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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A small core in Vesta inferred from Dawn’s observations

Vesta’s large-scale interior structure had previously been constrained primarily using the gravity and shape data from the Dawn mission. However, these data alone still allow a wide range of possibilities for the differentiation state of the body. The moment of inertia is arguably the most diagnostic parameter related to the radial density distribution of a planetary body, making it crucial for assessing the body’s state of internal differentiation. Determining the moment of inertia requires additional measurements of the amplitudes of small rotational motions, such as precession and nutation. Here we report an updated estimate of the moment of inertia of Vesta inferred from Dawn’s Doppler tracking via the Deep Space Network and onboard imaging data. The recovered value for Vesta’s normalized polar moment of inertia is $\overline{C}$/MR 2 = 0.4208 ± 0.0047 (where M is the mass of Vesta and R is the reference radius), which is only 6.6% lower than the homogeneous value of 0.4505. This value, combined with the gravity field and global shape, suggests that Vesta’s interior has limited density stratification beneath its howardite–eucrite–diogenite-dominated crust. We propose two possible origin scenarios that are consistent with the observed constraints. In the first scenario, Vesta’s interior did not undergo full differentiation due to late accretion. In the second scenario, Vesta originated as an impact remnant of a larger differentiated body re-accreted with non-chondritic bulk composition produced from a catastrophic impact. Vesta did not experience complete differentiation in either scenario, suggesting that its current state reflects a complex interplay between its accretion timing, thermal evolution, redistribution of 26 Al bearing melt and/or impact processes.

CNEOS 2014-01-08 bolide↗
DOE OSTI2025

Theory for the anomalous phase behavior of inertial active Brownian particles

In contrast to equilibrium systems, inertia can profoundly impact the phase behavior of active systems. This has been made particularly evident in recent years, with motility-induced phase separation (MIPS) exhibiting several intriguing dependencies on translational inertia. Here, we report extensive simulations characterizing the phase behavior of inertial active Brownian particles and develop a mechanical theory for the complete phase diagram without appealing to equilibrium notions. Our theory qualitatively captures all aspects of liquid-gas coexistence, including the critical value of inertia above which MIPS ceases. Notably, our findings highlight that particle softness, and not inertia, is responsible for the MIPS reentrance effect at the center of a proposed active refrigeration cycle.

Feng, Jiechao↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗
DOE OSTI2024

Low-temperature Leidenfrost-like jumping of sessile droplets on microstructured surfaces

The Leidenfrost effect—the levitation and hovering of liquid droplets on hot solid surfaces—generally requires a sufficiently high substrate temperature to activate liquid vaporization. Here, in this paper, we report the modulation of Leidenfrost-like jumping of sessile water microdroplets on micropillared surfaces at a relatively low temperature. Compared to traditional Leidenfrost effect occurring above 230 °C, the fin-array-like micropillars enable water microdroplets to levitate and jump off the surface within milliseconds at a temperature of 130 °C by triggering the inertia-controlled growth of individual vapour bubbles at the droplet base. We demonstrate that droplet jumping, resulting from momentum interactions between the expanding vapour bubble and the droplet, can be modulated by tailoring of the thermal boundary layer thickness through pillar height. This enables regulation of the bubble expansion between the inertia-controlled mode and the heat-transfer-limited mode. The two bubble-growth modes give rise to distinct droplet jumping behaviours characterized by constant velocity and constant energy regimes, respectively. This heating strategy allows the straightforward purging of wetting liquid droplets on rough or structured surfaces in a controlled manner, with potential applications including the rapid removal of fouling media, even when located in surface cavities.

42 ENGINEERING↗
DOE OSTI2025

Stability Analysis of Power Systems with High Penetration of State-of-the-Art Inverter Technologies

With the increasing level of inverter-based resources (IBRs) in modern power systems, this paper presents a small-signal stability analysis for power systems comprising synchronous generators (SGs) and IBRs. Four types of inverter controls are considered: two grid-following (GFL) controls, with or without grid support functions; droop-based grid-forming (GFM) controls; and virtual oscillator control-based GFM. We also analyze the impact of STATCOM and synchronous condensers on system stability to assess their role in the energy mix transition. With the small-signal dynamic behavior of the major technologies modeled, this paper provides stringent stability assessments using the IEEE 39-bus benchmark system modified to simulate future power systems. The exhaustive test cases allow for (a) assessing the impacts of different types and controls of generation and supplementary grid assets, as well as system inertia and line impedance on grid stability, and (b) elucidating pathways for the stabilization of IBR-dominated power systems. The analysis also indicates that future power systems can be stabilized with only a fraction of the total generation as voltage sources without SGs or significant system inertia if they are well distributed. This study provides insights into future power system operations with a high level of IBRs that can also be used for planning and operation studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

A Physics-Based Digital Twin for Wave Elevation and Seabed Moment Estimation of Offshore Monopiles: Preprint

In this work, we present a proof of concept of a physics-based digital twin for a monopile structure (with overhead inertia) subjected to wave loading. The digital twin is formulated using reduced-order models derived from first principles and combined with a Kalman filter for state estimation. The proposed framework estimates the monopile top motion, the wave elevation, and the section forces and moments along the pile using primarily acceleration measurements at the monopile top. Key innovations include the use of a hydrodynamic shape function to represent distributed wave loading in a compact and computationally efficient manner, and the introduction of a shaping filter to augment the state-space with wave kinematics. Synthetic measurement data are generated using OpenFAST and used as a reference to assess the performance of the digital twin. Results demonstrate that the wave elevation can be accurately reconstructed without direct sea-state measurements as long as the wave regime is inertia-dominated. Under the ideal tested conditions, the total hydrodynamic force and sea-bed bending moment are estimated with relative errors on the order of 1% and correlation coefficients exceeding 96%. Future work will evaluate the estimator's performance under operational uncertainties and more complex loading conditions.

17 WIND ENERGY↗
DOE OSTI2026

Quantum Choreography of the Nucleus: Rotations, Vibrations, and Emergent Structure

Abstract Nuclei are complex many-body quantum systems where interactions of the neutrons and protons via the strong, the weak, and the electromagnetic forces lead to the emergence of simple patterns of energy states that have been described by various theoretical approaches. One of the goals of all the theoretical models is the development of a universal theory that can be applied across the entire chart of nuclides. Significant progress has been made by experiments as well as the increasing sophistication of models, but a universal theory has yet to be established. A recent review of nuclei in the Z = 50–82 region of the chart of nuclides has analyzed all the available compiled data from several decades of studies towards a clarification of the low-lying structure of nuclei. Other reviews have reported and explained the emergence of multiple different shapes in nuclei at somewhat higher excitation energies than the ground state. Some have challenged the interpretation of the first excited K π = 0 + band as a vibration of ground state. This work attempts to provide a guide to determining the nature of the first excited K π = 0 + band in nuclei by the combined use of nuclear lifetimes, energy level evolutions, dynamic moments of inertia, and intrinsic quadrupole moments extracted from transition probabilities. The result is that for a subset of the nuclei in this region, the K π = 0 + band is consistent with the traditional 𝛽-vibration description of an oscillation built on the ground state.

CHFB+5DCH↗
DOE OSTI2024

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel-wind energy system is considered and modeled as a switching system between normal, faulted, and post-fault modes. Further, a safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33-bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

barrier function↗
DOE OSTI2024

The ReSWARM microgravity flight experiments: Planning, control, and model estimation for on‐orbit close proximity operations

Abstract On‐orbit close proximity operations involve robotic spacecraft maneuvering and making decisions for a growing number of mission scenarios demanding autonomy, including on‐orbit assembly, repair, and astronaut assistance. Of these scenarios, on‐orbit assembly is an enabling technology that will allow large space structures to be built in situ, using smaller building block modules. However, like many of these scenarios, robotic on‐orbit assembly involves several technical hurdles, such as changing system models. For instance, grappled modules moved by a free‐flying “assembler” robot can cause significant changes in the combined system inertia, which have cascading impacts on motion planning and control portions of the autonomy stack. Further, on‐orbit assembly and other scenarios require collision‐avoiding motion planning, particularly when operating in a “construction site” scenario of multiple assembler robots and structures. Multiple key technologies that address these complicating factors for autonomous microgravity close proximity operations are detailed in this work, in particular: (1) application of global long‐horizon planning, accomplished using offline and online sampling‐based planner options that consider the system dynamics; (2) adaptation of the recently proposed RATTLE information‐aware planning framework for on‐orbit reconfiguration model learning; and (3) connection with robust control tools to provide low‐level control robustness using current system knowledge. These approaches were demonstrated for an autonomous on‐orbit assembly use case by the RElative Satellite sWarming and Robotic Maneuvering (ReSWARM) experiments using NASA's Astrobee robots on the International Space Station. Results of the ReSWARM experiments are provided along with significant operational and implementation detail discussing the practicalities of hardware implementation and unique aspects of working with the Astrobee free‐flyer robots in microgravity. ReSWARM provides a base set of planning and control tools for robotic close proximity operations, demonstrates them in microgravity, and outlines some of the important hardware aspects that future autonomous free‐flyers will need to consider.

Robotics↗
DOE OSTI2025

Main bearing response in a waked 15-MW floating wind turbine in below-rated conditions

Increased wind turbine size raises unknowns related to structural flexibility. Moreover, moving to deeper waters, component reliability becomes more critical. This work investigates main bearing response dependence on drivetrain flexibility and wake impingement in a two-turbine wind farm. A 15-MW floating direct-drive turbine is considered. Large eddy simulations (LES) are employed to model neutral, stable and unstable atmospheric conditions at below-rated mean wind speed, while the engineering codes OpenFAST and FAST.Farm simulate turbine and wake behavior. Results indicate significant sensitivities in fatigue estimates to lateral distance between the upstream and downstream turbine. The trends are most substantial in stable conditions, where the waked downwind main bearing sees twice the fatigue damage estimates of the upstream turbine for one position and 50% for another. Main bearing fatigue sensitivity to drivetrain flexibility is minor, while properly including generator rotor inertia loads is important for the axial forces of the locating (axially fixed) bearing, especially in stable conditions.

17 WIND ENERGY↗
DOE OSTI2026

Observations of the Marine Atmospheric Boundary Layer’s Response to a Solar Eclipse

The atmospheric response to the solar eclipse of 8 April 2024 in North America is investigated with a specific focus on the marine atmospheric boundary layer (MABL). We leverage measurements collected during the Third Wind Forecast Improvement Project (WFIP3), including Doppler lidars, sonic anemometers, and thermodynamic profiler data to investigate the atmospheric response across sites that experienced partial eclipse conditions with nearly 90% obscuration. Using these measurements, we examine eclipse-induced changes in key meteorological parameters, such as temperature, wind speed, and turbulent fluxes. Most previous eclipse studies have been conducted over land, whereas this study provides new observations for both coastal and marine environments, offering additional insight into eclipse-driven variability in the MABL. The findings confirm a notable decrease in downwelling shortwave radiation during the eclipse, which results in rapid cooling of surface air. The temperature reduction ranges from $1.2^\circ \text {C}$ to $1.4^\circ \text {C}$ in coastal regions and from $0.3^\circ \text {C}$ to $0.5^\circ \text {C}$ over the ocean. This analysis suggests that the MABL’s higher thermal inertia compared to coastal regions moderates the temperature decrease during the eclipse. Wind speed exhibits a more complex behavior, as it is influenced by both the MABL and preexisting synoptic conditions. Although a reduction in wind speed is observable up to approximately 140 m above ground level (AGL) at more inland sites, at other locations closer to the coast, this reduction is constrained to the lowest 100 m AGL. Turbulence parameters retrieved from sonic anemometers, such as turbulence kinetic energy, turbulent heat flux, and friction velocity, decrease during the eclipse at coastal sites, accompanied by a brief transition of atmospheric stability from unstable to neutral or weakly stable conditions. For the open-ocean sites, the variability in turbulence statistics and atmospheric stability is minimal during the occurrence of the eclipse.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Thermal Response of a Lithium Vapor Divertor to Cyclical Operation

The lithium vapor divertor concept is being developed as a method to achieve detached divertor conditions in a tokamak while minimizing impurity radiation losses from the core plasma. SOLPS-ITER modeling has previously been used to identify some of the geometric constraints and required lithium evaporation rate of a lithium vapor divertor in a medium-sized tokamak during steady-state operation. Here an updated conceptual design based on these operating requirements is introduced and the thermal response of the system is modeled during cyclical operation, consistent with operation in a short-pulse tokamak. Controllability of the temperature of the lithium capillary porous system (CPS) is achieved by adopting a design where there is no line-of-sight for radiation from the plasma to reach the heated CPS surface. Operational strategies to minimize the amount of lithium evaporated between plasma discharges while achieving steady evaporation rates during plasma discharges are discussed and modeled here. The optimal feedforward control strategy demonstrated in this work is to ramp up the temperature of the evaporator as quickly as possible immediately before a plasma discharge and then reduce the heating to match the desired steady-state net evaporation rate just before the plasma discharge begins, allowing the thermal inertia of the system to stabilize the evaporation rate during the first second of the plasma discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Initial assessment of alternative carbon fiber geometries for design of cost-effective compressive performance: Size effect studies

Carbon fiber provides opportunity to reduce weight in structural composites, including wind turbine blades, due to the material's superior specific stiffness and specific strength compared to alternatives. Despite these advantages, cost and compressive performance are considered weaknesses for carbon fiber products available today. Studies to produce low-cost carbon fiber alternatives, including the use of textile-derived precursor systems, have shown progress and merit through the DOE/ORNL low-cost carbon fiber initiatives. Here, this work focuses on enabling increases in compressive strength through design of the carbon fiber geometry, applicable to both textile and conventional precursor systems, while also providing opportunities to reduce carbon fiber processing costs. Fiber-resin interface and fiber alignment are among the most frequently cited factors controlling composite compressive performance. However, it is believed that there is opportunity in traditionally unexplored routes to increasing compressive strength through alteration of the carbon fiber geometry by increasing the fiber area moment of inertia and/or the fiber perimeter and interfacial area. This paper presents initial results from manufacturing carbon fiber materials to assess the impacts of carbon fiber size on tested composite compressive performance with projected neutral or even beneficial impact on fiber and composite manufacturing economics. Carbon fiber systems with increasing size illustrate a favorable correlation for compressive performance greater than predicted from a micromechanical failure model. The manufacturing and mechanical test results support the hypothesis of this work that alterations to fiber geometry can be used to produce improvements of the compressive strength of carbon fiber reinforced polymers and provide incentive for related work in designing alternative shapes to further enhance compressive performance.

42 ENGINEERING↗
DOE OSTI2025

Facets of hydro power and future trends in a Nordic Context

Hydropower technologies bolster high penetration of variable renewable energies (VREs) in the net zero emissions scenarios. Nevertheless, there are various challenges to meeting the ambitious goal, such as stability, reliability, resiliency, security, lack of reactive power, voltage support and inertia, large-scale storage deployment and coordination, interconnectedness, demand-side response, higher thermal cycles with increased start/stops, and inadequate Levelized Cost of Energy (LCOE) for system-wise VRE integration and profitability. This survey conducts a bottom-up analysis to unveil the opportunities to utilize hydropower facilities and disentangle the nested problem for intertwining design features, control algorithms, operation, optimization approaches, incentives, services, and market mechanisms using a three-pillar framework perspective: grid owners, power producers, and machine designers. The survey identified emerging trends in real-time and capacity markets, flexible power systems, and enhanced grid capabilities, including advanced voltage support and updated grid codes. These developments present significant opportunities for hydropower, such as achieving super-flexibility through hybridization, expanded reactive power capabilities, and advanced operational modes like a synchronous condenser and power adequator functionalities. These opportunities require novel design philosophies — including new winding, stator, and rotor configurations, optimized ventilation, and active cooling systems — to enhance performance under stressed grid and climate conditions. Finally, integrating climate and energy models for multi-basin optimization with finer spatial and temporal granularity enhances the planning accuracy for water management of hydropower while addressing environmental challenges. The review delivers helpful prospective suggestions and tools that would serve researchers, power engineers, and stakeholders in making decisions about hydropower technologies and services in 2050 and beyond.

13 HYDRO ENERGY↗
DOE OSTI2025

Influence of strain-rate on the response of elastomeric architected materials

Architected materials have shown substantial promise in impact mitigation and protective applications, and there has accordingly been great interest in better characterizing their response at elevated strain rates due to impact. There remains ambiguity regarding the contribution of inertial and material responses to strain rate sensitivity, and, in particular, when these effects begin to gain dominance in the impact response of an architected material. The response of soft polymer architected materials as a function of strain rate, in particular, has been little investigated. We characterize the experimental impact response of four soft polymer architected lattice geometries across varying strain rates in the intermediate strain rate regime (∼10 3 s −1 ) using split-Hopkinson pressure bar loading and high speed video characterization of the resulting deformation fields. In conclusion, our results highlight the interplay of influence between constituent material, lattice geometry, length scale, and strain rate in determining the onset of significant inertia effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Analysis of Line Distance Elements for Various Ibr Controllers and System Conditions

The large-scale penetration of inverter-based resources in power systems has challenged protection engineers because of the different fault behaviors these sources provide compared to conventional generation systems. The main challenges include a low level of fault current magnitude, unpredictable angles of sequence currents, and lack of inertia that can lead to maloperation of conventional phasor-based protection elements. This paper presents a sensitivity analysis of transmission line distance protection elements during phase-to-ground and phase-to-phase faults for different inverter controllers and power system conditions. It also summarizes which line protection elements remain secure near IBR terminations and identifies the ones affected by the inverter-based response. The paper concludes by highlighting that regulating negative-sequence current injection during the fault aids correct protection decisions, but does not address the entire challenge. Finally, alternative protection elements to those affected by the inverter fault response are discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗