainties when comparing their predictions against the observed data. In Fiscal Year (FY)-23, we initiated the Uncertainty Quantification (UQ) work by using Bayesian methods to establish a level of model trustworthiness and further improve it, with a particular emphasis on TRI-Structural isOtropic (TRISO) nuclear fuel. This year, we further expanded on that UQ work by investigating an approach to quantifying model inadequacy and accounting for lower-length scale (LLS) effects in TRISO silver (Ag) release modeling. Furthermore, we are implementing parallel active learning capabilities to reduce the computational cost (i.e., required computational resources and elapsed time) of performing UQ. Specifically, we utilized The Kennedy O’Hagan framework for Bayesian uncertainty quantification (KOH) to account for model inadequacy in TRISO Ag release predictions made by BISON. The KOH framework represents an improvement over the standard Bayesian framework used in FY-23. Explicitly accounting for model inadequacy in the Bayesian framework helps establish the level of experimental noise uncertainty in the Advanced Gas Reactor (AGR) data. We compared the inverse UQ results obtained from both the standard Bayesian and KOH frameworks in light of the AGR-2/3/4 data, and also compared the predictive UQ results obtained from these two frameworks in light of the AGR-1 data. Next, we investigated the impact of considering LLS effects in the Ag release simulations. We developed an expanded database of LLS simulated effective diffusivities for Ag, covering a wide range of microstructures and temperatures. Using this database, we developed a framework for incorporating LLS effects into the engineering-scale Ag release UQ. We developed both parametric and non-parametric approaches for bridging the length scales. We then investigated the inverse UQ results in light of the AGR-2/3/4 data and the predictive UQ results in light of the AGR-1 data, and compared the LLS-informed approach and the Arrhenius equation, which does not include microstructure information. Finally, we discussed implementing parallel active learning capabilities in the Multiphysics Object Oriented Simulation Environment (MOOSE)/BISON to reduce the computational cost (i.e., computational resources and elapsed time) of Bayesian UQ. For verification purposes, we first tested these new capabil ities on a species interaction problem. We then demonstrated them on the TRISO Ag release application, showing that parallel active learning capabilities can enhance the accuracy of UQ while also substantially reducing the computational cost in comparison to the reference methods developed in FY-23.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1988

Integration of symbolic and algorithmic hardware and software for the automation of space station subsystems

Expert systems that require access to data bases, complex simulations and real time instrumentation have both symbolic and algorithmic needs. Both of these needs could be met using a general purpose workstation running both symbolic and algorithmic codes, or separate, specialized computers networked together. The later approach was chosen to implement TEXSYS, the thermal expert system, developed by the NASA Ames Research Center in conjunction with the Johnson Space Center to demonstrate the ability of an expert system to autonomously monitor the thermal control system of the space station. TEXSYS has been implemented on a Symbolics workstation, and will be linked to a microVAX computer that will control a thermal test bed. The integration options and several possible solutions are presented.

Gregg, Hugh↗
NASA NTRS1990

A real time neural net estimator of fatigue life

A neural net architecture is proposed to estimate, in real-time, the fatigue life of mechanical components, as part of the Intelligent Control System for Reusable Rocket Engines. Arbitrary component loading values were used as input to train a two hidden-layer feedforward neural net to estimate component fatigue damage. The ability of the net to learn, based on a local strain approach, the mapping between load sequence and fatigue damage has been demonstrated for a uniaxial specimen. Because of its demonstrated performance, the neural computation may be extended to complex cases where the loads are biaxial or triaxial, and the geometry of the component is complex (e.g., turbopump blades). The generality of the approach is such that load/damage mappings can be directly extracted from experimental data without requiring any knowledge of the stress/strain profile of the component. In addition, the parallel network architecture allows real-time life calculations even for high frequency vibrations. Owing to its distributed nature, the neural implementation will be robust and reliable, enabling its use in hostile environments such as rocket engines. This neural net estimator of fatigue life is seen as the enabling technology to achieve component life prognosis, and therefore would be an important part of life extending control for reusable rocket engines.

Troudet, T.↗
NASA NTRS2003

Experiences with Testing the Largest Ground System NASA Has Ever Built

In the 1980s, the National Aeronautics and Space Administration (NASA) embarked upon a major Earth-focused program called Mission to Planet Earth. The Goddard Space Flight Center (GSFC) was selected to manage and develop a key component - the Earth Observing System (EOS). The EOS consisted of four major missions designed to monitor the Earth. The missions included 4 spacecraft. Terra (launched December 1999), Aqua (launched May 2002), ICESat (Ice, Cloud, and Land Elevation Satellite, launched January 2003), and Aura (scheduled for launch January 2004). The purpose of these missions was to provide support for NASA s long-term research effort for determining how human-induced and natural changes affect our global environment. The EOS Data and Information System (EOSDIS), a globally distributed, large-scale scientific system, was built to support EOS. Its primary function is to capture, collect, process, and distribute the most voluminous set of remotely sensed scientific data to date estimated to be 350 Gbytes per day. The EOSDIS is composed of a diverse set of elements with functional capabilities that require the implementation of a complex set of computers, high-speed networks, mission-unique equipment, and associated Information Technology (IT) software along with mission-specific software. All missions are constrained by schedule, budget, and staffing resources, and rigorous testing has been shown to be critical to the success of each mission. This paper addresses the challenges associated with the planning, test definition. resource scheduling, execution, and discrepancy reporting involved in the mission readiness testing of a ground system on the scale of EOSDIS. The size and complexity of the mission systems supporting the Aqua flight operations, for example, combined with the limited resources available, prompted the project to challenge the prevailing testing culture. The resulting success of the Aqua Mission Readiness Testing (MRT) program was due in no small measure to re-structuring the traditional programmatic and technical approach to a more efficient and robust program. Programmatically, it meant gaining the endorsement, commitment, and cooperation of the numerous subsystem element managers and other stakeholder organizations. Technically, it required an MRT program that was agile, could rapidly adapt to requirements changes, and was flexible in its overall approach. Furthermore, this paper addresses the following questions: 1. What are the key ingredients (e.g., test tools, organization) needed to conduct a successful MRT program? 2. What distinguishes EOS MRT from the traditional system testing approach? 3. Where should the focus of testing be since it is infeasible to test every element or subsystem? 4. How can MRT be applied effectively to other systems or missions? To provide answers to these questions, this paper relies heavily on real-life, hands-on experiences ("lessons learned") gained during mission readiness testing of the Terra ground system and, most recently, the Aqua and ICESat missions. Moreover, this paper explores how lessons learned were turned into lessons applied for the upcoming Aura mission. Although derived from the EOS missions, MRT techniques and strategies can be applied to enhance the testing of other missions.

Lehtonen, Ken↗
DOE OSTI2024

A Distributed Model Identification Algorithm for Multi-Agent Systems: Preprint

In this study, we investigate agent-based approach for system model identification with emphasis on power distribution system applications. Departing from conventional practices of relying on historical data for offline model identification, we adopt online update approach utilizing real-time data by employing the latest data points for gradient computation. This methodology offers advantages including a large reduction in the communication network's bandwidth requirements by minimizing the data exchanged at each iteration and enabling the model to adapt in real-time to disturbances. Furthermore, we extend our model identification process from linear frameworks to more complex non-linear convex models. This extension is validated through numerical studies demonstrating improved control performance for a synthetic IEEE test case.

data-driven control↗
DOE OSTI2023

Data for "Enhancing 2-Pyrone Synthase Efficiency by High-Throughput Mass-Spectrometric Quantification and In Vitro/In Vivo Catalytic Performance Correlation"

Engineering efficient biocatalysts is essential for metabolic engineering to produce valuable bioproducts from renewable resources. However, due to the complexity of cellular metabolic networks, it is challenging to translate success in vitro into high performance in cells. To meet such a challenge, an accurate and efficient quantification method is necessary to screen a large set of mutants from complex cell culture and a careful correlation between the catalysis parameters in vitro and performance in cells is required. In this study, we employed a mass-spectrometry based high-throughput quantitative method to screen new mutants of 2-pyrone synthase (2PS) for triacetic acid lactone (TAL) biosynthesis through directed evolution in E. coli. From the process, we discovered two mutants with the highest improvement (46 fold) in titer and the fastest kcat (44 fold) over the wild type 2PS, respectively, among those reported in the literature. A careful examination of the correlation between intracellular substrate concentration, Michaelis-Menten parameters and TAL titer for these two mutants reveals that a fast reaction rate under limiting intracellular substrate concentrations is important for in-cell biocatalysis. Such properties can be tuned by protein engineering and synthetic biology to adopt these engineered proteins for the maximum activities in different intracellular environments.

catalysis↗
DOE OSTI2025

Safe Physics-Informed Machine Learning for Dynamics and Control

This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques enhance the modeling and control of complex dynamical systems, ensuring safety and stability remains a critical challenge, especially in safety-critical applications like autonomous vehicles, robotics, medical decision-making, and energy systems. We explore various approaches for embedding and ensuring safety constraints, including structural priors, Lyapunov and Control Barrier Functions, predictive control, projections, and robust optimization techniques. Additionally, we delve into methods for uncertainty quantification and safety verification, including reachability analysis and neural network verification tools, which help validate that control policies remain within safe operating bounds even in uncertain environments. The paper includes illustrative examples demonstrating the implementation aspects of safe learning frameworks that combine the strengths of data-driven approaches with the rigor of physical principles, offering a path toward the safe control of complex dynamical systems.

Drgona, Jan↗