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DOE OSTI2026

Uncertainty-Aware Machine Learning for Small-Angle X-ray Scattering Analysis in Autonomous Experimentation

Small-angle X-ray scattering (SAXS) is a powerful high-throughput characterization tool for probing nanoscale structure in native sample environments, providing real-time morphological information such as nanoparticle size and shape during synthesis. However, automated SAXS data analysis for extracting meaningful structural parameters is non-trivial and remains a bottleneck in closed-loop experimentation towards autonomous materials discovery, which demands fast, reliable, and uncertainty-aware data analysis. Here, we develop a machine-learning approach for automated SAXS analysis tailored to closed-loop nanoparticle synthesis. A Random Forest (RF) regression model is trained on 100,000 synthetic SAXS curves generated from polydisperse spherical nanoparticles with realistic background contributions. Using normalized one-dimensional SAXS intensity profiles as input, the RF model directly predicts nanoparticle radius, size polydispersity, and background parameters, while the ensemble standard deviation across trees provides built-in uncertainty quantification (UQ). On synthetic data, we show that combining fit-quality metrics (R 2 , MAE) with thresholds on prediction uncertainty reliably identifies accurate parameter estimates without access to ground truth. We then apply the trained model to 365 experimental SAXS profiles of citrate-reduced gold nanoparticles synthesized using an automated droplet-flow microreactor with in situ SAXS at a synchrotron beamline, classifying the results into high- and low-confidence subsets based on UQ metrics. Finally, we integrate RF-based SAXS analysis into a simulated closed-loop optimization campaign using Gaussian process Bayesian optimization to minimize nanoparticle polydispersity, benchmarking against conventional automated Levenberg–Marquardt fitting. The RF-guided campaign exhibits substantially faster convergence and lower relative opportunity cost (∼0.07 vs ∼0.3), demonstrating that uncertainty-aware machine-learning SAXS analysis significantly enhances the efficiency and robustness of autonomous nanomaterials synthesis workflows.

Bayesian optimization↗

DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗

NASA NTRS1973

An analysis of a charring ablator with thermal nonequilibrium, chemical kinetics, and mass transfer

The differential equations governing the transient response of a one-dimensional ablative thermal protection system are presented for thermal nonequilibrium between the pyrolysis gases and the char layer and with finite rate chemical reactions occurring. The system consists of three layers (the char layer, the uncharred layer, and an optical insulation layer) with concentrated heat sinks at the back surface and between the second and third layers. The equations are solved numerically by using a modified implicit finite difference scheme to obtain solutions for the thickness of the charred and uncharred layers, surface recession and pyrolysis rates, solid temperatures, porosity profiles, and profiles of pyrolysis-gas temperature, pressure, composition, and flow rate. Good agreement is obtained between numerical results and exact solutions for a number of simplified cases. The complete numerical analysis is used to obtain solutions for an ablative system subjected to a constant heating environment. Effects of thermal, chemical, and mass transfer processes are shown.

Clark, R. K.↗

DOE OSTI2026

Coupled heat and mass transfer in internally cooled silica gel-coated aluminum foam heat exchangers for dehumidification

Solid desiccant dehumidifiers offer significant potential to improve humidity control in buildings due to their ability to independently regulate latent (humidity) and sensible (temperature) loads. However, adsorption of water vapor by desiccants is an exothermic process; the resulting heat of adsorption increases both the desiccant bed temperature and the temperature of the air flowing over the bed, thereby limiting the performance of desiccant dehumidifiers. To address this problem, desiccant-coated heat exchanger prototypes were developed by coating silica gel onto aluminum foam substrates and integrated with chilled water circulation for effective removal of the heat of adsorption. Prototype heat exchangers with two different pore densities (10 and 20 pores per inch (PPI)) and two different desiccant loadings (∼10.36% and ∼17.80%) were fabricated. Experiments were conducted by varying the inlet air face velocity, chilled water inlet temperature, and chilled water flow rate to investigate the coupled heat and mass transfer characteristics of the prototype heat exchangers over a wide range of operating conditions. The underlying transport mechanisms were analyzed using transient desiccant bed temperature, outlet air temperature, and outlet humidity profiles. The results demonstrate that internal cooling significantly enhances dehumidification performance by maintaining more favorable thermodynamic conditions for water vapor adsorption. Under identical operating conditions, a 20 PPI heat exchanger coated with 25.05 g of silica gel achieved 98.98% higher cumulative water uptake and 97.75% higher moisture removal capacity than the corresponding non-cooled case after 5 min of adsorption. This substantial enhancement was further supported by a validated one-dimensional coupled heat and mass transfer model developed in the present study. To date, this is one of the first experimental studies to systematically investigate the combined effects of internal cooling, foam pore density, and desiccant loading on the performance of silica-gel-coated metal foam heat exchangers under HVAC-relevant operating conditions.

42 ENGINEERING↗

NASA NTRS1978

The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings

Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.

Weatherill, W. H.↗

DOE OSTI2025

Understanding the Effects of Inhomogeneities at the Back Interface of CdTe‐Based Solar Cells Using 2D Modeling

One-dimensional modeling cannot capture lateral inhomogeneities in CdTe-based devices. Here, we use 2D modeling to investigate the role of varying energetics at the back interface. We consider improvements in the back interface layer (BIL) through either reducing back surface recombination velocity (BSRV) or decreasing the downward band bending near the back interface. We show that when the BSRV is reduced, but strong downward band bending remains, there is no change in the device performance until the BSRV of 90% of the back interface is improved by the BIL. On the other hand, any coverage with a BIL that improves band bending results in device improvements. We use band bending, back interface recombination current densities, and voltage dependent current flow through the device to understand these improvements. The modeling shows that lateral flow of carriers greatly affects device performance, which is not captured in parallel diode modeling, and demonstrates improved understanding with 2D modeling.

2D modelling↗

NASA NTRS1975

Application of blast wave theory to explosive propulsion

An analysis was carried out by using blast wave theory to delineate the important aspects of detonating explosives in nozzles, such as flow and wave phenomena, characteristic length and time scales, and the parameters on which the specific impulse is dependent. The propulsive system utilizes the momentum of the ambient gas set into motion in the nozzle by the explosion. A somewhat simplified model was considered for the situation where the mass of ambient gas in the nozzle is much greater than the mass of gas produced in the explosion, a condition of interest for dense atmospheres, e.g., near the surface of Venus. Instantaneous detonation and energy release was presumed to occur at the apex of a conical nozzle, and the shock wave generated by the explosion was taken to propagate as a spherical wave, thereby setting the ambient gas in the nozzle into one-dimensional radially outward motion.

Back, L. H.↗

DOE OSTI2025

Development, Verification, and Validation of an OpenFOAM-Based Solver for Modeling Inertial Fusion Energy Chambers

Our work seeks to introduce a computational tool tailored to the physics of inertial fusion energy chambers, in particular, those concepts based on thick liquid walls. In this approach, the structural materials are protected by several neutron mean-free-paths of renewable liquid and thus will be able to survive much longer than un-shielded walls, with virtually all structures lasting for the life of the plant and enabling the use of commercially available and qualified materials. The OpenFOAM-based solver named rhoCentralFoam has been used as a starting point. rhoCentralFoam belongs to the standard OpenFOAM solver toolset. It is a high-speed, explicit compressible flow solver with shock-capturing capability. While the main features have been retained, the solver had to be restructured to make use of tabular data for equations of states, a necessary addition to model the complex thermo-physical properties of ionized gasses. This entailed the need to change the independent state variables used by the solver, resulting in a new thermodynamic library and slightly different solution algorithm. Moreover, a radiation heat transfer model based on the P-1 approximation was added to the solver. The solver is verified against an analytical solution from the Sedov-Taylor-Neumann test problem to showcase the ability of the hydrodynamic solvers to handle strong shocks, whereas the P-1 model was verified using a simple one-dimensional problem with an analytical solution. Additionally, a validation case involving shock-wave propagation through jet array is presented, and the results are compared with experimental data from the open literature. Lastly, in order to showcase the utility of the solver for practical cases, we applied the refined solver to two representative scenarios: gas venting within the HYLIFE-II chamber and the compression of the gas following the partial ablation of the liquid wall.

Chamber dynamics↗

DOE OSTI2025

A real-time distributed solid oxide electrolysis cell (SOEC) model for cyber-physical simulation

System integration and dynamic operability between SOEC and balance-of-plant (BoP) components are major technical challenges before realizing rapid load following of SOEC systems. Cyber-physical simulation (CPS) is a leading-edge digital engineering approach and is regarded as the next step beyond Digital Twins. CPS approach can be used to research SOEC system integration and develop dynamic controls prior to actual pilot testing without using a real SOEC. To seamlessly couple with BoP hardware and access non-observable operational parameters (e.g., local temperature gradient) during transients, a distributed one-dimensional (1D) real-time SOEC model was developed. Its real-time execution was demonstrated for 20 to 640 nodes at the fixed time step of 5 ms. A higher excess air ratio enabled smaller local temperature gradients on SOEC solid materials and faster transients upon current density step change from 0.15 to 0.55 A cm -2 . During the transients, the magnitude of the peak temperature gradient nearly doubled in 10 s from -3.5 to -5.9 °C cm -1 . This represents a significant operating risk that can impact the dynamic operability of SOEC systems. In addition, the local temperature gradient was found to change directions on all nodes in SOEC solid materials, with the greatest impact on the upstream nodes. The SOEC model was also tested at the thermal neutral voltage using actual process air flow parameters as variable model inputs. Variable process air temperatures were found to induce alternating local temperature gradients on SOEC solid materials. These are new operational mechanisms for SOEC degradation relevant for load following operational modes yet distinct from previous reports. To mitigate these unfavorable features, the SOEC can be operated at voltages that are slightly (±20 mV) deviated from the thermal neutral voltage. Here, the corresponding net thermal energy change was less than 1.6% of the electric power consumption. This 1D real-time SOEC model established the basis of cyber-physical simulation of SOEC hybrid systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗

DOE OSTI2025

Unraveling membrane electrode assembly design for electrochemical conversion of carbon dioxide to formate/formic acid

This work presents a one-dimensional continuum modeling approach to investigate various cell architectures used for electrochemical conversion of CO 2 to formate/formic acid. Ion transport is simulated by a system of generalized modified Poisson–Nernst–Planck (GMPNP) equations that reflect the reactive transport phenomena including steric effects as the electrolyte solutions become concentrated. In the cathode catalyst layer, ionic current contributions from both the supporting electrolyte and solid-state ionomer are considered. Voltage and CO 2 utilization breakdowns are utilized to deconvolute the impacts of the cell architecture. The origins of (bi)carbonate formation in the cathode are explored, as the subsequent decrease in CO 2 availability is a key reason for low faradaic efficiencies to formate/formic acid. In addition, the role of a supporting electrolyte (KOH) is investigated to understand its tradeoffs: while the K + ions can improve both conductivity and electrochemically active surface area in the cathode, the presence of OH − ions raises the pH and leads to deleterious formation of (bi)carbonates. To this end, we also present parametric studies on the concentration and flow rate of supplied KOH to the cell, to establish a path towards eliminating the need for a supporting electrolyte.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Time-dependent-bases with local CUR decomposition method for accelerating turbulent combustion simulations

Here, this study presents a novel reduced-order modeling framework, Time-Dependent Bases with Local CUR decomposition (TDB-L-CUR), designed to efficiently and accurately approximate the species transport equations in reacting flow simulations. The method extends the existing TDB-CUR approach for chemically reacting flows (Jung et al. Comput. Methods Appl. Mech. Engrg. 437 (2025) 117758), which leverages matrix decomposition techniques to form a global-in-space, time-dependent low-dimensional manifold. While TDB-CUR performs well in homogeneous systems, it may be less well-suited to spatially heterogeneous systems such as turbulent flames, where higher-rank approximations are typically required. The proposed TDB-L-CUR framework introduces two methodological extensions to the baseline approach. First, it applies unsupervised clustering to partition the physical domain into distinct regions, enabling spatially localized manifold construction, thereby reducing the rank required for the reduced-order representation. Second, it incorporates a computational singular perturbation (CSP)-based scheme for identifying and penalizing fast species, allowing for spatio-temporally adaptive mitigation of chemical stiffness. The proposed framework is validated on a hierarchy of test cases, including a one-dimensional premixed flame, a two-dimensional nonpremixed ignition case with vortex interaction, and a three-dimensional turbulent premixed flame. TDB-L-CUR significantly improves accuracy over TDB-CUR while further reducing computational cost. The fully on-the-fly formulation of TDB-L-CUR (i.e., requiring no offline training or prior knowledge) makes it a robust and scalable tool for reduced-order modeling of reactive flows.

Local manifold↗

DOE OSTI2025

ForestFlow: predicting the Lyman-α forest clustering from linear to nonlinear scales

On large scales, the Lyman-α forest provides insights into the expansion history of the Universe, while on small scales, it imposes strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses. This work introduces ForestFlow, a novel framework that bridges the gap between large- and small-scale analyses, which have traditionally relied on distinct modeling approaches. Using conditional normalizing flows, ForestFlow predicts the two Lyman-α linear biases (b δ and b η ) and six parameters describing small-scale deviations of the three-dimensional flux power spectrum (P 3D ) from linear theory as a function of cosmology and intergalactic medium physics. These are then combined with a Boltzmann solver to make consistent predictions, from arbitrarily large scales down to the nonlinear regime, for P 3D and any other statistics derived from it. Trained on a suite of 30 fixed-and-paired cosmological hydrodynamical simulations spanning redshifts from z = 2 to 4.5, ForestFlow achieves 3 and 1.5% precision in describing P 3D and the one-dimensional flux power spectrum (P 1D ) from linear scales to k = 5 Mpc −1 and k ∥ = 4 Mpc −1 , respectively. Thanks to its conditional parameterization, ForestFlow shows similar performance for ionization histories and two ΛCDM model extensions – massive neutrinos and curvature – even though none of these are included in the training set. This framework will enable full-scale cosmological analyses of Lyman-α forest measurements from the DESI survey.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1972

Analysis of heat transfer in a porous cooled wall with variable pressure and temperature along the coolant exit boundary

Fluid from a reservior at constant pressure and temperature is forced through a porous wall of uniform thickness. The boundary through which the fluid exits has specified variations in pressure and temperature along it in one direction so that the flow and heat transfer are two-dimensional. The local fluid and matrix temperatures are assumed to be equal and therefore a single energy equation governs the temperature distribution within the wall. The solution is obtained by transforming this energy equation into potential plane coordinates, which results in a separable equation. A technique yielding an integral equation is used to adapt the general solution so that it satisfies the variable-pressure boundary condition. Analytical expressions are given for the normal exit velocity and heat flux along the exit boundary. Illustrative examples are carried out which indicate to what extent the solution is locally one-dimensional.

Siegel, R.↗

NASA NTRS1972

Ring structure of a neutral gas cloud studied in a one-dimensional expansion into space

A one dimensional treatment of the expansion of a gas cloud of uncharged particles into vacuum is discussed. It is determined that the whole cloud does not change from continuum to free molecular flow at the same time. Some regions of the cloud make the transition sooner than others. An explanation of the ring structure observed during barium cloud experiments is presented using this conclusion. An analysis of the velocity distributions for the two kinds of flow yields a velocity distribution for the whole cloud that exhibits ring structure.

Davidson, R. E.↗

NASA NTRS1973

Measurement capabilities of a one-dimensional LDV system

The capability is investigated of a single component laser Doppler velocimeter (LDV) system for the measurement of three dimensional mean and turbulent flow statistics. Sets of general equations defining the parameters measured by a single component LDV system are derived. Solutions to the equations for different configurations of a single forward scatter LDV system show that three-dimensional mean velocity measurements can be made with a minimum restriction on the precision for detecting the Doppler frequency. Measurements of the three-dimensional cross products and correlation parameters are shown to require a significantly higher precision in the Doppler frequency detection.

Cliff, W. C.↗

NASA NTRS1973

Further discrete variable results for a panel flutter optimization problem

Numerical solutions are presented for the problem of minimum weight design of a thin one-dimensional, simply supported, solid panel in compression, with one side exposed to a parallel high supersonic air flow. The flutter speed is held fixed and a minimum thickness constraint is imposed.

Pierson, B. L.↗

NASA NTRS1975

Upgrading of AMTRAN on the datacraft DC 6024

A number of new software extensions and modifications to the AMTRAN system were completed. These modifications include input/output alterations, one-dimensional and two-dimensional array improvements, and disk storage of data enhancements. In order to promote a better understanding of the AMTRAN system software structure, a general description of the AMTRAN modules and their interrelationships was provided. A few sample statements have also been traced through the compilation and execution stages in order to illustrate the flow of system logic. In addition, the previous documentation was updated to reflect these modifications.

Beasley, P. E.↗