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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Deep Learning Methods for Symbolic Calculations in HEP

This project develops machine learning methods to accelerate symbolic calculations in high-energy physics. Using sequence-to-sequence transformer models, we construct frameworks to predict squared amplitudes and related quantities for Standard Model processes, including quantum electrodynamics, quantum chromodynamics, and electroweak interactions. The results demonstrate that deep learning can successfully learn complex symbolic relationships and provide a scalable approach to symbolic computation with potential applications in precision calculations and collider phenomenology.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Agentic Diagrammatica: Towards Autonomous Symbolic Computation in High Energy Physics

We present Diagrammatica, a symbolic computation extension to the HEPTAPOD agentic framework, which enables LLM agents to plan and execute multi-step theoretical calculations. Symbolic computation poses a distinctive reliability challenge for LLM agents, as correctness is governed by implicit mathematical conventions that are not encoded in a form that can be easily checked in the computational backend. We identify two complementary remedies, tool-constrained computation and targeted knowledge grounding, and pursue the first as the primary architecture. Concretely, we concentrate the agent's action distribution onto tool calls with convention-fixing semantics, in which the agent specifies a compact, human-auditable diagram specification and a trusted backend performs the symbolic or numerical manipulations exactly. The toolkit provides two complementary calculation paths consuming a shared diagram specification: Naive Dimensional Analysis (NDA) for order-of-magnitude rate estimates and Exact Diagrammatic Analysis (EDA) for tree-level symbolic calculations via automatic FeynCalc code generation, both supplemented by automatic Feynman diagram enumeration and a navigable theory knowledge base. The architecture is validated on two benchmarks: (1) an exhaustive catalog of all tree-level, single-vertex $1\to 2$ partial decay widths across scalar, fermion, and vector parents, with complete massless and threshold limits and Standard Model validation; and (2) an NDA sensitivity study of the muon decay multiplicity $μ^+ \to ν_μ\barν_e + n(e^+e^-) + e^-$, determining the maximum observable $n$ at current and planned muon experiments.

Menzo, Tony [Alabama U.; Fermilab] (ORCID:00000002↗
DOE OSTI2023

Nonlinear photoconductivities and quantum geometry of chiral multifold fermions

Here, chiral multifold fermions are quasiparticles that appear only in chiral crystals such as transition metal silicides in the cubic B20 structure (i.e., the CoSi family), and they may show exotic physical properties. Here we study the injection and shift photoconductivities and also the related geometrical quantities for several types of chiral multifold fermions, including spin-1/2 as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple-point, and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal symmorphic model to describe the triple-point fermions (TPF). We also consider the more realistic model Hamiltonian for the CoSi family including both linear and quadratic terms. We find that injection currents due to circularly polarized light are quantized as a result of the Chern numbers carried by the multifold fermions within the linear models. Surprisingly, we discover that in the TPF model, the linear shift conductivities, responsible for the shift current generation by linearly polarized light, are proportional to the pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Isotropic N-point basis functions and their properties

Isotropic functions of positions r 1 , r 2 ,..., r N , i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch–Gordan coefficients. An orthonormal basis of such functions provides a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed in terms of 6-j and 9-j symbols. Finally, the calculation of relations among the basis functions is facilitated by 'Yutsis' diagrams for the addition and recoupling of angular momenta.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗
DOE OSTI2025

SDA: a symbolic differential algebra package in C++

Truncated Power Series Algebra (TPSA), or Differential Algebra (DA), is a well-established tool in accelerator physics, commonly used for generating high-order maps of dynamic systems, as well as in symplectic tracking, normal form analysis, verified integration, optimization, and fast multipole methods. This package is the first to perform symbolic DA computations, enabling traceability of initial condition contributions and runtime reduction for repeated DA calculations, potentially expanding DA’s applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Evaluation of Thermal Neutron Scattering Law and Cross Sections for Calcium Hydride

Presented in this paper are the calculated thermal scattering law (TSL) and thermal neutron scattering cross sections for Calcium Hydride, hereafter referred to by its chemical symbol CaH 2 . The only other such data prior to this evaluation are thermal neutron scattering libraries in the JEFF database, which suffer from nonphysical features and inaccuracies. The data in this evaluation are calculated from first principles; Density Functional Theory (DFT) is used to calculate the phonon density of states (DOS), which is the primary input required to calculate the TSL. The TSL and cross sections have been evaluated for the three non-equivalent atom cites in the CaH 2: Ca, H 1 , and H 2 . Each evaluation has been submitted to the NNDC for consideration in the next ENDF/B release.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Quasilinear theory: the lost ponderomotive effects and why they matter

Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling of the metal–insulator transition temperature in alio-valently doped VO 2 through symbolic regression

The correlated semiconductor vanadium dioxide (VO 2 ) exhibits an insulator–metal transition (IMT) near room temperature, which is of interest in various device applications. Precise IMT temperature control is crucial to determine the use cases across technologies such as thermochromic windows, actuators for robots or neuronal oscillators. Doping the cation or anion sites can modulate the IMT by several tens of degrees and control hysteresis. However, modeling the effects of control parameters (e.g., doping concentration, type of dopants) is challenging due to complex experimental procedures and limited data, hindering the use of traditional data-driven machine learning approaches. Symbolic regression (SR) can bridge this gap by identifying nonlinear expressions connecting key input parameters to target properties, even with small data sets. In this work, we develop SR models to capture the IMT trends in VO 2 influenced by different dopant parameters. Using experimental data from the literature, our study reveals a dual nature of the IMT temperature with varying tungsten (W) doping concentrations. The symbolic model captures data trends and accounts for experimental variability, providing a complementary approach to first-principles calculations. Our feature-driven analysis across a broader class of dopants informs selectivity and provides qualitative insights into tuning phase transition properties valuable for neuromorphic computing and thermochromic windows.

36 MATERIALS SCIENCE↗
DOE OSTI2023

SYMBA: symbolic computation of squared amplitudes in high energy physics with machine learning

The cross section is one of the most important physical quantities in high-energy physics and the most time consuming to compute. While machine learning has proven to be highly successful in numerical calculations in high-energy physics, analytical calculations using machine learning are still in their infancy. In this work, we use a sequence-to-sequence model, specifically, a transformer, to compute a key element of the cross section calculation, namely, the squared amplitude of an interaction. We show that a transformer model is able to predict correctly 97.6% and 99% of squared amplitudes of quantum chromodynamics and quantum electrodynamics processes, respectively, at a speed that is up to orders of magnitude faster than current symbolic computation frameworks. We discuss the performance of the current model, its limitations and possible future directions for this work.

97 MATHEMATICS AND COMPUTING↗
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 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 OSTI2020

Quadrupolar interactions between acceptor pairs in $\mathcal{p}$-doped semiconductors

Here, we consider the interaction between acceptor pairs in doped semiconductors in the limit of large interacceptor separation relevant for low doping densities. Modeling individual acceptors via the spherical model of Baldereschi and Lipari, we calculate matrix elements of the quadrupole tensor between the four degenerate ground states and show that the acceptor has a nonzero quadrupole moment. As a result, the dominant contribution to the large-separation acceptor-acceptor interaction comes from direct (charge-density) terms rather than exchange terms. The quadrupole is the leading nonzero moment, so the electric quadrupole-quadrupole interaction dominates for large separation. We calculate the matrix elements of the quadrupole-quadrupole interaction Hamiltonian in a product-state basis and diagonalize, obtaining a closed-form expression for the energies and degeneracies of the sixteen-state energy spectrum. All dependence on material parameters enters via an overall prefactor, resulting in surprisingly simple and universal results. This simplicity is due, in part, to a mathematical happenstance, the nontrivial vanishing of a particular Wigner 6-$\mathcal{j}$ symbol, $^\{\frac{^2_3}{\small2} \frac{^2_3}{\small2} \frac{^2_3}{\small2}$$^\}$ = 0. Results are relevant to the control of two-qubit interactions in quantum computing implementations based on acceptor spins, as well as calculations of the thermodynamic properties of insulating $\mathcal{p}$-type semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$

We present compact analytic results for the one-loop amplitude for the process 0 → $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$, relevant for both the production of a pair of Z and W-bosons in association with a jet. We focus on the gauge-invariant contribution mediated by a loop of quarks. We explicitly include all effects of the loop-quark mass m, appropriate for the production of a pair of Z-bosons. In the limit m → 0, our results are also applicable to the production of W-boson pairs, mediated by a loop of massless quarks. Implemented in a numerical code, the results are fast. The calculation uses novel advancements in spinor-helicity simplification techniques, for the first time applied beyond five-point massless kinematics. We make use of primary decompositions from algebraic-geometry, which now involve non-radical ideals, and p-adic numbers from number theory. We show how to infer whether numerator polynomials belong to symbolic powers of non-radical ideals through numerical evaluations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Electron correlation and relativistic effects in the excited states of radium monofluoride

Highly accurate and precise electronic structure calculations of heavy radioactive atoms and their molecules are important for several research areas, including chemical, nuclear, and particle physics. Ab initio quantum chemistry can elucidate structural details in these systems that emerge from the interplay of relativistic and electron correlation effects, but the large number of electrons complicates the calculations, and the scarcity of experiments prevents insightful theory-experiment comparisons. Here we report the spectroscopy of the 14 lowest excited electronic states in the radioactive molecule radium monofluoride (RaF), which is proposed as a sensitive probe for searches of new physics. The observed excitation energies are compared with state-of-the-art relativistic Fock-space coupled cluster calculations, which achieve an agreement of ≥99.64% (within ~12 meV) with experiment for all states. Guided by theory, a firm assignment of the angular momentum and term symbol is made for 10 states and a tentative assignment for 4 states. The role of high-order electron correlation and quantum electrodynamics effects in the excitation energies is studied and found to be important for all states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Unraveling Fundamental Activity–Stability Relationships in Rutile Oxides

The oxygen evolution reaction (OER) is a key anodic half-cell reaction that accompanies several critical electrochemical reduction reactions of interest to a variety of applications. Despite steady advances in understanding and qualitatively predicting OER activity and selectivity trends, a comprehensive description or prediction of material aqueous (in)stability and degradation mechanisms remains elusive, even though these processes critically influence device lifetime and economic feasibility. In this work, we investigate the interplay, or lack thereof, between OER activity and material aqueous stability across rutile oxides, with a particular focus on iridium oxide (IrO 2 ). By applying a Born–Haber cycle, we calculate the thermodynamic driving force for metal dissolution as a function of the applied bias and electrolyte conditions. We apply interpretable machine learning techniques, including principal component analysis and symbolic regression, to analyze trends across rutile oxides and find that key thermodynamic descriptors for OER activity and surface stability are only very weakly correlated. Instead, the local atomic environment─especially electronic structure signatures for interactions between the active site and its neighbors─plays a more important role in predicting material stability. Leveraging these insights, we investigate the impact of doping IrO 2 with a range of transition metals and show that the stability of Ir active sites can be tuned largely independently of its predicted OER activity. These insights lay the foundation for material design to improve stability with respect to corrosion, with the ultimate aim to enhance long-term stability without sacrificing catalytic performance in the OER.

evolution reactions↗
DOE OSTI2022

An Interactive Visualization Tool for Large-Scale Building Stock Modeling: Preprint

Recent advancements in data science and high-performance computing are making it easier to run millions of building simulations, but meaningful visualization of such large datasets remains a challenge. This paper presents a new tool developed to view the results of large-scale OpenStudio simulations of national, regional, or local building stocks. The tool processes millions of simulations to calculate measure savings, utility bills, carbon emissions, primary energy, and cost-effectiveness metrics at a high geographic resolution. Interactive visualizations of the building characteristics, consumption, and measure savings data include proportional symbol maps and histogram plots and can be filtered by any building characteristic.

big data↗
DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗