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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.

Peters, B. C., Jr.↗
DOE OSTI2025

Design and Development of Novel Equiatomic Refractory Multi Principal elemental Alloys Based on MoNbTi System for Use in Irradiation Environments

Multi Principal Elemental Alloys (MPEA) have emerged as promising materials for next-generation nuclear reactors due to their exceptional irradiation resistance. Eight equiatomic MPEA based on the MoNbTi system, comprising of elements with low thermal neutron absorption cross-sections were explored using a combined approach employing empirical parameter estimations, and CALPHAD simulations by which the phases and elemental segregation observed in all the alloys in the as-cast state were predicted. Solution heat treatment at 1500°C transformed five alloys into single-phase matrix materials, enhancing homogeneity and reducing hardness. The densities of the alloys ranged between 6.47 to 7.68 g/cm3, hardness between 472 and 656 VHN, Young’s modulus between 142 GPa to 169 GPa, shear modulus between 54 GPa and 62 GPa, bulk modulus between 117 GPa to 194 GPa and Poisson’s ratio between 0.3 to 0.35. The in-situ high temperature Xray diffraction results, differential scanning calorimetry and dilatometry results up to 1000°C suggested the high temperature phase stability of the MPEA. Subsequent ageing heat treatment at 800 and 1000 oC for 96 hours revealed significant secondary phase precipitation in MoNbTiZr, MoNbTiZrV, and MoNbTiCrA. Oxidation studies at 800 oC for 24 hours in air revealed superior oxidation resistance and cubic rate law dependence in Cr containing MPEA especially in MoNbTiCrAl, while severe mass gain resulting in total disintegration and exfoliation in MoNbTiZr and MoNbTiZrV. This comprehensive study underscores the potential of novel MPEA as promising materials for advanced nuclear reactor applications, shedding light on their microstructural control, mechanical properties, thermal stability, and oxidation resistance.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1987

Estimation of canopy parameters of row planted vegetation canopies using reflectance data for only four view directions

A procedure for estimating leaf area index (LAI) and percentage of ground cover (GC) for inhomogeneous row planted vegetation canopies using measurement of canopy reflectance (CR) data for only four directions is presented. This procedure, referred to as 'reconstructive inversion', uses the CR data for these directions to first 'reconstruct' the complete bidirectional surface, which is then used to estimate the canopy parameters using the standard inversion of a CR model technique. The technique has been successfully applied to soybeam and corn canopies in various stages of growth.

Goel, Narendra S.↗
DOE OSTI2026

Toward real-time optimization through model reduction and model discrepancy sensitivities

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within wall-clock-time limitations. However, this is often unattainable for complex systems, such as those modeled by nonlinear partial differential equations. One strategy for mitigating this issue is to construct a reduced-order model (ROM) that enables more rapid optimization. In particular, the use of nonintrusive ROMs—those that do not require access to the full-order model at evaluation time—is popular because they facilitate the computation of optimization solutions within the wall-clock time requirements. However, the optimization solution will be unreliable if the iterates move outside the ROM training data. This article proposes the use of hyper-differential sensitivity analysis with respect to model discrepancy (HDSA-MD) as a computationally efficient tool to augment ROM-constrained optimization and improve its reliability. The proposed approach consists of two phases: (i) an offline phase where several full-order model evaluations are computed to train the ROM, and (ii) an online phase where a ROM-constrained optimization problem is solved, a limited number of full-order model evaluations are computed, and HDSA-MD is used to enhance the optimization solution. Numerical results are demonstrated for two examples, atmospheric contaminant control and wildfire ignition location estimation, in which a ROM is trained offline using inaccurate atmospheric data. In conclusion, the HDSA-MD update yields a significant improvement in the ROM-constrained optimization solution using only one full-order model evaluation online with corrected atmospheric data.

PDE-constrained optimization↗
DOE OSTI2025

Mapping Incidence and Prevalence Peak Data for SIR Modeling Applications

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that forecast wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model’s starting parameters and peak incidence as a system of two equations that can be solved computationally. We demonstrate how to calculate SIR parameter estimates – which describe disease dynamics such as transmission and recovery rates – using this method, and determine that there is a noticeable loss in accuracy whenever prevalence data is misspecified as incidence data. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Multi-Region SEIR Model Incorporating Inter-County Mobility and Time-Dependent Transmission Dynamics: Application to COVID-19 Disease Outbreak Data in North Carolina.

Classical infectious disease compartmental models typically do not incorporate spatial heterogeneity or mobility. We develop a multi-region susceptible-exposed-infected-recovered (SEIR) model in which disease dynamics are coupled via inter-region mobility and the transmission rate is both region and time dependent. We calibrate the model using rolling averages of daily COVID-19 data in all 100 North Carolina counties. Mobility parameters are prescribed using daily inter-county commuter data. The number of transmission rate parameters is substantially reduced by hypothesizing that the dynamics correlate with county-level population density. Parameter estimation is carried out using several objective functions with error terms at different scales. An additive combination of least squares error at the county-level and the state-level, along with a quadratic transmission rate polynomial, yields the lowest overall error at both spatial scales. The calibrated model is used to simulate regional effects of perturbing disease transmission rates in adjacent counties and to illustrate effects of the state’s mobility infrastructure on disease dynamics and spread for a new disease outbreak.

COVID-19 modeling↗
DOE OSTI2025

Better practices for inferring ecosystem water use strategy from eddy covariance data

Eddy covariance data are critical for inferring ecosystem water use strategies. Yet, such inferences are sensitive to a range of assumptions applied across studies, hindering our understanding of water use strategies within and across eddy covariance sites. A recent analysis across 151 FLUXNET2015 and AmeriFlux-FLUXNET datasets found that poor model performance was the key driver of non-robust inferences of ecosystem water use strategies. Here, we leverage this previous analysis to (i) identify the specific assumptions that improve inference model performance across most sites, (ii) explain the mechanisms behind the performance improvements, and (iii) check whether better performance improves water use inference. We find that the common practice of fitting a model to canopy conductance (G c ) derived from the evapotranspiration (ET) observations, rather than to observed ET itself, artificially amplifies data errors and degrades the model performance. Next, accounting for vegetation dynamics by applying a growing season filter or incorporating satellite LAI data improves performance, but the former practice may remove soil water stress periods. Lastly, using the leaf-to-air vapor pressure deficit (VPD l ) derived from ET observations as a model input may artificially inflate performance. Based on these results, we recommend selecting observed ET (rather than derived G c ) as the response variable, carefully accounting for vegetation dynamics, and avoiding derived VPD l as a model input; these best practices improve model performance by c. 20% and robustness by c. 80% across all eddy covariance sites. Nevertheless, the performance improvements do not always correspond to more robust inference of water use strategies, as model parameter selection and surface energy budget closure corrections still strongly influence the ecosystem water use parameter estimation in a site-specific manner.

AmeriFlux↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
DOE OSTI2025

Application of a temporal multiscale method for efficient simulation of degradation in PEM Water Electrolysis under dynamic operating conditions

Hydrogen is emerging as a vital energy carrier, driven by the need to reduce carbon emissions. Proton Electrolyte Membrane Water Electrolysis (PEMWE) enables hydrogen production under fluctuating renewable power conditions but requires improved understanding and stability of the anode catalyst layer under dynamic operating conditions, especially with low noble metal loadings. Long-term degradation experiments are both time-consuming and costly; therefore, a systematic, model-aided approach is essential. In the present work, a temporal multiscale method is applied to reduce the computational effort of simulating long-term degradation processes in PEMWE, with an exemplary focus on catalyst dissolution. A mechanistic model incorporating the oxygen evolution reaction, catalyst dissolution, and hydrogen permeation from the cathode to the anode was hypothesized and implemented. In this way, the local periodicity of transport and reaction processes in dynamic PEMWE operation, which influence the gradual degradation of the catalyst layer, is captured. The temporal multiscale method significantly reduces the computational effort of simulation, decreasing processing time from hours to mere minutes. This efficiency gain is attributed to the limited evolution of Slow-Scale variables during each period of time P of the Fast-Scale variables. Consequently, simulation is required only until local periodicity is achieved within each Slow-Scale time step. Hence, the fully resolved dynamic problem is decoupled into these two scales, employing a heterogeneous multiscale technique. The developed approach effectively accelerates parameter estimation and predictive simulations, supporting systematic modeling of PEMWE degradation under dynamic conditions.

08 HYDROGEN↗
DOE OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗
DOE OSTI2025

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗
DOE OSTI2025

Bayesian model-data comparison incorporating theoretical uncertainties

Accurate comparisons between theoretical models and experimental data are critical for scientific progress. However, inferred physical model parameters can vary significantly with the chosen physics model, highlighting the importance of properly accounting for theoretical uncertainties. In this Letter, we present a Bayesian framework that explicitly quantifies these uncertainties by statistically modeling theory errors, guided by qualitative knowledge of a theory’s varying reliability across the input domain. We demonstrate the effectiveness of this approach using two systems: a simple ball drop experiment and multi-stage heavy-ion simulations. In both cases incorporating model discrepancy leads to improved parameter estimates, with systematic improvements observed as additional experimental observables are integrated.

Bayesian methods↗
DOE OSTI2024

Multivariable degradation modeling and life prediction using multivariate fractional Brownian motion

In system prognostics and health management, multivariable degradation models have been widely developed to predict the life of complex systems using degradation data of multiple Performance Characteristics (PCs). Recent studies have detected a Long-Term Memory (LTM) effect among the degradation process of various PCs, implying a strong coupling phenomenon between the future degradation behavior and historical degradation trajectory. Although the LTM has been widely integrated into single-PC-based degradation modeling, it has not been considered in multi-PC-based scenarios. To capture LTM among multiple PCs, this article proposes a novel LTM-integrated Multivariate Degradation Model (MDM) for system life prediction based on multivariate fractional Brownian motion, which simultaneously incorporates the cross-correlation among different PCs. To estimate parameters of the LTM-integrated MDM, a maximum likelihood method is developed. Here, two likelihood-ratio hypothesis tests are developed to test the existence of the overall and individual LTM effect among multiple PCs. Both simulation studies and physical experiments on the performance degradation of solar energy conversion and storage devices are conducted to validate the proposed model. Results reveal that the proposed LTM-integrated MDM significantly outperforms existing MDMs in life prediction, while the lifetime uncertainty is heavily underestimated by those traditional approaches that neglect the LTM.

42 ENGINEERING↗
DOE OSTI2025

Modeling and Optimization of a Rotating Packed Bed Contactor with a Tetraamine-Appended Metal−Organic Framework for CO 2 Capture

A potential contactor technology for sorbent-based CO 2 capture is the rotating packed bed that contains separate sections for continuous adsorption and desorption. A heat exchanger can be embedded to remove heat in the adsorption section and add heat in the desorption section. In this work, we develop a two-dimensional (2D) model of a rotating packed bed for use in CO 2 capture applications. Mass and energy balances for the model are developed based on a Ljungström-type air preheater, which accounts for the counter-current axial flow of gas phases in separate sections of the bed and the rotation of a solid sorbent, which cycles between adsorption and desorption sections. The sorbent used for this analysis is the tetraamine-appended metal−organic framework Mg 2 (dobpdc)(3−4− 3), chosen for its stability and affinity for CO 2 at low partial pressures, such as those from a natural gas power plant source. An optimization problem is solved that considers the trade-off between maximizing the productivity of the bed and minimizing energy consumption. Maximum productivity and minimum energy are found to be 8.53 kg/h/m 3 and 3.84 MJ/kg, respectively, when these objectives are optimized independently. It is observed that the flue gas pressure and bed rotational speed are the desired operating variables to vary for model-based design of experiments to reduce uncertainty in parameter estimation, as these two variables yielded the most information content based on the Fisher information matrix.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2024

Electrically Powered High-Salinity Brine Separation Using Dimethyl Ether

Dewatering highly saline aqueous streams, from mining and geothermal leachates to industrial wastewater, is essential for effective resource recovery and safe disposal. Membraneless water extraction (MWE) uses a low-polarity solvent to separate water from concentrated aqueous solutions. In this study, we design a new MWE that uses dimethyl ether (DME) to selectively extract water from high-salinity brines, leveraging the volatility of DME to achieve rapid solvent recovery. By separating water and dissolved salts at a liquid–liquid interface, MWE minimizes the deleterious effects of scaling on vulnerable membrane and heat exchanger surfaces, reducing the need for extensive pretreatment and expensive materials. We begin by developing a computational framework for a multistage counterflow liquid–liquid contactor, which extracts water into DME, coupled with a multistage solvent regenerator that uses vapor compression to efficiently separate the desalinated water from the DME extractant. Excess Gibbs free energy and equation of state frameworks are used to model fluid phase equilibria in water–DME–sodium chloride (NaCl) mixtures, with interaction parameters estimated from experimental data. Incorporating equilibrium calculations into a system-scale computational model, we examine the performance of MWE using DME for the first time. Our analysis demonstrates that MWE can concentrate seawater desalination brine (>1.0 mol NaCl kg –1 ) to zero-liquid discharge salinities, with an energy consumption of under 50 kW h per m 3 of water extracted with a solvent recovery ratio greater than 99.9%. We highlight the importance of staging the vapor compression process to simultaneously minimize energy consumption while enabling brine concentration and product water solvent contamination. Finally, the thermodynamic framework developed here allows for the robust evaluation of new MWE solvents and systems for critical brine concentration and fractional precipitation applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Automatic Generation of Chemical Mechanisms for Electrochemical Systems: Solid Electrolyte Interphase Formation in Lithium Batteries

Electrolytes in many lithium ion batteries decompose at the low potentials near the anode. The decomposition products form a layer termed the solid electrolyte interphase (SEI). The composition and growth of the SEI layer significantly affect both the capacity fade and safety of lithium ion batteries. However, SEI formation and growth kinetics are not well understood. In this work, we present an extension of the Reaction Mechanism Generator (RMG) software to automatically generate mechanisms for SEI formation. We extend RMG’s solvation correction framework to account for kinetic solvent effects and demonstrate the accuracy of our technique. We calculate thermochemical parameters for 252 species and rate coefficients for 69 reactions, most with associated solvation corrections. This and additional quantum chemistry data are used to extend RMG’s thermodynamic group additivity and solute parameter estimation schemes to handle lithiated species and add 14 new reaction families to RMG. RMG is additionally extended to simulate electrocatalytic systems. Lastly, we demonstrate RMG on the decomposition of acetonitrile and ethylene carbonate near a battery anode. Furthermore, while this framework does not yet resolve individual ions, as appropriate thermochemistry estimators are not available, and thus, cannot yet resolve more complex electrochemical pathways, RMG is able to generate reasonable pathways for SEI formation that match literature pathways and products. In particular, RMG identifies a new important reaction pathway that is not present in literature.

Chemical reactions↗
DOE OSTI2026

Mechanistic Insights for Plasma-Catalytic CO 2 Reduction over TiO 2 in a Dielectric Barrier Discharge Reactor

Reaction kinetics experiments coupled with phenomenological kinetic modeling and parameter estimation are used to elicit insights into the mechanism and active sites for the plasma-catalytic dissociation of CO 2 on TiO 2 . Experimental and model insights showed that gas-phase reactions contribute at least two-thirds of the overall product formation at explored conditions; weak temperature dependence, strong sensitivity to specific energy input (SEI), apparent first order in CO 2 , and positive influence of cofed argon (Ar) and oxygen (O 2 ) for the gas-phase contributions all suggest that expected plasma reaction steps such as electron-impact and high-energy collisions are the dominant modes for CO 2 dissociation. The Arrhenius-like expression for gas contributions resulted in a preexponential of 4.40 × 10 –3 s –1 , an E SEI,g of 7.90 × 10 –4 mol/kJ, and an E a,g of 1.00 × 10 –3 J/mol. For surface contributions, the small apparent barrier of 16.3 kJ/mol, relatively weaker dependence on SEI, first-order dependence on CO 2 , and insensitivity to cofed Ar and O 2 all point to CO 2 dissociation on TiO 2 surface facets without vacancies and aided by plasma (leading to vibrationally excited CO 2 and/or a reactive surface with significant surface charge accumulation). The Arrhenius-like expression resulted in a preexponential of 7.81 × 10 –2 s –1 , an E SEI,s of 1.90 × 10 –3 mol/kJ, and an E a,s of 1.63 × 10 4 J/mol. The derived kinetic model further enabled a systematic evaluation of the effect of inputs (plasma power, flow rate, CO 2 inlet concentration, and temperature) to identify process trends and optimal operating conditions.

catalyst↗
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↗