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NASA NTRS1992

Data integration in multi-sensor based robotic workstations

A relaxation labeling algorithm is developed. The major advantage of this algorithm over the existing ones is that the mathematic operation is simplified. The simplification eases the analysis of the convergence properties. Both the theoretical and application aspects of the proposed algorithm are investigated. The local convergence properties of a labeling process with n labels and m labels are established. The investigation of the interaction among the nodes in a multinode labeling process reveals some insight into the mathematical issues involved in the relaxation operations.

Chen, Qin↗

DOE OSTI2025

Employing a Hardware-in-the-Loop Approach to Realize a Fully Homomorphic Controller for a Small Modular Advanced High Temperature Reactor

This paper addresses the cybersecurity challenges of advanced nuclear reactors by integrating fully homomorphic encryption (FHE) into their control systems, enabling encrypted processing of control signals without compromising functionality. Advanced nuclear reactors, including Small Modular Reactors (SMRs) and microreactors, aim to achieve autonomous and remote operations, reducing costs and enhancing competitiveness. However, these advancements expand the attack surface for cyberattacks, particularly in autonomous and remote operation scenarios. Cyberattacks can exploit vulnerabilities to manipulate physical processes, causing shutdowns, asset damage, or public harm. Such attacks begin with passive reconnaissance, where adversaries intercept communications or observe behaviors to gather information, which is then leveraged to execute cyber-physical attacks by injecting malicious commands. Nuclear power must adopt cybersecurity protection measures to secure the integrity and availability of their digital control systems. This paper demonstrates the application of FHE to secure operations by enabling encrypted processing of sensitive signals and parameters -- ensuring privacy without exposing data. FHE supports secure mathematical operations on encrypted data without requiring decryption. Using a hardware-in-the-loop (HIL) approach, this paper implements an FHE-integrated controller on a BeagleBone Black (BBB) controlling a simulation of the Small Modular Advanced High Temperature Reactor (SmAHTR). By doing so, the encrypted controller protects the integrity of critical set points and control signals during transmission and processing. Thus, FHE-integrated controllers enhance secure operations of advanced nuclear reactors while maintaining functionality.

control systems↗

NASA NTRS1993

Spatial operator algebra for flexible multibody dynamics

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations.

Jain, A.↗

NASA NTRS1996

BPSK Demodulation Using Digital Signal Processing

A digital communications signal is a sinusoidal waveform that is modified by a binary (digital) information signal. The sinusoidal waveform is called the carrier. The carrier may be modified in amplitude, frequency, phase, or a combination of these. In this project a binary phase shift keyed (BPSK) signal is the communication signal. In a BPSK signal the phase of the carrier is set to one of two states, 180 degrees apart, by a binary (i.e., 1 or 0) information signal. A digital signal is a sampled version of a "real world" time continuous signal. The digital signal is generated by sampling the continuous signal at discrete points in time. The rate at which the signal is sampled is called the sampling rate (f(s)). The device that performs this operation is called an analog-to-digital (A/D) converter or a digitizer. The digital signal is composed of the sequence of individual values of the sampled BPSK signal. Digital signal processing (DSP) is the modification of the digital signal by mathematical operations. A device that performs this processing is called a digital signal processor. After processing, the digital signal may then be converted back to an analog signal using a digital-to-analog (D/A) converter. The goal of this project is to develop a system that will recover the digital information from a BPSK signal using DSP techniques. The project is broken down into the following steps: (1) Development of the algorithms required to demodulate the BPSK signal; (2) Simulation of the system; and (3) Implementation a BPSK receiver using digital signal processing hardware.

Garcia, Thomas R.↗

DOE OSTI2025

AutoUncertainties: A Python Package for Uncertainty Propagation

Propagation of uncertainties is of great utility in the experimental sciences. While the rules of (linear) uncertainty propagation are straightforward, managing many variables with uncertainty information can quickly become complicated in large scientific software stacks. Often, this requires programmers to keep track of many variables and implement custom error propagation rules for each mathematical operator and function. The Python package AutoUncertainties, described here, provides a solution to this problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Considerations for using Privacy Preserving Machine Learning Techniques for Safeguards

In international nuclear safeguards, the International Atomic Energy Agency (IAEA) is tasked with inspecting and verifying nuclear facilities and their activities. Data analytics and machine learning to support inspections require large amounts of data that nuclear facility operators may consider proprietary or sensitive, so the IAEA may not have full access. Allowing computation over private data without compromising its security therefore has value for safeguards inspections and analysis. Privacy-preserving machine learning (PPML) consists of security-focused techniques that allow data analytics and machine learning algorithms to run on sensitive data without revealing it. This includes ideas like homomorphic encryption (HE), secure multiparty computation (SMPC), and secure enclaves. HE allows algorithms and mathematical operations to be conducted directly on the encrypted data instead of first decrypting it. With SMPC, multiple entities collaboratively compute over distributed data such that no party is able to directly view any others’ original data. Secure enclaves allow computation to take place in a separate and heavily blocked-off section of a CPU. Techniques like these allow for several potential use cases in which the security of data is essential. With SMPC, machine learning models can be trained over the input data from multiple entities, resulting in a model that all users can benefit from without leaking the input data from any particular entity. With SMPC or a zero-knowledge proof (ZKP), an algorithm returning some single answer or truth value can be run on someone else’s data without ever needing to see that data, potentially allowing for verification or proof of some underlying question. HE can allow for outsourcing computation on data to a hostile or untrusted environment. Although most of the research in this field resides within the health and financial domains, tools from PPML may have similar applications in nuclear safeguards. Allowing the IAEA to compute over proprietary information, such as process models and raw sensor data using PPML techniques, provides the baseline for running complex analytics without needing direct unencrypted access to the underlying data, maintaining its privacy. Important limitations to consider for these techniques include the efficiency and level of security required. The security of HE and SMPC come at the cost of speed—the significant amount of overhead means that algorithms implemented in these protocols and encryption schemes are slower than when run on plaintext. Additionally, several important parameters determine what techniques or protocols are used based on the security requirements. SMPC protocols may need to be selected for resistance against a party that attempts to deviate from the protocol to distort the result or gain access to additional information, and a protocol secure against these attacks may further increase the overhead of the algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Practical Probabilistic Programming

Recent advances in probabilistic programming languages (PPLs) have provided the capability for exact inference: computing a closed-form probability distribution for a given probabilistic program. In particular, the new language Roulette uses a language oriented programming (LOP) approach, wherein analysts build new programming languages on top of a set of primitives provided by Roulette, which then translates these structures into a weighted model counting problem which can be solved by automated reasoning tools. However, because Roulette provides few convenience features, developing these new languages is challenging even for expert users. We developed a standard library of common probability functions for Roulette with the goal of improved usability. This included approximation of continuous probability density functions using discrete probability mass functions. We demonstrated this approach by modeling a cosmic ray striking a RAM controller. We found that Roulette provides a powerful interface for highly expressive probabilistic programs to be generated. In collaboration with the NNSA Advanced Simulation and Computing program, which resulted in development of a tool called Circulette, we were able to model complex circuits expressed in Verilog using probabilistic programs with an expressivity not previously possible. Our research question that motivated the development of a Roulette standard library was to determine whether non-experts could use a PPL to model relevant problems regarding radiation effects on microelectronics. This standard library improved the expressivity of Roulette by implementing common probability density functions, mathematical operators on distributions, and support for empirical distributions. While Roulette is a powerful modeling language, the untyped, LOP approach makes error messages difficult to understand and requires expert aid. We recommend further research on Roulette, especially with its error messages, to enable improved usability. At the same time, this project demonstrated that for users familiar with Roulette and the LOP approach, Roulette provides powerful new capabilities that can be integrated with other Sandia modeling capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Inventory of Public Key Cryptography in US Electric Vehicle Charging

Electric vehicles (EVs) and charging infrastructure are networked systems, which employ high-level communications in support of charging and grid service decisions. Public key cryptography (PKC) underlies much of the security and privacy protections of the information exchange. We are entering a new epoch where quantum computing threats must be seriously considered. A sufficiently large quantum computer, so named Cryptographically Relevant Quantum Computer (QRQC), will be able to perform the mathematical operations to efficiently attack the underpinnings of traditional PKC, thus jeopardizing the digital foundations for trust, communications security, and data security. Estimates suggest a QRQC can break public key encryption and digital signatures in the manner of tens to hundreds of hours, compared to traditional computing that would demand more than 10 18 years in a brute force-style attack. A consensus belief of quantum theorists, quantum experimenters, and cryptographers suggest that the quantum threat will be likely realized in the next twenty years. To address the threat, post-quantum cryptography, which is cryptosystems that are designed to be secure against both traditional and quantum computing threats, must be adopted. Migration from traditional PKC to quantum-resilient cryptography is a global undertaking and likely represents the largest transition in computing history. The nascent state of EV public key infrastructure, combined with limited adoption of the vehicle secure charging features, presents an opportunity to establish a preference for quantum-resistant cryptography as a step on the migration path. Delays will stunt the efforts as rapidly accelerating EVs sales and huge infrastructure investments will create large growing bases of long-lived vehicles and infrastructure. Migration preparations can commence while NIST continues the process to standardize post-quantum cryptography (PQC), which are quantum-resilient algorithms designed to be secure against traditional and quantum computing threats. The first step in preparing EV charging is to identify the presence of traditional public key cryptography algorithms and applications. With this objective in mind, this report is intended to advise the vehicle manufacturers, charging station manufacturers, charging station operators, charge network providers and other EV charging stakeholders with information on traditional PKC application and the potential risks when PKC becomes insecure. This report, the first in a series of reports discussing the topics existing at the confluence of post-quantum cryptography adoption and EV charging, identifies traditional public key applications employed and identifies potential consequences of leaving EV charging infrastructure vulnerable to quantum computing. The focus remains squarely on the of EV charging and infrastructure with respect to PKC and is believed by the authors to complement the NIST SP 1800-38 Migration to Post-Quantum Cryptography. While the report is centered on infrastructure, there are implications to vehicles.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

EI_MS_ML

The unambiguous identification of compounds from their electron ionization mass (EI-MS) spectra remains a significant unsolved problem in the field of metabolomics and analytical chemistry as a whole. Typically EI-MS spectra are compared using various mathematical operations that convert the spectral similarity or differences into a distance-like metric that roughly approximates the similarity of any two spectra. A commonly used metric for this is the cosine similarity metric which has values close to one for very similar spectra and a value of zero for very dissimilar spectra; however, no metric is perfect. Due to the prevalence of structurally-similar compounds such as isomers and the prevalence of certain fragmentation patterns across structurally-dissimilar compounds, the unambiguous assignment of EI-MS spectra compounds remains difficult. Frequently, querying an observed EI-MS spectrum against a large database such as the NIST17 library yields multiple possible assignments requiring the end user to distinguish between multiple high scoring hits, or multiple low scoring hits while keeping in mind that the correct hit may not be in the database at all. Although techniques such as orthogonal information from techniques such as chromatography can greatly aid in unambiguous assignment, this also requires more complicated experimental designs and access to more complicated analytical instrumentation. Substructures can be trivially detected and represented as strings using a previously published technique called node coloring from a known chemical structure. However, for experimentally-derived EI-MS spectra this information must be derived from the spectra itself (i.e., because we do not know what compound it represents). To achieve this, the software uses techniques from the field of machine learning and a large training dataset of EI-MS spectra corresponding to known structures annotated with substructure strings, to build models that can predict the presence of a given chemical substructure from an EI-MS spectrum directly.If these predictions are of high-quality (i.e., are unlikely to be false positives), the presence of one or more predicted substructures can be used to constrain the number of possible hits for a query spectrum. Mathematically, this restriction could be expressed in many forms, but the most straight-forward implementation is to weight the cosine similarity of a query spectrum and a plausible database match with a Tanimoto-like coefficient based on the ratio of the number of substructures predicted to the number of substructures present in the potential database hit. Determining which combination of models best reduces assignment ambiguity will be achieved using a combination of manual curation and optimization techniques such as genetic algorithms. This software will perform all the steps necessary to construct said models from a training dataset and evaluate them using a holdout dataset. Various statistical analyses can be performed to determine if this approach does decrease assignment ambiguity. For example, if this approach works, on average, the rank-order of the correct assignment for the holdout set of EI-MS spectra should decrease and the weighted cosine similarities for most of the possible matches in the database should be better than the unweighted cosine similarities. Furthermore, this same pipeline can be used on real experimental data to generate less ambiguous assignments.

Mitchell, Joshua↗

DOE OSTI2021

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real–world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. Herein we present a novel deterministic mixed–integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics–based constraints on the first and second derivatives.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Revealing topology in metals using experimental protocols inspired by K-theory

Topological metals are conducting materials with gapless band structures and nontrivial edge-localized resonances. Their discovery has proven elusive because traditional topological classification methods require band gaps to define topological robustness. Inspired by recent theoretical developments that leverage techniques from the field of C*-algebras to identify topological metals, here, we directly observe topological phenomena in gapless acoustic crystals and realize a general experimental technique to demonstrate their topology. Specifically, we not only observe robust boundary-localized states in a topological acoustic metal, but also re-interpret a composite operator—mathematically derived from the K-theory of the problem—as a new Hamiltonian whose physical implementation allows us to directly observe a topological spectral flow and measure the topological invariants. Our observations and experimental protocols may offer insights for discovering topological behaviour across a wide array of artificial and natural materials that lack bulk band gaps.

36 MATERIALS SCIENCE↗

DOE OSTI2025

SymbolNet: neural symbolic regression with adaptive dynamic pruning for compression

Abstract Compact symbolic expressions have been shown to be more efficient than neural network (NN) models in terms of resource consumption and inference speed when implemented on custom hardware such as field-programmable gate arrays (FPGAs), while maintaining comparable accuracy (Tsoi et al 2024 EPJ Web Conf. 295 09036). These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming (GP), the search algorithm of most symbolic regression (SR) methods. Contrary to GP, the NN approach to SR offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose S y m b o l N e t , a NN approach to SR specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing SR methods that struggle with datasets containing more than O ( 10 ) inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).

Tsoi, Ho Fung (ORCID:0000000225502184)↗

DOE OSTI2026

LibraryX: A Framework for Cross-Library-Call Optimization

Scientific applications utilize performance libraries as a software engineering concept: these libraries encapsulate important and well-understood (mathematical) operations, allow for reuse, and are implemented and tuned by experts. Domain scientists then implement complex algorithms based on these domainspecific libraries. While individual library calls are optimized, larger performance gains across sequences of calls—sometimes spanning multiple libraries—are often unrealized, forcing a trade-off between performance and implementation complexity.To overcome this issue, we propose LibraryX, an approach and a system that allows for cross-library-call optimization even when library calls stem from multiple performance libraries. LibraryX annotates library calls with semantic information and optimizes entire directed acyclic graphs (DAGs) of calls dynamically using the SPIRAL code generation system. We demonstrate its effectiveness across a range of memory bound workloads, achieving significant speedups on Nvidia, AMD, and Intel accelerators compared to code using native libraries without cross-call optimization.

Rao, Sanil [Carnegie Mellon University,Department ↗

DOE OSTI2020

CSBCOO SPMM: Compressed Sparse Block Coordinate format sparse matrix dense vector multiply benchmark (CSBCOO SPMM) v1.0

The purpose of this microbenchmark is to provide a means to explore different programming methodologies using a simple, but not trivial, mathematical kernel. The kernel is based on the matrix vector product in the MFDn nuclear configuration interaction code's LOBPCG eigensolver. This particular mathematical operation is a key element in the solution of systems of equations and block eigensolvers.

Cook, Brandon↗

DOE OSTI2022

WORM (Write One, Read Many)

WORM (Write One, Run Many) is an easy to use, cross platform, embedded and extensible, functional programming language designed to facilitate the creation of input-decks for computer codes that use standard ASCII text files for input. WORM makes it easy to create generic (yet, complex and powerful) reusable models. Additionally its nature allows for complex calculations and routines to be coded once and easily reused, further simplifying the creation of input decks. WORM (Write One, Run Many) is a powerful and versatile tool designed to improve the efficiency of today’s criticality safety analyst by allowing: + input decks for parametric studies to be created quickly and easily, + calculations and variables to be imbedded into any input deck, thus allowing for meaningful parameter specifications, + problems to be specified using any combination of units, and + complex mathematically defined models to be created. A very simple syntax is employed, and therefore the WORM is easy to learn. A WORM model is essentially a standard input deck with some of its numerical values replaced by WORM code. WORM code may include and evaluate the following mathematical operators and functions: addition, subtraction, multiplication, division, exponentiation, modulus, sine, cosine, tangent, arcsine, arccosine, arctangent, the natural logarithm, logarithm base 10, integer truncation, absolute value, and random number. Several common constants, e.g., pi, e, and Avogadros’s Number (both as 6.022e23 and 0.6022), are predefined in WORM. Additionally, many unit conversion factors are also predefined: millimeters, meters, inches, feet, yards, and mils to centimeters; kilograms, pounds, and ounces to grams; liters, milliliters, gallons, and fluid ounces to cubic centimeters; and angular degrees to radians. For parametric studies, WORM supports various shorthand list specifications: the explicit step size, linear interpolation, and logarithmic interpolation. The list notation sequentially assigns multiple values to a name. WORM creates an input deck for each value of the name. If multiple lists are used, WORM steps through each list individually, i.e., WORM creates input decks corresponding to each and every permutation of the list values. Additionally, a library of standard material definitions and Perl subroutines are included. Any one of these files can be incorporated into the subject model with a simple WORM read command. WORM is completely written in Perl, the Practical Extraction and Reporting Language. Perl is one of the most portable programming languages available today. As such, the WORM works on practically any computer platform.

Sartor, Raymond↗

DOE OSTI2025

QCUncertainty/sigma

Sigma is a header-only C++ library for uncertainty propagation throughout mathematical operations on floating point values.

Waldrop, Jonathan M.↗

DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗

DOE OSTI2024

Homomorphic Encryption for Electrical Metering Aggregation: Protecting the Privacy of Building Tenants

Electrical meters are devices that measure consumer electricity usage. The data collected by these meters is necessary for utility billing and electrical grid management but can also be used to assess the environmental impact of buildings. Prior research has found that unprotected metering data could potentially be used to infer some information about the behaviors of building tenants by detecting changes in electricity usage. For example, a period of low electricity usage could suggest that the tenants are not in the building. As smart metering becomes more common, there is a growing need for data privacy protections for metering data that do not negatively impact the quality and availability of data used for energy management and billing applications. To identify potential solutions, we developed a Python-based data aggregation platform to analyze the potential efficacy of privacy-enhancing technologies for energy metering applications. This platform aggregates groups of metering sites into virtual buildings, which could potentially detach changes in electrical activity from individual tenants, making it more difficult to track the activity of a specific tenant. To further protect data during analysis, this project utilizes homomorphic encryption as part of its initial approach. Homomorphic encryption offers a means of protecting energy consumption data while permitting mathematical operations to be performed without the need to know the data contents. This allows for data to be processed into usable statistics without revealing energy consumption information. A series of homomorphic encryption libraries were evaluated to determine their applicability and limitations in the context of metering data. The use of these techniques may help to reassure consumers and encourage further adoption of smart grid infrastructure.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗