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DOE OSTI2025

MCNP® Code Version 6.3.1 Release Notes

The Monte Carlo N-Particle® (MCNP® ) code is a general-purpose, continuous-energy, generalized-geometry, time-dependent, radiation transport code developed by the MCNP development team. MCNP calculations provide predictive capabilities that can replace expensive or impossible-to-perform experiments. Specific application problems include simulations of experimental diagnostics, intrinsic radiation, radiation detection and measurement, criticality safety, nuclear threat reduction and response, radiation health protection, nuclear weapons effects, and nuclear forensics. This MCNP code, version 6.3.1, follows the MCNP6.3.0 version. Since the release of MCNP6.3.0, a variety of bug fixes and code enhancements have been completed for MCNP6.3.1. A few new features have also been added to this release to support both ongoing research and the release of the latest ENDF/B-VIII.1 nuclear data library. The MCNP code, version 6.3.1, theory and user input information is documented in MCNP® Code Version 6.3.1 Theory & User Manual, the build guidance for various platforms is documented in MCNP® Code Version 6.3.1 Build Guide, and the verification and validation testing for various application benchmark test suites is documented in MCNP® Code Version 6.3.1 Verification & Validation Testing.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Even Higher-Level Synthesis: An Exploration of AI Hardware Accelerators using HLS4ML

With the rise of artificial intelligence, the popularization of deep learning, and a constantly evolving industry, the demand for flexible and efficient tools has never been greater. As algorithms grow more complex, their runtime and energy consumption increase exponentially. Customized hardware accelerators, long used for specific mathematical operations, remain essential for managing modern applications' computational and power demands. Hardware accelerators can speed up complex computations by orders of magnitude, but their manual design and verification processes are often challenging and time-consuming. High-Level Synthesis (HLS) provides a solution by transforming high-level algorithm descriptions, typically written in C++ or SystemC, into synthesizable RTL suitable for hardware implementation. This approach reduces development time for RTL engineers while offering flexibility beyond what traditional handwritten RTL can provide. We extended this capability to the machine-learning domain with the open-source framework hls4ml, which allows neural networks trained in Python frameworks like Tensorflow or PyTorch to be synthesized into efficient hardware representations for the traditional FPGA and ASIC flows. This breakthrough addresses the growing need for reduced design turnaround and easy verification of ML hardware accelerators with low latency and power efficiency constraints. During this tutorial, we will demonstrate how Python complements HLS by simplifying the ML design process, bridging the gap between software and hardware development. Attendees will explore how we translate neural networks modeled in Python into fixed-point C++ models suitable for HLS workflows. We will dive into strategies like Value-Range Analysis and Quantization-Aware Training, which optimize these designs for deployment and evaluate their accuracy, power consumption, and energy efficiency. To exemplify these concepts, experts from Fermilab will share their experiences applying this technology to high-energy physics experiments, where real-time, low-latency processing is critical. Over the years, Fermilab engineers have demonstrated how deep neural networks, optimized for hardware using hls4ml, can meet the stringent requirements of trigger systems at the CERN Large Hadron Collider. These systems rely on rapid decision-making to process immense data volumes while retaining only the most relevant events for further analysis. The application of hls4ml has also been extended to innovative technologies like smart pixel arrays. These smart pixels integrate ML inference capabilities directly into sensor devices, enabling localized data processing at the pixel level. This approach drastically reduces the need to transmit raw data to external processing units, significantly decreasing power consumption and latency. By embedding neural networks within the pixel architecture, the smart pixels can identify and prioritize relevant data in real time, providing a highly efficient solution for edge computing in scenarios such as particle detectors and imaging systems. Fermilab's work highlights the potential of hardware-accelerated ML in scenarios where both speed and power efficiency are mission-critical. Through this tutorial, attendees will gain valuable insights into the challenges and solutions of deploying ML in hardware. Understanding how HLS and hls4ml streamline the development of neural network-based hardware accelerators is fundamental for the industry's future. Participants will learn how these technologies are shaping the future of AI and scientific computing.

Di Guglielmo, Giuseppe [Fermilab]↗
DOE OSTI2025

Real-time neutron multiplicity and source localization for criticality safety during fuel debris removal

Advancing neutron detection and analysis techniques for complex radiation environments is an ongoing focus in nuclear instrumentation and monitoring. This proposal presents research and development of a generalized real-time neutron monitoring and analysis system, applicable to any detector capable of producing time-tagged neutron count data. While the work is demonstrated using the Neutron Multiplication Analysis Detector (NoMAD), a modular 15-tube helium-3 (He-3) array, due to its availability, spatial resolution, and flexible deployment, the methods developed are extensible to other systems, including organic scintillators and fast digital detectors. This research investigates two complementary analytical techniques for real-time characterization of neutron emitting sources: neutron multiplicity estimation based on the Hage-Cifarelli formalism and spatial localization using supervised machine learning applied to spatial count rate patterns. These methods are designed to operate under dynamic, evolving conditions such as fuel debris retrieval or reactor startup, where neutron-emitting material geometries may be partially unknown or changing over time. By integrating statistical neutron emission data with spatial localization, this research aims to develop and evaluate methods for real time neutron monitoring, source characterization, and material verification. Key contributions include implementation of a low-latency data pipeline for continuous neutron multiplicity analysis, development and validation of machine learning models for spatial inference, and experimental evaluation of system performance under variable measurement conditions. The outcomes are intended to support applications in nuclear safeguards, verification, emergency response, and reactor startup.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Advancements in NEAMS Tool Capabilities for Multiphysics Simulation of Fast Reactor Core Bowing and Identification of Validation Test Data

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves Multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Last year, thermal fluids and mechanics were coupled on a multi-assembly benchmark problem based on ABR-1000 design. This year, the reactor physics code Griffin was assessed for readiness of core bowing calculations. Preliminary integration of Griffin’s ring-heterogeneous model with thermal fluids and thermal mechanics solvers was performed. Specifically, thermal-mechanics and reactor physics were coupled for single- and multi-assembly problems, and reactor physics and subchannel methods were coupled for a single assembly model. Finally, the workflow of all three physics was preliminarily demonstrated on a single assembly model. Caveats and future development needed have been identified. To supplement the multiphysics demonstration, verification and assessment efforts of thermos-mechanical capabilities for modeling thermo-mechanical core bowing behavior were continued by analyzing IAEA Verification Problem 5 which includes radiation swelling and creep. Additionally, a small core reactor physics benchmark defined by Japan Atomic Energy Agency (JAEA) was performed to assess neutronics models for estimating reactivity feedback. Finally, Fast Flux Test Facility (FFTF) validation test data for core bowing phenomena has been identified and summarized, with a recommended path forward for validation once this capability is mature.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Code Coverage Status of the ARC Code DASSH-F

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DASSH-F serves as a steady state thermal hydraulic capability within the ARC system and replaces the SE2-ANL software that preceded it. This document identifies the set of test problems used to assess the code coverage for DASSH-F. The goal is to document what parts of the existing DASSH-F code are touched by the set of test problems and which are not. Because the verification work remains to be done on DASSH-F, one can assume that most of these issues will be resolved as part of that work. The code coverage analysis of DASSH-F was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DASSH-F. The code coverage tables are given for each submodule of DASSH-F. Because DASSH-F links to modules in DIF3D, some details on coverage changes to the DIF3D linked files is provided. As will be seen, most of the uncovered parts/files can be ignored because they are either for error message and debugging output or obviously not needed by DASSH-F today. Seven features of the DASSH-F code were identified to not be covered by the existing testing suite and thus additional verification test problems are suggested to fully cover these sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

High-Temperature Gas-Cooled Reactors Multiphysics Simulation Demonstration and Code Validation

This study presents a comprehensive benchmarking and verification effort of several thermal-hydraulic and multiphysics capabilities for high-temperature gas-cooled reactor applications. The first part of this effort focuses on the running-in verification of Griffin’s multiphysics capabilities, specifically for simulating the evolution of pebble-bed reactor cores from startup to equilibrium. Since Fiscal Year 2024, improvements and enhancements have been implemented in Griffin, including simplifying the process to specify streamlines and developing the online cross-section generation capability. In the absence of validation data, code-to-code comparisons are conducted with kugelpy, showing good agreement for integral quantities like k-eff predictions and predictions for maximum power density. However, accuracy issues are noted for more detailed quantities like the spatial distribution of fission rate densities which will require further work to address. The second part of this report presents an improved System Analysis Module (SAM) core channel model where the effects of cross flow are considered during the pressurized loss of forced cooling transient, resulting in an improved agreement of the predicted pebble temperature with respect to the predictions from the SAM 2D porous media model. Additionally, the wall channeling effect due to variable porosity at the near wall region of the core is also investigated. Furthermore, to demonstrate Griffin’s online cross-section generation capability, a Multiphysics simulation is performed by coupling Griffin to the SAM core channel model. In the third part of the report, as a part of the Organisation for Economic Co-operation and Development/Nuclear Energy Agency (OECD/NEA) thermal-hydraulic code validation benchmark activity for a high-temperature gas-cooled reactor, the High Temperature Test Facility (HTTF) is investigated first using the NekRS computational fluid dynamics (CFD) code to study the flow mixing phenomenon in the lower plenum of the facility. Then, code-to-code and code-to-data comparisons are performed for Test PG27, which is a pressurized conduction cooldown (PCC) test, using five different codes by six organizations from five countries. The different simulations show good agreements in terms of the general trend but there are differences in some results such as the peak temperatures of different regions and heat removal rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Theorems in Service of Sound Composition, Rapid Modeling and Scalable Analysis

This project extends the state of the art in formal verification modeling with modules and automatically checkable data-sharing patterns such that component modules can retain their assurance case when composed within a larger system. For users, smaller models make reasoning easier and help to ensure they accurately reflect text specifications. For automated methods, smaller models give exponential benefits for verification algorithm execution time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Determination of Scale Bar for AGHCF Metallography Data

The DOE Nuclear Energy Advanced Reactor Technologies (ART) Fast Reactor Program (FRP) has supported the development of several databases containing information on the safety performance of fast reactors, components, and fuels. This growing collection of legacy experimental data, operating data, and analysis is available online to registered users. Metallography data represents one of the most critical types of post-irradiation examination (PIE) data being collected, organized, and archived in several ART Fast Reactor Databases (https://frdb.ne.anl.gov), including the Metallic Fuels Irradiation & Physics Database (FIPD), Out-of-Pile Transient Database (OPTD), and TREAT (the Transient Reactor Test Facility) Experimental Relational Database (TREXR). These databases contain three principal sets of metallography data. The first set comprises metallography data from Experimental Breeder Reactor-II (EBR-II) and Fast Flux Test Facility (FFTF) irradiated fuel pins examined in the Hot Fuel Examination Facility (HFEF). The second set consists of metallography data from EBR-II irradiated fuel pins examined in the Alpha-Gamma Hot Cell Facility (AGHCF). The third set includes metallography data from transient-tested fuel pins (including both out-of-pile furnace tests and TREAT tests) examined in AGHCF. Since both the second and third sets were generated in AGHCF, they are governed by identical specifications. The metallography data in the databases consist of digital images scanned from either positive or negative photographic films. To analyze the microstructure of a fuel pin, a series of preparatory steps are required, including sectioning, epoxy mounting, mechanical grinding and polishing, and etching. Following sample preparation, specimens are transferred for metallographic examination. The AGHCF and HFEF metallography data were generated using optical microscopes manufactured by Leitz and Bausch and Lomb (B&L). Images were recorded on Polaroid film at preset magnifications. Magnification verification for the Leitz and B&L metallographs was conducted every two months prior to 1989 and at least every six months from 1989 through the conclusion of the IFR program. Magnifications determined from imaging of microslide standards were compared to the instrument settings for magnifications ranging from 50× to 500×. If the magnifications determined from standards deviated from the instrument settings, adjustments were made to the bellows extension until agreement was achieved. The specifications for AGHCF and HFEF legacy metallography data have been established based on available hard-copy and digital records, most of which have been incorporated into the data repositories associated with FIPD, OPTD, and TREXR. Detailed specifications including hard-copy records, digitized records, cutting diagrams and sectioning schemes, high-magnification photographs, photomosaics (composites), information tags, scale bars, and magnification verification procedures can be found in a separate report.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Requirements Description of DASSH-F

This report reviews the modeling and simulation capabilities of Argonne National Laboratory’s DASSH code that is used in present reactor analysis activities. These capabilities will be used to establish the set of verification tasks necessary to verify DASSH for use on commercial projects. A similar approach was taken for the PERSENT, REBUS and DIF3D software packages. The DASSH program is a thermal analysis code designed to rapidly allow a reactor design engineer to obtain flow rates requirements that satisfy peak temperature constraints in the domain. DASSH is a follow-on development to the SE2-ANL software and SUPERENERGY-2 software that it is based upon. DASSH was designed to account for both neutron and gamma heating and is inherently connected to the GAMSOR part of the ARC suite of fast reactor analysis software. SE2-ANL is a developed piece of software from the 1980s while DASSH is a modern implementation with notable improvements in geometry handling. The most important upgrade of DASSH relative to SE2-ANL is that it can analyze multiple time points in a single run where SE2-ANL can only treat a single time point. This allows the user to understand the impact of and search the flow distribution for the entire operational period of a reactor design considering pressure drop, peak coolant and fuel temperatures, and thermal striping. DASSH has three input paths that have to be verified. The first input path builds the geometry and power distribution based upon the DIF3D model but ignores the gamma heating aspects of the problem. The second input path also builds the geometry from the DIF3D model but it takes the neutron and gamma heating distributions from GAMSOR. The third input path is to take the geometry and power distribution directly from user input (i.e. not coupled to DIF3D or GAMSOR). DASSH also has many built in correlations for material properties along with a user defined specification of the fuel, structure, and coolant properties. There are correlations for flow split, mixing, pressure drop, and heat transfer coefficients (subchannel rather than a direct methodology). In total, verification of DASSH will require an extensive testing to cover all possible user features of the software.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Annual Summary Report for the Remote-Handled Low-Level Waste Disposal Facility—FY 2025

The U.S. Department of Energy (DOE) requires the performance assessment (PA) (Department of Energy Idaho Operations Office [DOE-ID] 2018a), composite analysis (CA) (DOE-ID 2012), and CA addendum (DOE-ID 2018b) for the Remote-Handled Low-Level Waste (RHLLW) Disposal Facility at the Idaho National Laboratory (INL) Site shall be maintained to evaluate changes that could affect the performance, design, and operating basis for the facility (DOE Manual 435.1-1 Change 3, “Radioactive Waste Management Manual,” Section IV.P. [4]). The RHLLW Disposal Facility became operational in September 2018 after the completion of operational readiness activities required by DOE Order 425.1D, “Verification of Readiness to Start Up or Restart Nuclear Facilities,” and the issuance of the startup authorization by the Startup Approval Authority (Boston 2018). The first waste disposals at the RHLLW Disposal Facility began in Fiscal Year (FY) 2019. In Fiscal Year (FY) 2025, no significant operational changes or other activities occurred that would cause deviation from the assumptions in the PA and CA pertaining to disposal geometry, verification of waste characteristics, tracking disposal inventories against total limits, facility closure design, or institutional controls. This FY 2025 annual summary report (ASR) documents the continued adequacy of the PA, CA, operating disposal authorization statement (ODAS) (ODAS 2018), ODAS technical-basis documents, and the radioactive waste management basis (RWMB) (INL 2024a) to meet DOE Order 435.1, “Radioactive Waste Management,” performance objectives for the RHLLW Disposal Facility. Annual review of the adequacy of the PA and CA at the RHLLW Disposal Facility ensures that conclusions of the analyses remain valid in accordance with requirements of DOE Order 435.1.

12 - MGMT OF RADIOACTIVE AND NON-RADIOACTIVE WASTE↗
DOE OSTI2026

Toward Trustworthy Autonomous Science: A Two-Year Community Roadmap

One year ago, the AISLE roadmap argued that autonomous laboratories operated as isolated islands and proposed a grassroots network organized around five critical dimensions. The field has since moved faster than that roadmap anticipated: multi-agent systems have produced experimentally validated hypotheses, self-driving laboratories have grown more interoperable and orchestrated, reasoning-trained and domain foundation models have raised the capability ceiling, and the Genesis Mission has placed autonomous experimentation at the center of U.S. federal science strategy, with industry emerging as a primary actor. Progress has met a sobering counter-current, including a corrected flagship discovery result, benchmarks showing that agents which rival experts on closed-ended questions still complete only a fraction of open-ended research, and fabricated citations surfacing at leading venues. We read this as the defining tension of the field: producing a candidate discovery is no longer the hard part, but verifying it is, and this asymmetry now limits autonomous science more than raw model capability. Accordingly, we update the roadmap around seven dimensions, revisiting the original five and elevating two former cross-cutting concerns, trust, verification, and reproducibility, and safety, security, and governance, to first-class status. We assess the original milestones (M1 through M14) as achieved, partially achieved, reframed, or open, add four new milestones (M15 through M18) for the elevated dimensions, and scope the path forward to a two-year horizon, with the first year concentrating on interfaces, protocol adoption, and the scaffolding of verification, and the second targeting federation, zero-trust coordination, and governance. Throughout, we position the grassroots network as the interoperability fabric that lets national programs, international initiatives, and commercial platforms connect rather than re-silo.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2026

FOCAL Campaign I: Advanced Wind Turbine Control Strategies

Campaign I of the Floating Offshore-wind Controls Advanced Laboratory Experimental Program (FOCAL) aims to generate a dataset enabling the validation of aerodynamic performance of a scaled turbine mounted on a rigid tower in a fixed condition. The turbine considered in the FOCAL testing campaigns is the IEA-Wind 15MW Reference Wind Turbine. This scaled model is capable of simulating advanced blade-pitch control strategies in a high-quality wind field. The turbine is fully instrumented to record a variety of parameters in real time such as structural loads and dynamics. The test data considered was generated at the University of Maine's Harold Alfond Wind and Wave (W2) testing facility. The Load Cases (LC) considered in this testing campaign are as follows: LC 1.X - Constant wind and blade-pitch with varying rotor speeds LC 2.X - Constant wind and rotor speed with varying blade-pitch LC 3.X - Varying wind with active closed-loop control Detailed properties on the modeled system are found in the following reference: Lenfest E., Floating Offshore-wind Controls Advanced Laboratory (FOCAL) Experimental Program - Campaign I: 1:70 Model-scale Testing of the IEA-Wind 15MW Reference Turbine. UMaine ASCC Report Number 23-40-1183. Details on the results of the verification and validation are found in the following reference: Mendoza, Nicole et al., "Verification and Validation of Model-Scale Turbine Performance and Control for the IEA Wind 15 MW Reference Wind Turbine," Energies, vol. 15, no. 20, 2022, https://doi.org/10.3390/en15207649.

17 WIND ENERGY↗
DOE OSTI2024

Thermochemical Nonequilibrium Modeling in a Continuous-Galerkin, Finite-Element Framework

The presented work discusses the implementation, verification, and validation of Park's two-temperature model in a scalable, computational fluid dynamics (CFD) code developed at the US Department of Energy's Oak Ridge National Laboratory (ORNL). The implementation of Park's two-temperature model was verified through 0D test cases involving an adiabatic reactor and a nitrogen thermal bath. The implementation was then validated through comparisons with other validated CFD codes and experimental data on a hypersonic cylinder and double cones. These are standard benchmark test cases for thermochemical non-equilibrium (TCNE) modeling, and all data are shared publicly. The verification and validation results showed that ORNL's in-house CFD code could model complex, high-speed flow problems with and without TCNE modeling. This work is essential for future research involving 3D shock wave/boundary layer interactions (SBLIs).

Nutter, Nicole↗
DOE OSTI2026

Characterization and effects of impurities on carbonate quantification in heterogenous matrices

Mineral carbonation simulates a natural weathering phenomena by breaking down silicates and oxides to form Ca & Mg carbonates. Various mineralization methods have been demonstrated as a potential technique to improve the quality of slags and tailings through neutralization and stabilization of problematic species to yield a product better suited for use in concrete. This study aims to characterize, quantify and analyze carbonates in various carbonated products such as mineralized CaCO 3 , CO 2 mineralized Steel Slags and Mine Tailings. More than 10 samples were analyzed for carbonate measurement and verification from industrial and academic partners that pioneer commercial CO 2 mineralization technologies. The samples were characterized primarily by using X-ray diffraction (XRD), Thermogravimetric Analyses (TGA), and Scanning Electron Microscopy (SEM) to gain insights into CaCO 3 content. A baseline characterization of lab-grade CaCO 3 and MgCO 3 also revealed important considerations for CaCO 3 measurement using TGA alone. The experiments using synthetic lab-grade samples also revealed that the presence of MgCO 3 /MgO can accelerate the decomposition of CaCO 3 and thus can affect measurement parameters. Lab-grade CaCO 3 samples dosed into steel slag and mine tailing also showed significant deviation in their decomposition behavior. These insights are used to inform the development of a standardized protocol for the measurement and verification of carbonate-bearing products.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Computational Fluid Dynamics Modeling to Facilitate Qualification of Stack Sampling Probe Location

Computational fluid dynamics (CFD) modeling was used to help evaluate modifications to a radiological effluent stack and assist with establishing a stack sampling location that met the mixing criteria for qualification. Requirements for stack sampling location are listed in the American National Standards Institute/Health Physics Society (ANSI/HPS) N13.1-2021 standard. Modeling was performed to help develop a suitable design for increasing building ventilation for the radiological effluent stack. The ANSI/HPS N13.1-2021 criteria for the air monitoring probe location are that the coefficient of variation of velocity uniformity, gaseous tracer uniformity, and particulate tracer uniformity must be less than or equal to 20%. Furthermore, no point in the sampling location may have a gaseous tracer concentration that varies from the mean concentration by more than 30%. Additionally, the flow angle at the sampling location must not be more than 20 degrees. The ANSI/HPS N13.1-2021 standard allows for models (physical or computational) to be employed to perform the full suite of qualification tests, followed by a more limited set of verification tests on the actual stack to qualify the stack sampling location. Here, a series of computational model simulations were employed to evaluate the stack qualification criteria. Significant time and re-source savings are achieved using CFD modeling. CFD modeling demonstrated that the stack meets the criteria at the sample probe location. Verification tests were performed on the modified stack to measure the velocity uniformity and flow angle at the stack sampling location, and results demonstrated that the CFD model results may be used to support the qualification of the stack sampling location.

Air Monitoring↗
DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗