Publications

Time Reversal (TR) is a signal processing technique that can be used to focus acoustic waves to a specific location in space, with most applications aiming to create an impulsive focus. This study instead aims to focus long-duration noise signals using TR. This paper seeks to generate higher amplitude noise at a desired location over an existing method of broadcasting equalized noise. Additionally, this paper explores various characteristics associated with focusing long duration noise using TR. The dependence of the focal amplitude on the duration of the focused signal is explored as well as the implications of using multiple sources when focusing noise. The focal amplitude decreases with longer duration and then levels off when the duration exceeds a few seconds. Coherent addition of focused noise is observed if all loudspeakers have coherent noise signals convolved with their reversed impulse responses. Lastly, focusing noise with a desired spectrum is explored.

Bentonite-based engineered barrier system (EBS) is a key component of many repository designs for the geological disposal of high-level radioactive waste. Given the complexity and interaction of the phenomena affecting the barrier system, coupled thermo-hydro-mechanical (THM) numerical analyses are a potentially useful tool for a better understanding of their behaviour. In this context, a Task (the Horonobe EBS experiment) was undertaken to study, using numerical analyses, the thermo-hydro-mechanical (and thermo-hydro) interactions in bentonite based engineered barriers within the international cooperative project DECOVALEX 2023. One full-scale in-situ experiment and four laboratory experiments, largely complementary, were selected for modelling. The Horonobe EBS experiment is a temperature-controlled non-isothermal experiment combined with artificial groundwater injection. The Horonobe EBS experiment consists of the heating and cooling phases. Six research teams performed the THM or TH (depended on research team approach) numerical analyses using a variety of computer codes, formulations and constitutive laws. For each experiment, the basic features of the analyses are described and the comparison between calculations and laboratory experiments and field observations are presented and discussed.

The creep behavior of 316 L stainless steel at room temperature was evaluated as a function of time and applied stress using a new high-Throughput approach. Several common creep models were evaluated against the observations, leading to deeper analysis of a stress-dependent modified logarithmic creep model. Within this model, multiple sources of uncertainty were compared. Aleatoric stochastic variation between samples under nominally identical conditions was identified as the primary contributor to uncertainty in creep response. Under any particular set of conditions, the sample-To-sample variability in creep strain was as high as a factor of two, highlighting the engineering importance of characterizing large statistical datasets. The model's extrapolation capabilities were assessed by comparing predictions derived from calibration on partial, shorter-duration subsets of the data. These findings underscore the importance of accounting for stochastic effects in predictive modeling of aging phenomena.

We introduce a grain boundary (GB) translation vector, tWS, to describe and quantify the domain of the microscopic degrees of freedom of GBs. It has long been recognized that for fixed macroscopic degrees of freedom of a GB there exists a large multiplicity of states characterized by different relative grain translations. More recently another degree of freedom, [n], the number of GB atoms, has emerged and is now recognized as an equally important component of GB structural multiplicity. In this work, we show that all GB microstates can be uniquely characterized by their value of tWS, which is located within the Wigner–Seitz (WS) cell of the Displacement-Shift-Complete lattice (DSCL) of the GB. The GB translation vector captures information about both the translation state and the number of GB atoms. We show that the density of GB microstates inside the WS cell of the DSCL is not uniform and can form clusters that correspond to different GB phases. The vectors connecting the centers of the clusters correspond to the Burgers vectors of GB phase junctions, which can be predicted without building the junctions. Using tWS, we quantify GB excess shear and argue that it is defined up to a DSCL vector, which has implications for thermodynamic equilibrium conditions. Additionally, this work generalizes the definition of the number of GB atoms [n] to asymmetric boundaries.

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. We propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5× improvement in accuracy and allows for taking an 8× larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

This study investigates the application of microbeads as an innovative encapsulation technique to protect electronic components from harsh mechanical strain. Traditional encapsulation methods using hard epoxy provide substantial mechanical support but create thermal expansion mismatch issues, potentially leading to electronic component failure. We explore the use of finely powdered microbeads to achieve protective structures combining stiffness and energy absorption. The research focuses on key variables, including microbead size, microbead roughness, compaction of microbeads, and circuit board mounting in the encapsulation, all of which influence the encapsulation’s effectiveness. Experimental setups and testing protocols were developed to assess the performance of various microbead materials under different impact conditions. Results demonstrate that microbead encapsulation significantly reduces strain on circuit boards, minimizing the risk of damage during mechanical shocks. However, challenges remain, such as optimizing microbead characteristics and modeling their behavior within large-scale circuit board assemblies. Despite these challenges, the findings suggest that microbead encapsulation offers a promising alternative to conventional methods, enhancing the durability and reliability of electronic components in high-stress environments.

Abstract not provided.

Defect reduction remains a critical objective in the integrated circuit manufacturing process, particularly within the highly re-entrant lithography modules where minimizing defects is crucial. Defects at the wafer edge can contaminate lithography modules and downstream processing equipment, leading to redistribution onto the wafer surface and adversely affecting overall device yield. A persistent challenge in the resist coating process is the formation of resist edge beads, driven by the strong Van der Waals attraction of excess photoresist (PR) to itself and the underlying substrate. The edge bead removal (EBR) process is a standard cleaning step designed to eliminate these edge beads and prevent potential contamination. In this study, we identify the sources of EBR induced defects and additional EBR process encroachment toward edge patterning during the EBR cleaning process. This study provides a comprehensive study aimed at optimizing the EBR cleaning process to effectively eliminate EBR-induced defects, thereby enhancing overall device yield. Specifically, we identify three primary defects induced by the EBR cleaning process: rainbow-type, finger-shaped, and teardrop-type defects. Our experimental study reveals that in addition to EBR rinse time, PR cast time is crucial parameters contributing to the formation of these defects. By properly optimizing the PR cast time and EBR rinse time, we were able to remove nearly 100 % of dense clusters of defects that were easily visible even at low magnification optical microscopy throughout the wafer edge. We observed that shorter PR casting times shows edge defects caused by inefficient EBR process because of insufficient time for PR to fully settle causing superfluous PR to continue flowing toward wafer edge during EBR clearing step, leading to partial removal of PR at the wafer edge and the formation of rainbow defects. Proper optimization of both PR casting time and EBR chemistries dispense time is essential to resolve these defects, ensuring efficient EBR cleaning process and improved overall device yield.

Many overarching standards, regulations, or other requirements necessitate that the critical temperature (Tcrit) of an energetic material be known or estimate prior to operations such as heating. However, they rarely, if ever, provide a specific method for doing so. While other methods exist to calculate Tcrit, such as the Frank-Kamenetskii equation, computer simulation, etc., these cannot be readily utilized for energetics that are physical mixtures (i.e. most pyrotechnics) or materials where detailed material properties required for such calculations are lacking. In this study, a COTS (commercial off-the-shelf) SBAT (Simulated Bulk Auto-ignition Test) apparatus is modified to perform Henkin cookoff tests. This creates a simple, efficient, and cost-effective solution to estimate required Tcrit values for energetic materials. After a historical overview of the evolution of the Henkin test, several common energetic materials (PETN, RDX, etc.) for which Tcrit has been readily calculated, and historical data is available, were analyzed for comparison and verification purposes. This was followed by a variety of pyrotechnic mixtures and other materials to where calculation methods cannot be readily used. The modified apparatus, as well as an updated sample shell sealing method, produced results that aligned well with historical data. It also produced reasonable Tcrit estimates for those materials where the Frank-Kamenetskii equation cannot be applied.

The Ghareb formation, a shallowly buried porous chalk in Israel, is currently a candidate for nuclear waste disposal. The potential repository is somewhat unique for its host rock and emplacement in shallow (500 m) engineered large diameter boreholes. Herein, the thermal properties of the Ghareb are determined to support design and performance assessment; the relevant properties measured are thermal conductivity, specific heat capacity, thermal diffusivity, and thermal expansion coefficient along with their relationship with varying temperature. For the temperature range of 40 to 275 °C, the thermal conductivity ranges from 0.30 to 1.10 W/m·K, the thermal diffusivity ranges from 0.20 to 0.72 mm2/s, and volumetric heat capacity ranges from 0.86 to 2.00 MJ/m3·K. Thermal strain measurements were used to estimate the linear thermal expansion coefficient to be 6·10–4–9·10–2 °C−1 from 40 to 300 °C. These measured properties were used in a thermomechanical model to estimate near-field stresses an hour and 10 years after waste emplacement; the borehole was found to be stable. Thermal loading after 10 years was predicted to elevate local pore pressures by 1–1.5 MPa. The laboratory measurements coupled with analyses are the first attempts at performance assessment characterization for this first of its kind potential repository setting with this chosen host rock.

The pharmaceutical drug product development process can be greatly accelerated through the use of modeling and simulation techniques to predict the manufacturability and performance of a given formulation. The anticipation and possible mitigation of tablet damage due to manufacturing stresses represents a specific area of interest in the pharmaceutical industry for predicting formulation and tableting performance. While the finite element method (FEM) has been extensively used for predicting the mechanical behavior of powder material in the compaction processes, a shortcoming of the approach is the inherent difficulty to predict discontinuities (e.g., damage or cracking) within a tablet as FEM is a continuum-based approach. In this work, we propose a novel method utilizing peridynamics (PD), a numerical method that can capture discontinuities such as tablet fracture, to predict the evolution of damage and breakage in pharmaceutical tablets. The approach links (1) the finite element method – to elucidate the behavior of powders during die compaction – with (2) the peridynamics modeling technique – to model the discontinuous nature of damage and predict tablet breakage during the critical stages of unloading and ejection from the compression die. This short communication presents a proof of concept including a workflow to calibrate the linked FEM-PD simulation models. It demonstrates promising results from a preliminary experimental validation of the approach. Following further development, this approach could be used to guide the optimization of compression processes through targeted changes to formulation material properties, compression process conditions, and/or tooling geometries to deliver improved process efficiency and tablet robustness.

Electrical resistivity tests can be used to evaluate the transport properties of concrete and provide a durability assessment. However, the electrical resistivity is largely dependent on the pore solution composition and recent work suggests that some aggregates have the capacity for cation uptake. This study first aims to provide further evidence for adsorption of cations on aggregate surfaces, without formation of reaction products (e.g. alkali-silica reaction). Secondly, hardened mortar samples were prepared using a fine aggregate with a high alkali affinity and a non-reactive fine aggregate as a control. The electrical resistivity of mortars was measured, and the pore solution of these mortars was obtained through high-pressure extraction. The effect of aggregate moisture dilution on the pore solution was decoupled by using a pore partitioning model. The results indicate that aggregate minerology can influence the pore solution composition through cation uptake. Specific minerals of minor quantity, like biotite, may be responsible for cation exchange. While adsorbed cations strongly affected pore solution and formation factor measurement, the bulk resistivity measurements on hardened mortar were only marginally influenced. Research on other implications of similar aggregate interactions with pore solutions are an intriguing area for future research.

This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.

The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.

As the power grid is undergoing rapid transformations, numerous questions are emerging about its vulnerability to wide-area extreme events (WAEE), which could influence its operations. Relatively few analyses have been conducted to date regarding the impact of correlated outages during WAEEs on the grid’s ability to balance resources with demand. This study addresses this gap by conducting a resource adequacy analysis for a hurricane-inspired WAEE on a 2035 synthetic power grid system for the United States. A sensitivity analysis was also conducted to characterize the relative impact of weather on unserved energy. Our results indicate that although the magnitude and duration of the shortfalls vary depending on weather conditions, persistent shortfalls are observed in some regions. Initial explorations indicate a strong correlation between transmission-constrained regions and regions with persistent shortfalls. Future work could generate empirically-grounded representations for generator outages as well as conduct causal analyses of these shortfalls to improve understanding of drivers as well as possible mitigation strategies. Continued exploration of extreme weather impacts on the grid is important to develop more robust understanding of the reliability and resilience of our power systems, especially as they undergo rapid transformations.

The daily conduct of high-risk, high-consequence work, by its very nature, can be mentally demanding. Research demonstrates that failure to manage or mitigate these demands can degrade psychological well-being and mental health. Degradations in employee well-being impact individual performance, jeopardizing safety and mission success in the workplace. This Commentary describes efforts taken at Sandia National Laboratories over the past eight years to evaluate, understand, learn from, and mitigate factors such as stress, burnout, work-life imbalances, and disengagement in the workplace that can degrade employee well-being. After evaluating these four facets of employee well-being, Sandia National Laboratories initiated several programs to address observations and outcomes, including the Thrive program, the Take 10 Initiative, work-life balance resources, employee resource groups such as the Sandia Parents Group, and Workplace Improvement Networks. Collectively, the intent of these programs is to ensure employee mental readiness to conduct hazardous high-risk work effectively and safely. Preliminary data suggest that these programs are succeeding. Other national laboratories and organizations, regardless of size, may wish to apply similar approaches to improve employee well-being and thereby increase the likelihood of mission success.

Photonic integrated circuits incorporating intersubband transitions are ideal for mid-infrared and terahertz nanophotonics. However, the design of epitaxies has long been inhibited by two factors: the modest predictivity of ab initio theory and the absence of absolute intersubband gain and loss measurements under operating conditions. Existing measurements either yield inaccurate gain profiles or do not accurately assess dependence on frequency, bias, and temperature. Here, we present a delay-resolved absolute-referencing method for accurate gain evaluation without these limitations, addressing a long-standing challenge. By creating a photonic circuit that allows broadband pulses to traverse different lengths of a gain medium, we measure the absolute transmission of intersubband structures. Gain profiles match theoretical predictions at lower temperatures, with gain and dispersion clamping after lasing, and faster-than-expected degradation occurs at higher temperatures. Our approach provides a precise experimental evaluation of temperature-dependent gain performance and gives insight into optimizing temperature performance and frequency comb designs.

This study challenges the assumption of the non-flammability of lithium metal all-solid-state batteries (LiSSBs) and other lithium metal batteries without flammable electrolytes. Through thermodynamic calculations and ex situ experiments, we reveal for the first time the risk of thermite reactions between lithium metal and LiFePO4 in both charged and discharged states. Reactivity is worsened by excess lithium metal in the cell, reaching final maximum adiabatic temperatures of 2,500°C in the charged state, which is hot enough to boil lithium. The thermite reaction triggers spontaneously at 500°C, with poor surface contact, while increasing surface contact through mixing initiates the reaction at room temperature in an inert environment. Despite its fast kinetics, this reaction is transport limited due to lithium passivation, leading to long burn times and reignition risks. Given the risk of lithium metal contacting the cathode during failure, understanding these reactions is crucial for ensuring the safe deployment of LiSSBs.

Silicon processing techniques such as atomic precision advanced manufacturing (APAM) and epitaxial growth require surface preparations that activate oxide desorption (typically >1000 °C) and promote surface reconstruction toward atomically clean, flat, and ordered Si(100)-2 × 1. We compare the aqueous and vapor phase cleaning of Si and Si/SiGe surfaces to prepare APAM-ready and epitaxy-ready surfaces at lower temperatures. Angle resolved X-ray photoelectron spectroscopy (ARXPS) and Fourier transform infrared (FTIR) spectroscopy indicate that vapor hydrogen fluoride (VHF) cleans dramatically reduce carbon surface contamination and allow the chemically prepared surface to reconstruct at lower temperatures, 600 °C for Si and 580 °C for a Si/Si0.7Ge0.3 heterostructure, into an ordered atomic terrace structure indicated by scanning tunneling microscopy (STM). After thermal treatment and vacuum hydrogen termination, we demonstrate STM hydrogen desorption lithography (HDL) on VHF-treated Si samples, creating reactive zones that enable area-selective chemistry by using a thermal budget similar to CMOS process flows. We anticipate that these results will establish new pathways to integrate APAM with Si foundry processing.

We quantify the effect of a nuclear-reactor environment on the hydrogen isotope equilibrium vapor pressure over pure zirconium and zirconium hydride. A vacuum-sealed capsule containing a zirconium foil with 6 atom% deuterium was irradiated at a neutron flux of ~10¹⁴ cm^-2 s^-1 at the University of Missouri Research Reactor (MURR). The internal stainless-steel (SS) sample holder acted as the heat source via gamma absorption. To measure low desorption pressures in a high-flux environment, we developed a method to transduce pressure from the measured sample temperature during irradiation, calibrating with known deuterium pressures in unirradiated capsules at various heating powers using an internal filament-heated system designed to mimic irradiation-induced heating. Our temperature-pressure transduction method operates similarly to a Pirani or thermocouple pressure gauge. The in-reactor measurements revealed a roughly 4-fold enhancement in desorption pressure after only 6 h of irradiation (~2 × 10¹⁸ cm^-2 neutron fluence) compared to thermal desorption in control experiments, indicating a nonthermal contribution from neutron irradiation. The slower temperature/pressure stabilization rate in the reactor suggests that desorption pressure enhancement increases with neutron fluence. Further, this enhancement signifies increased solubility of hydrogen isotopes in zirconium during irradiation. We propose that high-energy neutron collisions with hydrogen isotopes in hydrides lead to their decomposition at lower temperatures, supersaturating the surrounding αZr lattice and resulting in higher desorption pressure, which continues to rise as more hydrides dissolve with increasing neutron fluence.

Ongoing research in isolating high-level nuclear waste and spent fuel has highlighted compacted bentonite as a suitable material for engineered barrier systems in deep geological repositories due to its extraordinary swelling and retention properties. This research focuses on the chemo-mechanical behavior of compacted bentonite exposed to different pore fluids with different concentrations and loading conditions. The study involves swelling pressure and compressibility experiments along with mineralogy analysis employing X-ray diffraction (XRD) and Cation exchange. The tests were conducted on BCV (a Mg/Ca- bentonite) compacted at a dry density of 1.48 ± .02 Mg/m³. An advanced chemical-mechanical constitutive model for unsaturated highly expansive clays was adopted to simulate the material response and better understand its behavior. The model is able to account for the main phenomena at both macro and microstructural levels and the interactions between them. The model successfully replicated experimental observations. The XRD analyses support the macroscopic observation, indicating that salinity impacts crystalline swelling as demonstrated by the reduction of basal spacing from 19.27 Å to 15.68 Å when the osmotic suction increases from 0 MPa to 33 MPa. The results suggested that the osmotic pressure generated by the concentration in the pore fluids promotes a reduction in swelling pressures, swelling strains, and crystalline swelling of clay minerals. Also, it affects the pre-consolidation stress and the compressibility of the compacted samples. In conclusion, it was also observed that both solution type and solution concentration impact the clay swelling pressure.

Here, a novel approach is presented for computing general rigid body motion based on a few known linear accelerations. This method utilizes linear acceleration data obtained from three distinct points on the body, all within a body-fixed reference frame. The only requirement is that the three chosen points must not be collinear. A system of differential-algebraic equations is derived, combining principles of rigid body kinematics with theory of the rotation group SO(3). These equations provide a framework for numerically computing various motion parameters, including angular velocity, angular acceleration, body orientation, velocity field, acceleration field, and displacement field. By numerically solving this system of equations, we can fully characterize rigid body motion in three-dimensional space. A numerical example is provided to demonstrate the practical implementation and efficacy of the proposed technique, illustrating its potential for accurate motion computation in various applications.

Sandia National Laboratories is currently investigating scalable architectural simulation capabilities, with a focus on simulating and evaluating highly scalable supercomputers for high-performance computing applications. This exploration is driven by the shift toward more specialized forms of compute and the need for a more diverse set of accurate models. This project will explore the use of General-Purpose Graphical Processing Units (GPGPUs) in high-performance computing using both physical systems and new simulator models – traditional GPUs as well as tightly-coupled SIMT accelerators.

Advancement of Earth System Models (ESMs) is becoming increasingly challenging due to a confluence of factors including increasing model complexity – to more fully represent the earth system, increasing spatial resolution - to achieve higher accuracy by resolving fine-scale dynamical to physical, biological, and chemical processes and their interaction, increasing ensemble size - to more accurately represent predictive uncertainty, and increased computing requirements – to enable more accurate and timely weather predictions and climate projections for societal benefit. The belief by many that computing will take care of itself is no longer valid given the disruptive changes in HPC that are driving up the cost of computing, increasing the difficulty of using emerging HPC effectively, and exposing limits in parallelism, portability and scalability of the ESM applications themselves.

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. 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.