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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 OSTI2025

Scaling laws in jet classification

We demonstrate the emergence of scaling laws in the benchmark top versus QCD jet classification problem in collider physics. Six distinct physically-motivated classifiers exhibit power-law scaling of the binary cross-entropy test loss as a function of training set size, with distinct power law indices. This result highlights the importance of comparing classifiers as a function of dataset size rather than for a fixed training set, as the optimal classifier may change considerably as the dataset is scaled up. We speculate on the interpretation of our results in terms of previous models of scaling laws observed in natural language and image datasets.

Batson, Joshua↗
DOE OSTI2026

Neural Scaling Laws for Jet Generation

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Amram, Oz [Fermilab]↗
DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Towards Scaling Law Analysis For Spatiotemporal Weather Data

Compute-optimal scaling laws are relatively well studied for NLP and CV, where objectives are typically single-step and targets are comparatively homogeneous. Weather forecasting is harder to characterize in the same framework: autoregressive rollouts compound errors over long horizons, outputs couple many physical channels with disparate scales and predictability, and globally pooled test metrics can disagree sharply with per-channel, late-lead behavior implied by short-horizon training. We extend neural scaling analysis for autoregressive weather forecasting from single-step training loss to long rollouts and per-channel metrics. We quantify (1) how prediction error is distributed across channels and how its growth rate evolves with forecast horizon, (2) if power law scaling holds for test error, relative to rollout length when error is pooled globally, and (3) how that fit varies jointly with horizon and channel for parameter, data, and compute-based scaling axes. We find strong cross-channel and cross-horizon heterogeneity: pooled scaling can look favorable while many channels degrade at late leads. We discuss implications for weighted objectives, horizon-aware curricula, and resource allocation across outputs.

Kiefer Jr, Alexander [ORNL] (ORCID:000000025398874↗
DOE OSTI2024

Invariant regimes of Spencer scaling law for magnetic compression of rotating FRC plasma

Abstract The scaling laws for the magnetic compression of a toroidally rotating field reversed configuration (FRC) have been investigated in this work. The magnetohydrodynamics (MHD) simulations of the magnetic compression on rotating FRCs employing the NIMROD code (Sovinec et al 2004 J. Comput. Phys. 195 355), are compared with the Spencer’s one-dimensional (1D) theory (Spencer et al 1983 Phys. Fluids 26 1564) for a wide range of initial flow speeds and profiles. The toroidal flow can influence the scalings directly through the alteration of the compressional work as also evidenced in the 1D adiabatic model, and indirectly by reshaping the initial equilibrium. However, in comparison to the static initial FRC equilibrium cases, the pressure and the radius scalings remain invariant for the magnetic compression ratio B w 2 / B w 1 up to 6 in presence of the initial equilibrium flow, suggesting a broader applicable regime of the Spencer scaling law for FRC magnetic compression. The invariant scaling has been proven a natural consequence of the conservation of angular momentum of both fluid and magnetic field during the dynamic compression process.

Ma, Yiming↗
DOE OSTI2025

A scaling law of the neutral penetration length and Balmer- α wing shape in high-temperature plasmas

Hydrogen atoms penetrating deep inside high-temperature magnetically confined plasmas by repetitive charge-exchange collisions result in a particle source of the plasma, which affects the plasma transport significantly. In this paper, we present an approximate solution of the fluid equations for neutral transport and an analytical representation of the neutral penetration length, in a simplified plasma geometry. This analysis predicts a power-law decay in the Balmer-α line wings which reflects the velocity distribution of the neutral atoms, with the power-law exponent analytically represented as well. These scaling laws are compared with a simple Monte–Carlo simulation and spectroscopic observations of Large Helical Device plasmas. Since the Balmer-α line wings are experimentally accessible, our formulation opens the possibility to quickly estimate the neutral penetration length from spectroscopic observations.

neutral opacity↗
DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗
DOE OSTI2026

Constraining the Dynamo Layers in Jupiter and Saturn with Observations and Scaling Laws

The dipole-dominated magnetic fields of Jupiter and Saturn provide evidence for active dynamos operating within their deep interiors, yet the depth of the convecting dynamo layers remains poorly constrained. While magnetic field observations, gravity data, and interior models each provide partial insight, they have not been combined into a single, self-consistent picture of the internal structure. Here, we develop a framework that links observed magnetic field strength with intrinsic heat flux and gravity-constrained interior structure using energy-based dynamo scaling laws. By relating the axial magnetic field strength to the convective power, we infer the radial thickness of the dynamo-generating region for both Jupiter and Saturn. The constants of proportionality in the scaling relations are derived using independent constraints from Earth observations, Jupiter observations, and numerical dynamo simulations. Applied to Jupiter, this framework shows how the inferred dynamo layer thickness is coupled to the outer boundary of the dynamo region. Thinner dynamo layers are predicted when the outer boundary shifts to shallower depths, and no solutions are possible when the outer boundary is less than 73% of Jupiter’s radius. These results constrain plausible geometries for future numerical dynamo simulations. Extending the analysis to Saturn, we find a thick, deep-seated dynamo layer with an outer radius at 42% of the radius to be most plausible. An alternative solution with an inner radius of the dynamo region at 60% of the planetary radius, as suggested by ring seismology models, requires a very thin dynamo layer, occupying only 2%–3% of the total radius.

Geosciences↗
DOE OSTI2024

Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies

ABSTRACT Observations suggest a co-evolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance r from the bulge center and the local virial equilibrium for permeated gases on scale r, a key parameter $\varepsilon _b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling (or the "specific" cooling rate per unit mass), and thus regulates the co-evolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon _b\propto (1+z)^{5/2}$. A higher $\varepsilon _b$ in the early Universe means a higher specific cooling rate that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon _b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon _b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass–size relation $M_b\propto \varepsilon _b^{2/3}r_b^{5/3}G^{-1}$, the dispersion–size relation $\sigma _b^2\propto (\varepsilon _b r_b)^{2/3}\propto (1+z)$, or the mass–dispersion relation $M_b\propto \varepsilon _b^{-1}G^{-1}\sigma _b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon _b M_{\rm BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon _b^2 M_{\rm BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon _b M_{\rm BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon _b^{4/5}M_{\rm BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi _{\rm BH}$, active galactic nucleus (AGN) mass function $\Phi _{\rm AGN}$, and duty cycle U that predict $\Phi _L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi _{\rm AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi _L$, and $U\propto M^{-1/5}$ at high redshift.

(galaxies:) quasars: supermassive black holes↗
DOE OSTI2025

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabytescale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling.

Li, Chaojian [ORNL] (ORCID:0000000340309777)↗
DOE OSTI2025

Asymptotic scaling laws for the stagnation conditions of Z-pinch implosions

Implosions of magnetically driven annular shells (Z pinches) are studied in the laboratory to produce high-energy-density plasmas. Such plasmas have a wide-range of applications including x-ray generation, controlled thermonuclear fusion, and astrophysics studies. In this work, we theoretically investigate the in-flight dynamics of a magnetically driven, imploding cylindrical shell that stagnates onto itself upon collision on axis. The converging flow of the Z-pinch is analyzed by considering the implosion trajectory in the (A, M) parametric plane, where A is the in-flight aspect ratio and M is the implosion Mach number. For an ideal implosion in the absence of instabilities and in the limit of A ≫ 1, we derive asymptotic scaling laws for hydrodynamic quantities evaluated at stagnation (e.g., density, temperature, and pressure) and for performance metrics (e.g., soft x-ray emission, K-shell x-ray emission, and neutron yield) as functions of target-design parameters.

Ruiz, D. E. [Sandia National Laboratories (SNL-NM)↗
DOE OSTI2026

Casimir-Polder potential on an excited atom near an atomic array

We develop a microscopic description of the fluctuation-mediated Casimir-Polder (CP) shifts on a 'test' two-level atom placed near a two-dimensional atomic array of two-level atoms. We derive the resonant and off-resonant CP potentials experienced by the excited test atom using fourth-order perturbation theory, under the assumption that the test atom resonance is far detuned from those of the array atoms. The total potential on the test atom can be described as the sum of the pairwise resonant and off-resonant potentials resulting from its interaction with the individual atoms of the array. We analyze the asymptotic scaling of CP shifts as a function of the test atom-array separation, and its dependence on various system parameters: array spacing and size, and dipole orientation of the array atoms. Our results bridge the description of CP potential across two distinct regimes: (i) from a single-atom limit where we recover the well-known two-atom Van der Waals potential, (ii) to a macroscopic boundary limit, where we demonstrate new asymptotic scaling laws. We demonstrate that these scaling laws can be tuned via the microscopic parameters of the atomic array, establishing atomically-controlled arrays as a versatile platform for tailoring fluctuation-induced QED phenomena.

FOS: Physical sciences↗
DOE OSTI2026

Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

Quantum spin models↗
DOE OSTI2025

Experimental and theoretical evidence of universality in superfluid vortex reconnections

The minimum separation between reconnecting vortices in fluids and superfluids obeys a universal scaling law with respect to time. The prereconnection and the postreconnection prefactors of this scaling law are different, a property related to irreversibility and to energy transfer and dissipation mechanisms. In the present work, we determine the temperature dependence of these prefactors in superfluid helium from experiments and a numeric model which fully accounts for the coupled dynamics of the superfluid vortex lines and the thermal normal fluid component. At all temperatures, we observe a pre- and postreconnection asymmetry similar to that observed in other superfluids and in classical viscous fluids, indicating that vortex reconnections display a universal behavior independent of the small-scale regularizing dynamics. We also numerically show that each vortex reconnection event represents a sudden injection of energy in the normal fluid. Finally we argue that in a turbulent flow, these punctuated energy injections can sustain the normal fluid in a perturbed state, provided that the density of superfluid vortices is large enough.

Reconnections↗
DOE OSTI2025

Electron-Only Magnetic Reconnection and Inverse Magnetic-Energy Transfer at Subion Scales

We derive, and validate numerically, an analytical model for electron-only magnetic reconnection applicable to strongly magnetized plasmas. Our model predicts subion-scale reconnection rates significantly higher than those pertaining to large-scale reconnection, aligning with recent observations and simulations. Here, we apply this reconnection model to the problem of inverse magnetic energy transfer at subion scales. We derive time-dependent scaling laws for the magnetic energy decay and the typical magnetic structure dimensions that differ from those previously found in the magnetohydrodynamics regime. These scaling laws are validated via two- and three-dimensional simulations, demonstrating that subion-scale magnetic fields can reach large, system-size scales via successive coalescence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗