Search NASA⌕ Search

SEARCH · Search NASA

Results for “error modeling”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error

Here, the repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. Error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology and localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.

36 MATERIALS SCIENCE↗

Data for A Hybrid Biophysical-Machine Learning Framework for Diurnal Surface Energy Flux Estimation Using Proximal Sensing

Thermal infrared-based remote sensing of surface energy fluxes has traditionally relied on high spatial resolution satellite data with revisit frequencies on the order of weeks. In this study, we evaluate a biophysics-based analytical surface energy balance model for predicting latent energy (LE) and sensible heat (H) fluxes using proximal sensing observations. The Surface Temperature Initiated Closure (STIC1.2) model has been extensively validated across a wide range of spatial and temporal scales using various satellite-derived thermal infrared data sets. Here we extend this validation by applying STIC at sub-hourly temporal resolution over multiple growing seasons for four distinct agricultural systems. We further develop and evaluate novel STIC variants that incorporate machine learning (ML) techniques to eliminate the need for surface energy balance observations, specifically net radiation and soil heat flux, thereby enhancing model applicability in data-sparse settings. The integration of a ML component to estimate surface available energy is shown to have strong predictive performance for both LE (R2 = 0.81–0.94) and H (R2 = 0.46–0.72) across all agricultural systems examined here, demonstrating the potential of hybrid biophysical-machine learning approaches for surface energy balance modeling with minimal data requirements. This study concludes with a novel application of explainable machine learning (exML) to diagnose sources of model error. This exML framework attributes residual prediction errors to both model input variables and environmental drivers not explicitly included in the simulation experiments. This approach provides a new pathway for improving model design and integrating previously overlooked yet influential variables into future model iterations.

AI/ML↗

Learn-as-you-go acceleration of cosmological parameter estimates

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

79 ASTRONOMY AND ASTROPHYSICS↗

A Method for the Quantification of Model Form Error Associated with Physical Systems

In the process of model validation, models are often declared valid when the differences between model predictions and experimental data sets are satisfactorily small. However, little consideration is given to the effectiveness of a model using parameters that deviate slightly from those that were fitted to data, such as a higher load level. Furthermore, few means exist to compare and choose between two or more models that reproduce data equally well. These issues can be addressed by analyzing model form error, which is the error associated with the differences between the physical phenomena captured by models and that of the real system. This report presents a new quantitative method for model form error analysis and applies it to data taken from experiments on tape joint bending vibrations. Two models for the tape joint system are compared, and suggestions for future improvements to the method are given. As the available data set is too small to draw any statistical conclusions, the focus of this paper is the development of a methodology that can be applied to general problems.

97 MATHEMATICS AND COMPUTING↗

Addressing Model Form Error for Time-Dependent Conservation Equations

Model form error of the type considered here is error due to an approximate or incorrect representation of physics by a computational model. Typical approaches to adjust a model based on observed differences between experiment and prediction are to calibrate the model parameters utilizing the observed discrepancies and to develop parameterized additive corrections to the model output. These approaches are generally not suitable if significant physics is missing from the model and the desired quantities of interest for an application are different than those used for calibration. The approach developed here is to build a corrected surrogate solver through a multi- step process: 1) Sampled simulation results are used to develop a surrogate computational solver that maintains the overall conservative principles of the unmodified governing equations, 2) the surrogate solver is applied to candidate linear and non-linear corrector terms to develop corrections that are consistent with the original conservative principles, 3) constant multipliers on the these terms are calibrated using the experimental observations, and 4) the resulting surrogate solver is used to predict application response for the quantity of interest. This approach and several other calibration-based approaches were applied to an example problem based on the diffusive Burgers' equation. While all the approaches provided some model correction when the measure/calibration quantity was the same as that for an application, only the present approach was able to adequately correct the CompSim results when the prediction quantity was different from the calibration quantity.

97 MATHEMATICS AND COMPUTING↗

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗

Characterization of Partially Observed Epidemics - Application to COVID-19

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

59 BASIC BIOLOGICAL SCIENCES↗

Improved Understanding of Coupled Water and Carbon Cycle Processes through Machine Learning Approaches

Focal Area(s): This white paper addresses how explainable machine learning (ML) algorithms can improve insights gained from complex data (Focal Area 3). We will also address how ML approaches related to sensor compression and low energy AI hardware can be used for efficient data acquisition (Focal Area 1). Science Challenge: We will focus on the coupled water cycle and carbon cycle processes in terrestrial ecosystems and terrestrial-aquatic interfaces. Thus, our approaches will be centered around several data-model integration challenges indicated in EESD strategic plans for two science focus areas: Terrestrial Ecosystem Science and Hydrobiogeochemistry. We can use AI to correct systematic model errors due to biases in either data or model structure/processes. Error patterns in model predictions usually vary by region, model, season etc. But there are systematic patterns in them. e.g., soil moisture tends to be overestimated in the arid western continental United States underestimated in wetter eastern USA; some land surface models tend to underestimate moisture in wet seasons and overestimate in dry seasons. Moreover, the consequences of extreme events (e.g., drought, extreme flooding, storm surges associated with tropical storms, hurricanes) on carbon cycle processes are not well represented in ecosystem and Earth system models. Redox-sensitive processes (e.g., rapid oxidation/reduction of iron and other redox-sensitive elements in soil microsites subjected to fluctuated hydrology) in terrestrial-aquatic interfaces further challenge model predictions of hot-spots (and hot-moments) due to poor understanding of underlying mechanisms. Thus, AI/ML approaches can be used to learn patterns in the data and model errors and use them to build model equations and correct process-based model errors.

54 ENVIRONMENTAL SCIENCES↗

Modeling, Analysis, and Control of Demand Response Resources

While the traditional goal of an electric power system has been to control supply to fulfill demand, the demand-side can plan an active role in power systems via Demand Response (DR), defined by the Department of Energy (DOE) as “a tariff or program established to motivate changes in electric use by end-use customers in response to changes in the price of electricity over time, or to give incentive payments designed to induce lower electricity use at times of high market prices or when grid reliability is jeopardized” [29]. DR can provide a variety of benefits including reducing peak electric loads when the power system is stressed and fast timescale energy balancing. Therefore, DR can improve grid reliability and reduce wholesale energy prices and their volatility. This dissertation focuses on analyzing both recent and emerging DR paradigms. Recent DR programs have focused on peak load reduction in commercial buildings and industrial facilities (C&I facilities). We present methods for using 15-minute-interval electric load data, commonly available from C&I facilities, to help building managers understand building energy consumption and ‘ask the right questions’ to discover opportunities for DR. Additionally, we present a regression-based model of whole building electric load, i.e., a baseline model, which allows us to quantify DR performance. We use this baseline model to understand the performance of 38 C&I facilities participating in an automated dynamic pricing DR program in California. In this program, facilities are expected to exhibit the same response each DR event. We find that baseline model error makes it difficult to precisely quantify changes in electricity consumption and understand if C&I facilities exhibit event-to-event variability in their response to DR signals. Therefore, we present a method to compute baseline model error and a metric to determine how much observed DR variability results from baseline model error rather than real variability in response. We find that, in general, baseline model error is large. Though some facilities exhibit real DR variability, most observed variability results from baseline model error. In some cases, however, aggregations of C&I facilities exhibit real DR variability, which could create challenges for power system operation. These results have implications for DR program design and deployment. Emerging DR paradigms focus on faster timescale DR. Here, we investigate methods to coordinate aggregations of residential thermostatically controlled loads (TCLs), including air conditioners and refrigerators, to manage frequency and energy imbalances in power systems. We focus on opportunities to centrally control loads with high accuracy but low requirements for sensing and communications infrastructure. Specifically, we compare cases when measured load state information (e.g., power consumption and temperature) is 1) available in real time; 2) available, but not in real time; and 3) not available. We develop Markov Chain models to describe the temperature state evolution of heterogeneous populations of TCLs, and use Kalman filtering for both state and joint parameter/state estimation. We present a look-ahead proportional controller to broadcast control signals to all TCLs, which always remain in their temperature dead-band. Simulations indicate that it is possible to achieve power tracking RMS errors in the range of 0.26–9.3% of steady state aggregated power consumption. Results depend upon the information available for system identification, state estimation, and control. We find that, depending upon the performance required, TCLs may not need to provide state information to the central controller in real time or at all. We also estimate the size of the TCL potential resource; potential revenue from participation in markets; and break-even costs associated with deploying DR-enabling technologies. We find that current TCL energy storage capacity in California is 8–11 GWh, with refrigerators contributing the most. Annual revenues from participation in regulation vary from $10 to $220 per TCL per year depending upon the type of TCL and climate zone, while load following and arbitrage revenues are more modest at $2 to $35 per TCL per year. These results lead to a number of policy recommendations that will make it easier to engage residential loads in fast timescale DR.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Ultra-deep mutant spectrum profiling: improving sequencing accuracy using overlapping read pairs

Backgound: High throughput sequencing is beginning to make a transformative impact in the area of viral evolution. Deep sequencing has the potential to reveal the mutant spectrum within a viral sample at high resolution, thus enabling the close examination of viral mutational dynamics both within- and between-hosts. The challenge however, is to accurately model the errors in the sequencing data and differentiate real viral mutations, particularly those that exist at low frequencies, from sequencing errors. Results: We demonstrate that overlapping read pairs (ORP) -- generated by combining short fragment sequencing libraries and longer sequencing reads -- significantly reduce sequencing error rates and improve rare variant detection accuracy. Using this sequencing protocol and an error model optimized for variant detection, we are able to capture a large number of genetic mutations present within a viral population at ultra-low frequency levels (<0.05%). Conclusions: Our rare variant detection strategies have important implications beyond viral evolution and can be applied to any basic and clinical research area that requires the identification of rare mutations.

59 BASIC BIOLOGICAL SCIENCES↗

PyOED: An Extensible Suite for Data Assimilation and Model-Constrained Optimal Design of Experiments

This article describes PyOED, a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for model-constrained OED. The package targets scientists and researchers interested in understanding the details of OED formulations and approaches. It is also meant to enable researchers to experiment with standard and innovative OED technologies with a wide range of test problems (e.g., simulation models). OED, inverse problems (e.g., Bayesian inversion), and data assimilation (DA) are closely related research fields, and their formulations overlap significantly. Thus, PyOED is continuously being expanded with a plethora of Bayesian inversion, DA, and OED methods as well as new scientific simulation models, observation error models, and observation operators. These pieces are added such that they can be permuted to enable testing OED methods in various settings of varying complexities. The PyOED core is completely written in Python and utilizes the inherent object-oriented capabilities; however, the current version of PyOED is meant to be extensible rather than scalable. Specifically, PyOED is developed to “enable rapid development and benchmarking of OED methods with minimal coding effort and to maximize code reutilization.” This article provides a brief description of the PyOED layout and philosophy and provides a set of exemplary test cases and tutorials to demonstrate the potential of the package.

97 MATHEMATICS AND COMPUTING↗

MultiPEM Toolbox: User Manual [Rev. 2]

This document explains use of the Multi-Phenomenology Explosion Monitoring (Multi PEM) Toolbox, a collection of R scripts for estimating the unknown device parameters of a new event with uncertainty quantification. The methodology and application used for illustration in this user manual are fully documented in a Los Alamos National Laboratory technical report hereafter designated “WPA” for reference. Additional details on the application are found in a recent journal article. Two assessment types are available: rapid and complete. Rapid assessments are conducted in two stages, as described in Section 2. In the first stage, calibration data are used to estimate forward and error model parameters (WPA, §5.1) and (if relevant) errors-in-variables yield values for calibration sources (WPA, §3, Equation (3)). In the second stage, new event data are used to estimate the unknown new event device parameters (WPA, §5.2) with uncertainty quantification. Two options for treating the inferred first stage parameters in second stage Bayesian analysis are available: fixing them at their maximum likelihood estimate (default), or multiple imputation. Multiple imputation involves utilizing several posterior samples (imputations) of the first stage parameters as fixed values in the second stage posterior sampling of the new event device parameters. Second stage sampling is conducted across imputations in parallel to improve computational efficiency. This method produces improved uncertainty quantification of the new event device parameters compared with the default treatment of the first stage parameters, at the expense of additional computation. Complete assessments are conducted in a single stage, as described in Section 3. Calibration and (if relevant) new event data are used simultaneously to estimate all forward model, error model, and (if relevant) new event device parameters with uncertainty quantification on the latter. As the name suggests, rapid assessments generally run substantially faster than complete assessments (even with multiple imputation), because the results of first stage analysis can be stored and incorporated into estimating a relatively low-dimensional space of new event device parameters whenever relevant new event data becomes available. On the other hand, complete assessments must be run on the full set of model and device parameters with calibration and new event data every time the latter becomes available.

97 MATHEMATICS AND COMPUTING↗

Model-form Error Correction using Universal Differential Equations for an Agent-Based Model of Infectious Disease

This report demonstrates universal differential equations (UDEs) as an approach to bridge the gap between ordinary differential equations (ODE) models and agent-based models (ABMs). Using UDE models as surrogates for ABMs allows us to preserve the foundational ODE that represents global disease dynamics while coupling it with a neural network model to approximate functions for the local behaviors of the ABM.

59 BASIC BIOLOGICAL SCIENCES↗

Accounting for erroneous model structures in biokinetic process models

In engineering practice, model-based design requires not only a good process-based model, but also a good description of stochastic disturbances and measurement errors to learn credible parameter values from observations. However, typical methods use Gaussian error models, which often cannot describe the complex temporal patterns of residuals. Consequently, this results in overconfidence in the identified parameters and, in turn, optimistic reactor designs. Here, we assess the strengths and weaknesses of a method to statistically describe these patterns with autocorrelated error models. This method produces increased widths of the credible prediction intervals following the inclusion of the bias term, in turn leading to more conservative design choices. However, we also show that the augmented error model is not a universal tool, as its application cannot guarantee the desired reliability of the resulting wastewater reactor design.

42 ENGINEERING↗

Direct numerical simulations in solid mechanics for quantifying the macroscale effects of microstructure and material model-form error

Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Furthermore, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.

36 MATERIALS SCIENCE↗

Model uncertainty in accelerator application simulations

Monte-Carlo nuclear reaction and transport codes are widely used to devise accelerator-based nuclear physics experiments; at the same time, many experiments are performed to validate the Monte-Carlo codes, which can be used for the design of full-scale nuclear power applications or the design of new benchmark experiments. Dedicated model benchmark studies investigate a broad range of nuclear reactions and quantities. Examples of these include isotope formation or secondary particle fluxes that result from the interactions of GeV-range hadrons with monoisotopic targets, which can be used to assess the respective systematic uncertainty of models. Such benchmark studies, as well as many nuclear application experiments and simulations carried out by various groups over the last few decades, enable us to draw methodological lessons. In this work, model uncertainty determined based on available experimental data allow us to identify the effects of practitioner expertise as well as the design of codes (user access to micro-scale parameters) on the range of uncertainties. We found that in cases when simulations are performed by code developers or users that are very experienced in performing simulations, the model to experiment quantity ratios generally agree with the limits determined by dedicated benchmark studies. In other cases, the ratios generally tend to be either smaller (underestimation of model error) or larger (overestimation of model error). A plausible explanation of the aforementioned effects is suggested.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗