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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

MINING NUCLEAR TRANSIENT DATA THROUGH SYMBOLIC CONVERSION

Dynamic Probabilistic Risk Assessment (DPRA) methodologies generate enormous amounts of data for a very large number of simulations. The data contain temporal information of both the state variables of the simulator and the temporal status of specific systems/components. In order to measure system performances, limitations and resilience, such data need to be carefully analyzed with the objective of discovering the correlations between sequence/timing of events and system dynamics. A first approach toward discovering these correlations from data generated by DPRA methodologies has been performed by organizing scenarios into groups using classification or clustering based algorithms. The identification of the correlations between system dynamics and timing/sequencing of events is performed by observing the temporal distribution of these events in each group of scenarios. Instead of performing “a posteriori” analysis of these correlations, this paper shows how it is possible to identify the correlations implicitly by performing a symbolic conversion of both continuous (temporal profiles of simulator state variables) and discrete (status of systems and components) data. Symbolic conversion is performed for each simulation by properly quantizing both continuous and discrete data and then converting them as a series of symbols. After merging both series together, a temporal phrase is obtained. This phrase preserves duration, coincidence and sequence of both continuous and discrete data in a uniform and consistent manner. In this paper it is also shown that by using specific distance measures, it is still possible to post-process such symbolic data using clustering and classification techniques but in considerably less time since the memory needed to store the data is greatly reduced by the symbolic conversion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

System and method for identifying and comparing code by semantic abstractions

Certain embodiments of the present invention are configured to facilitate analyzing computer code more efficiently. For example, by conducting a first level abstraction (e.g., symbolic interpretation and algebraic simplification) and a second level abstraction (e.g., generalization) of the computer code, the analysis may more accurately account for variations in the code that may occur as a result of register renaming, instruction reordering, choice of instructions, etc. while minimizing the cost of computations required to perform the analysis.

Lakhotia, Arun↗
DOE OSTI2019

Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach

Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

42 ENGINEERING↗
DOE OSTI2026

MINLP for regularized symbolic regression with applications to data-driven modeling of critical minerals processes

The poster summarizes recent advances in symbolic regression developed as part of the PrOMMiS project over the past year. In particular, it describes the comparison of surrogates for critical minerals (CM) & rare earth element (REE) recovery flowsheets obtained via symbolic regression and ALAMO. It also compares the predictive ability and solvability of optimization models that incorporate these surrogates.

36 MATERIALS SCIENCE↗
DOE OSTI2013

First and second order approximations to stage numbers in multicomponent enrichment cascades

This paper describes closed form, Taylor series approximations to the number product stages in a multicomponent enrichment cascade. Such closed form approximations are required when a symbolic, rather than a numeric, algorithm is used to compute the optimal cascade state. Both first and second order approximations were implemented. The first order solution was found to be grossly incorrect, having the wrong functional form over the entire domain. On the other hand, the second order solution shows excellent agreement with the 'true' solution over the domain of interest. An implementation of the symbolic, second order solver is available in the free and open source PyNE library. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗
DOE OSTI2025

SA-GAT-SR: self-adaptable graph attention networks with symbolic regression for high-fidelity material property prediction

Recent advances in machine learning have demonstrated an enormous utility of deep learning approaches, particularly Graph Neural Networks (GNNs) for materials science. These methods have emerged as powerful tools for high-throughput prediction of material properties, offering a compelling enhancement and alternative to traditional first-principles calculations. While the community has predominantly focused on developing increasingly complex and universal models to enhance predictive accuracy, such approaches often lack physical interpretability and insights into materials behavior. Here, we introduce a novel computational paradigm—Self-Adaptable Graph Attention Networks integrated with Symbolic Regression (SA-GAT-SR)—that synergistically combines the predictive capability of GNNs with the interpretative power of symbolic regression. Our framework employs a self-adaptable encoding algorithm that automatically identifies and adjust attention weights so as to screen critical features from an expansive 180-dimensional feature space while maintaining O(n) computational scaling. The integrated SR module subsequently distills these features into compact analytical expressions that explicitly reveal quantum-mechanically meaningful relationships, achieving 23 × acceleration compared to conventional SR implementations that heavily rely on first-principle calculations-derived features as input. This work suggests a new framework in computational materials science, bridging the gap between predictive accuracy and physical interpretability, offering valuable physical insights into material behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Coherent states, 6j symbols and properties of the next to leading order asymptotic expansions

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the coherent states and perform a partial stationary point analysis with respect to the smearing parameters. This allows us to transform the variables from group elements to dihedral angles of a tetrahedron resulting in an effective action, which coincides with the action of first order Regge calculus associated to a tetrahedron. To perform the remaining stationary point analysis, we compute its Hessian matrix and obtain the correct measure factor. Furthermore, we expand the discussion of the asymptotic formula to next to leading order terms, prove some of their properties and derive a recursion relation for the full 6j symbol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A two-loop four-point form factor at function level

Recently, the maximally-helicity-violating four-point form factor for the chiral stress-energy tensor in planar $\mathcal{N}$ = 4 super Yang-Mills was computed to three loops at the level of the symbol associated with multiple polylogarithms. It exhibits antipodal self-duality, or invariance under the combined action of a kinematic map and reversing the ordering of letters in the symbol. Here we lift the two-loop form factor from symbol level to function level. We provide an iterated representation of the function’s derivatives (coproducts). In order to do so, we find a three-parameter limit of the five-parameter phase space where the symbol’s letters are all rational. We also use function-level information about dihedral symmetries and the soft, collinear, and factorization limits, as well as limits governed by the form-factor operator product expansion (FFOPE). We provide plots of the remainder function on several kinematic slices, and show that the result is compatible with the FFOPE data. We further verify that antipodal self-duality is valid at two loops beyond the level of the symbol.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Formal Modules for Relative Formal Lubin–Tate Groups

Relative formal Lubin–Tate groups are studied, namely, their structure, the ring of endomorphisms, and the group of points. The primary elements are considered, and an explicit formula for the generalized Hilbert symbol is derived.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

SRBench++: Principled Benchmarking of Symbolic Regression With Domain-Expert Interpretation

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main promise of this approach is that it may return an interpretable model that can be insightful to users, while maintaining high accuracy. The current standard for benchmarking these algorithms is SRBench, which evaluates methods on hundreds of datasets that are a mix of real-world and simulated processes spanning multiple domains. At present, the ability of SRBench to evaluate interpretability is limited to measuring the size of expressions on real-world data, and the exactness of model forms on synthetic data. In practice, model size is only one of many factors used by subject experts to determine how interpretable a model truly is. Furthermore, SRBench does not characterize algorithm performance on specific, challenging sub-tasks of regression such as feature selection and evasion of local minima. In this work, we propose and evaluate an approach to benchmarking SR algorithms that addresses these limitations of SRBench by 1) incorporating expert evaluations of interpretability on a domain-specific task, and 2) evaluating algorithms over distinct properties of data science tasks. We evaluate 12 modern symbolic regression algorithms on these benchmarks and present an in-depth analysis of the results, discuss current challenges of symbolic regression algorithms and highlight possible improvements for the benchmark itself.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SBOL Visual: A Graphical Language for Genetic Designs

Synthetic Biology Open Language (SBOL) Visual is a graphical standard for genetic engineering. We report that it consists of symbols representing DNA subsequences, including regulatory elements and DNA assembly features. These symbols can be used to draw illustrations for communication and instruction, and as image assets for computer-aided design. SBOL Visual is a community standard, freely available for personal, academic, and commercial use (Creative Commons CC0 license). We provide prototypical symbol images that have been used in scientific publications and software tools. We encourage users to use and modify them freely, and to join the SBOL Visual community: http://www.sbolstandard.org/visual.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Multicarrier chaotic communications in multipath fading channels without channel estimation

A multi-carrier chaotic shift keying(MC-CSK) communication scheme with low probability of interception(LPI) is proposed in this article. We apply chaotic spreading sequences in the frequency domain, mapping a different chip of a chaotic sequence to an individual orthogonal frequency division multiplexing(OFDM) subcarrier. In each block size of $M$ OFDM symbols, we use one pilot OFDM symbol inserted time-spaced in all-frequency to transmit the reference chaotic signal and use the other M-1 OFDM symbols to transmit the information-bearing signals each spreaded by the reference chaotic signal. At the receiver, we construct a differential detector after DFT and recover the information bits from the correlations between the pilot OFDM symbol and the other M-1 OFDM symbols in each block size of M. Performance analysis and computer simulations show that the MC-CSK outperforms differential chaos shift keying(DCSK) in AWGN channels with high bandwidth efficiency for the block size of M=2 and that the MC-CSK exploits effectively the frequent diversity of the multipath channel.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Program Verification for Extreme-Scale Applications (Final Scientific/Technical Report)

The project seeks to develop tools and techniques to help software developers verify the correctness and accuracy of their code. The target domain is scientific software of the kind widely used and developed in the Department of Energy research community, with a particular focus on "extreme scale" programs - those that are expected to involve possibly millions of parallel threads of execution. The report covers the University of Delaware contribution to the collaborative project. The project had a number of successful outcomes, especially regarding the development and extension of the CIVL software verification framework. CIVL is a verification tool for C or Fortran programs that use MPI, OpenMP, CUDA, and/or Pthreads for parallelization. CIVL went through vast improvements and extensions, and was successfully applied to a number of challenging codes. It found a subtle bug in the Devito PDE framework. It was able to verify the functional correctness of a conjugate gradient solver using a novel probabilistic technique with vanishingly small chance of error. CIVL was used very successfully in verification competitions, and the CIVL solutions to the competition challenges were presented and published. CIVL was also used successfully by other researchers on a computational chemistry kernel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗
DOE OSTI2024

Complexity-calibrated benchmarks for machine learning reveal when prediction algorithms succeed and mislead

Abstract Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a “next-generation” reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano’s inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoir computers with reasonably long memory traces have an error probability that is at least $$\sim 60\%$$ ∼ 60 % higher than the minimal attainable error probability in predicting the next observation. More generally, it appears that popular recurrent neural networks fall far short of optimally predicting such complex processes. These results highlight the need for a new generation of optimized recurrent neural network architectures. Alongside this finding, we present concentration-of-measure results for randomly-generated but complex processes. One conclusion is that large probabilistic state machines—specifically, large $$\epsilon$$ ϵ -machines—are key to generating challenging and structurally-unbiased stimuli for ground-truthing recurrent neural network architectures.

97 MATHEMATICS AND COMPUTING↗