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DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

DOE OSTI2025

Turbulent Processes that Influence Boundary-Layer Cloud Structure (Final Technical Report)

Many models of the atmosphere simulate vertical profiles of observable fields, such as temperature, moisture, and vertical velocity. To assess the realism of such model output, it is important to evaluate the modeled profiles against observations. However, many extant evaluations consist of comparing time averaged profiles from the model and the observations. Such time averages can smooth out unrealistic features that appear in instantaneous profiles. In this way, the time averages may obscure certain model errors from detection. For instance, many models misrepresent turbulent processes, leading to profiles that are too smoothed out or too noisy. E.g., if a model has coarse vertical resolution and overly strong diffusion, then the model may be unable to produce observed sharp peaks. On the other hand, a model may have artificial approximations that produce spurious jumps in the vertical. Much can be learned by browsing through instantaneous snapshots of model output. But the volume of output produced by a global model is far too great to rely purely on visual inspection. In addition, we need a way to statistically characterize the profiles, so that anomalies can be detected more conveniently.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Doppler-Lidar Evaluation of HRRR-Model Skill at Simulating Summertime Wind Regimes in the Columbia River Basin during WFIP2

Complex-terrain locations often have repeatable near-surface wind patterns, such as synoptic gap flows and local thermally forced flows. An example is the Columbia River Valley in east-central Oregon-Washington, a significant wind-energy-generation region and the site of the Second Wind-Forecast Improvement Project (WFIP2). Data from three Doppler lidars deployed during WFIP2 define and characterize summertime wind regimes and their large-scale contexts, and provide insight into NWP model errors by examining differences in the ability of a model [NOAA’s High-Resolution Rapid-Refresh (HRRR-version1)] to forecast wind-speed profiles for different regimes. Seven regimes were identified based on daily time series of the lidar-measured rotor-layer winds, which then suggested two broad categories. First, in three regimes the primary dynamic forcing was the large-scale pressure gradient. Second, in two regimes the dominant forcing was the diurnal heating-cooling cycle (regional sea-breeze-type dynamics), including the marine intrusion previously described, which generates strong nocturnal winds over the region. The other two included a hybrid regime and a non-conforming regime. For the large-scale pressure-gradient regimes, HRRR had wind-speed biases of ~1 m s -1 and RMSEs of 2-3 m s -1 . Errors were much larger for the thermally forced regimes, owing to the premature demise of the strong nocturnal flow in HRRR. Thus, the more dominant the role of surface heating in generating the flow, the larger the errors. Major errors could result from surface heating of the atmosphere, boundary-layer responses to that heating, and associated terrain interactions. Finally, measurement/modeling research programs should be aimed at determining which modeled processes produce the largest errors, so those processes can be improved and errors reduced.

17 WIND ENERGY↗

DOE OSTI2022

The Economic Impact of Battery Degradation Modelling Uncertainty

Battery energy storage systems (BESS) are used for a variety of applications, with their economic benefit often being the decisive factor for deployment. A multitude of physico-chemical aging mechanisms lead to capacity fade over a BESS life cycle. The models that are used to describe this capacity fade are prone to inherent model errors. Through a holistic techno-economic modelling approach, we investigate the impact of battery degradation modelling uncertainty on the economic benefit of representative BESS applications. Here, it is shown how improved parameter fit quality can reduce the resulting economic uncertainty. Furthermore, we highlight that the consideration of degradation modelling uncertainty is especially crucial when: (i) the cash flow highly depends on the available battery capacity, (ii) a fixed, e.g. warranty mandated, state of health limit acts as the threshold for battery end-of-life, (iii) long evaluation periods and low discount rates are the focus of economic evaluation.

aging↗

DOE OSTI2024

Performance-based earthquake early warning for tall buildings

The ShakeAlert Earthquake Early Warning (EEW) system aims to issue an advance warning to residents on the West Coast of the United States seconds before the ground shaking arrives, if the expected ground shaking exceeds a certain threshold. However, residents in tall buildings may experience much greater motion due to the dynamic response of the buildings. Therefore, there is an ongoing effort to extend ShakeAlert to include the contribution of building response to provide a more accurate estimation of the expected shaking intensity for tall buildings. Currently, the supposedly ideal solution of analyzing detailed finite element models of buildings under predicted ground-motion time histories is not theoretically or practically feasible. The authors have recently investigated existing simple methods to estimate peak floor acceleration (PFA) and determined these simple formulas are not practically suitable. Instead, this article explores another approach by extending the Pacific Earthquake Engineering Research Center (PEER) performance-based earthquake engineering (PBEE) to EEW, considering that every component involved in building response prediction is uncertain in the EEW scenario. Additionally, while this idea is not new and has been proposed by other researchers, it has two shortcomings: (1) the simple beam model used for response prediction is prone to modeling uncertainty, which has not been quantified, and (2) the ground motions used for probabilistic demand models are not suitable for EEW applications. In this article, we address these two issues by incorporating modeling errors into the parameters of the beam model and using a new set of ground motions, respectively. We demonstrate how this approach could practically work using data from a 52-story building in downtown Los Angeles. Using the criteria and thresholds employed by previous researchers, we show that if peak ground acceleration (PGA) is accurately estimated, this approach can predict the expected level of human comfort in tall buildings.

58 GEOSCIENCES↗

DOE OSTI2026

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Quasi-stationary Planetary Scale Waves in Modern Climate Models

We evaluate climate model simulations of geopotential height at the largest space-time scales, considering the first Fourier components (in longitude) of long-term climatological means. Quasi-stationary planetary scale waves emerge from this analysis. Variations of these waves are important components of climate change, for example associated with regional drought. Systematic examination of their long-term climatology provides context for understanding their evolution in time. We compare four reanalysis datasets with “historical runs” from the latest version of the Coupled Model Intercomparison Project (CMIP) and find general agreement, but we also identify model errors outside the range of both observational uncertainty and the uncertainty implied by interannual variability. Errors in wave phase have possible implications for climate model projections of regional climate and of shifting weather patterns. One model in the set we examine, originally created nearly 20 years before the others, exhibits noticeably greater errors.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Machine‐learning‐based construction of barrier functions and models for safe model predictive control

Abstract In this paper, we propose a control Lyapunov‐barrier function‐based model predictive control method utilizing a feed‐forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed‐forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed‐loop stability while preventing the closed‐loop states from entering unsafe regions in state‐space under sample‐and‐hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state‐space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.

Chen, Scarlett↗

DOE OSTI2021

Data-assisted combustion simulations with dynamic submodel assignment using random forests

This investigation outlines a data-assisted approach that employs random forest classifiers for local and dynamic submodel assignment in turbulent-combustion simulations. This method is demonstrated in simulations of a single-element GOX/GCH4 rocket combustor; a priori as well as a posteriori assessments are conducted to (i) evaluate the accuracy and adjustability of the classifier for targeting different quantities of interest (QoIs), and (ii) assess improvements, resulting from the data-assisted combustion model assignment, in predicting target QoIs during simulation runtime. Results from the a priori study show that random forests, trained with local flow properties as input variables and combustion model errors as training labels, assign three different combustion models – finite-rate chemistry (FRC), flamelet progress variable (FPV) model, and inert mixing (IM) – with reasonable classification performance even when targeting multiple QoIs. Applications in a posteriori studies demonstrate improved predictions from data-assisted simulations, in temperature and CO mass fraction, when compared with monolithic FPV calculations. An additional a posteriori data-assisted simulation of a modified configuration demonstrates that the present approach can be successfully applied to different configurations, as long as thermophysical behavior can be represented by the training data. Furthermore, these results demonstrate that this data-driven framework holds promise for dynamic combustion submodel assignments in reacting flow simulations.

42 ENGINEERING↗

DOE OSTI2023

Impact of Seasonal Snow-Cover Change on the Observed and Simulated State of the Atmospheric Boundary Layer in a High-Altitude Mountain Valley

The structure and evolution of the atmospheric boundary layer (ABL) under clear-sky fair weather conditions over mountainous terrain is dominated by the diurnal cycle of the surface energy balance and thus strongly depends on surface snow cover. We use data from three passive ground-based infrared spectrometers deployed in the East River Valley in Colorado's Rocky Mountains to investigate the response of the thermal ABL structure to changes in surface energy balance during the seasonal transition from low to high snow cover. Temperature profiles were retrieved from the infrared radiances using the optimal estimation physical retrieval Tropospheric Remotely Observed Profiling via Optimal Estimation. A nocturnal surface inversion formed in the valley during clear-sky days, which was subsequently mixed out during daytime with the development of a convective boundary layer when snow cover was low. Over high snow cover, a very shallow convective boundary layer formed, above which the inversion persisted through the daytime hours. We compare these observations to NOAA's operational High-Resolution-Rapid-Refresh model and find large warm biases on clear-sky days resulting from the model's inability to form strong nocturnal inversions and to maintain the stable stratification in the valley during daytime when there was snow on the ground. We suggest several factors contributing to the large model errors. These are (a) the inability of the model to represent well-developed thermally driven flows likely due to the too coarse horizontal grid spacing (3 km), (b) too much convective mixing during daytime, and (c) too strong vertical coupling between the valley atmosphere and the free troposphere.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A multi-year short-range hindcast experiment with CESM1 for evaluating climate model moist processes from diurnal to interannual timescales

Abstract. We present a multi-year short-range hindcast experiment and its experimental design for better evaluation of both the mean state and variability of atmospheric moist processes in climate models from diurnal to interannual timescales and facilitate model development. We used the Community Earth System Model version 1 as the base model and performed a suite of 3 d hindcasts initialized every day starting at 00:00 Z from 1997 to 2012. Three processes – the diurnal cycle of clouds during different cloud regimes over the central US, precipitation and diabatic heating associated with the Madden–Julian Oscillation (MJO), and the response of precipitation, surface radiative and heat fluxes, as well as zonal wind stress to sea surface temperature anomalies associated with the El Niño–Southern Oscillation – are evaluated as examples to demonstrate how one can better utilize simulations from this experiment to gain insights into model errors and their connection to physical parameterizations or large-scale state. This is achieved by comparing the hindcasts with corresponding long-term observations for periods based on different phenomena. These analyses can only be done through this multi-year hindcast approach to establish robust statistics of the processes under well-controlled large-scale environment because these phenomena are either a result of interannual climate variability or only happen a few times in a given year (e.g., MJO, or cloud regime types). Furthermore, comparison of hindcasts to the typical simulations in climate mode with the same model allows one to infer what portion of a model's climate error directly comes from fast errors in the parameterizations of moist processes. As demonstrated here, model biases in the mean state and variability associated with parameterized moist processes usually develop within a few days and manifest within weeks to affect the simulations of large-scale circulation and ultimately the climate mean state and variability. Therefore, model developers can achieve additional useful understanding of the underlying problems in model physics by conducting a multi-year hindcast experiment.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Dark Energy Survey Year 6 Results: Point-Spread Function Modeling

We present the point-spread function (PSF) modeling for weak lensing shear measurement using the full six years of the Dark Energy Survey (DES Y6) data. We review the PSF estimation procedure using the PIFF (PSFs In the Full FOV) software package and describe the key improvements made to PIFF and modeling diagnostics since the DES year three (Y3) analysis: (i) use of external Gaia and infrared photometry catalogs to ensure higher purity of the stellar sample used for model fitting, (ii) addition of color-dependent PSF modeling, the first for any weak lensing analysis, and (iii) inclusion of model diagnostics inspecting fourth-order moments, which can bias weak lensing measurements to a similar degree as second-order modeling errors. Through a comprehensive set of diagnostic tests, we demonstrate the improved accuracy of the Y6 models evident in significantly smaller systematic errors than those of the Y3 analysis, in which all g band data were excluded due to insufficiently accurate PSF models. For the Y6 weak lensing analysis, we include g band photometry data in addition to the riz bands, providing a fourth band for photometric redshift estimation. Looking forward to the next generation of wide-field surveys, we describe several ongoing improvements to PIFF, which will be the default PSF modeling software for weak lensing analyses for the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

The rigorous upscaling of advection-dominated transport in heterogeneous porous media via the Method of Finite Averages

Systems involving advection-dominated transport through heterogeneous porous and fractured media are ubiquitous in subsurface engineering applications. However, upscaling such systems continues to challenge rigorous modeling efforts, particularly when advection is stronger than diffusion at fine spatial scales (i.e., when the Péclet number is greater than one at length scales that characterize a system’s unit-cells, representative elementary volumes, or averaging regions). Here, in this work, we propose and validate a strategy for extending the Method of Finite Averages (MoFA), a rigorous upscaling methodology for heterogeneous porous media, to upscale transport systems experiencing stronger advection than diffusion at fine scales (i.e., fine-scale Péclet numbers greater than one). We detail the strategy, the physical conditions under which it can be applied while retaining a priori modeling error guarantees, and implement the strategy to obtain a MoFA model for advective-diffusive transport that accommodates advective physics at fine spatial scales. We then perform two numerical experiments considering systems with system-scale Péclet numbers of 300 and 1000 — which correspond to fine-scale Péclet numbers of 30 and 100, respectively — to verify that the error guarantees are met under the strategy. After, we conduct a numerical study to demonstrate the strategy’s advantages over the original MoFA methodology. The results suggest that rigorously-upscaled transport models for heterogeneous porous media experiencing advective physics at finer spatial scales can be derived through MoFA and resolved orders of magnitude faster than their pore-scale counterparts. The results also suggest that the presented strategy is limited to modeling shallow concentration gradients when there are large differences between the time scales related to advection and a system’s temporally-varying boundary conditions. This limitation hinders the strategy’s practicality in modeling more advective systems, and as such, opportunity exists for developing additional strategies that accommodate rapidly-varying boundary conditions — and consequentially, steeper concentration gradients — while modeling advective systems with MoFA.

36 MATERIALS SCIENCE↗

DOE OSTI2021

TQEA: Temporal Quantum Error Analysis

For the last few years quantum computers have captured researchers’ interest in solving complicated problems in finance, chemistry, machine learning, and many other NP problems. Quantum computing benefits from parallel computation, entanglement, and calculation speedup compared to classical computing. Even though the operations and number of qubits in quantum computers are limited, previous research showed that using quantum computers can be beneficial. These benefits gained researchers’ interest to work on the improvement of quantum computers and overcome the limitations by building more advanced quantum computers with fault tolerance capability, more physical qubits, and better operational gates. In practice, Quantum applications would be translated into Quantum Circuits and each circuit can contain one or many entanglements (s), single qubits operations, and readouts. The importance of running Quantum applications with controlled errors or without errors is critical to the desired result from Quantum readout. In this paper, we study the characteristics of superconducting quantum machines along with the previously proposed methods of Quantum error detection/correction and in order to build a better error model we propose a temporal method for analyzing the the behavior of qubits errors (T1 and T2), frequency of operation, entanglement errors, and readout errors. In order to detect and predict the behavior of each machine, we use simple exponential smoothing analysis on heuristic calibration data. Finally, based on observation, we show that based on frequency, qubits, readout and single operation errors we can build a temporal based model to study and predict the outcome of runs on each Quantum machine.

Baheri, Betis↗

DOE OSTI2025

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Perturbative readout-error mitigation for near-term quantum computers

Readout errors on near-term quantum computers can introduce significant error to the empirical probability distribution sampled from the output of a quantum circuit. These errors can be mitigated by classical postprocessing given the access of an experimental response matrix that describes the error associated with the measurement of each computational basis state. However, the resources required to characterize a complete response matrix and to compute the corrected probability distribution scale exponentially with the number of qubits, n . In this work, we modify standard matrix inversion techniques using perturbative approximations with significantly reduced complexity and bounded error when the likelihood of high-order bit-flip events is strongly suppressed. Given a characteristic error rate q , we discuss a method to recover the probability of the all-zeros bit string p 0 by sampling only a small subspace of the response matrix before inverting readout error, resulting in a relative speedup of poly [ 2 n / ( n w ) ] , which we motivate using a simplified error model for which the approximation incurs only O ( q w ) error for some integer w . We then provide a generalized technique to efficiently recover full output distributions with O ( q w ) error in the perturbative limit. These approximate techniques for readout-error correction may greatly accelerate near-term quantum computing applications.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Quasiprobabilistic Readout Correction of Midcircuit Measurements for Adaptive Feedback via Measurement Randomized Compiling

Quantum measurements are a fundamental component of quantum computing. However, on present-day quantum computers, measurements can be more error prone than quantum gates and are susceptible to nonunital errors as well as nonlocal correlations due to measurement crosstalk. While readout errors can be mitigated in postprocessing, this is inefficient in the number of qubits due to a combinatorially large number of possible states that need to be characterized. In this work, we show that measurement errors can be tailored into a simple stochastic error model using randomized compiling, enabling the efficient mitigation of readout errors via quasiprobability distributions reconstructed from the measurement of a single preparation state in an exponentially large confusion matrix. We demonstrate the scalability and power of this approach by correcting readout errors without matrix inversion on a large number of different preparation states applied to a register of eight superconducting transmon qubits. Moreover, we show that this method can be extended to midcircuit measurements used for active feedback via quasiprobabilistic error cancellation, and we demonstrate the correction of measurement errors on an ancilla qubit used to detect and actively correct bit-flip errors on an entangled memory qubit. Our approach enables the correction of readout errors on large numbers of qubits and offers a strategy for correcting readout errors in adaptive circuits in which the results of midcircuit measurements are used to perform conditional operations on nonlocal qubits in real time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗