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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Interpretable Deep Learning for the Earth System with Fractal Nets

Focal Area 3: Explainable AI Our confidence in the projections made by Earth System Models (ESMs) depends on understanding them to be, in some important respects, faithful representations of the Earth system. Here we present an “explainable Artificial Intelligence (AI)” method that allows us to uncover the dynamical structure of the observed and modeled Earth system, discover hidden links across wide spatiotemporal scales, target model development efforts at poorly-represented dynamics, and optimize observed or modeled data collection to maximize predictive information. Science Challenge: Dynamical system science for the Earth system poses unique challenges given the large degree of internal climate variability. Thus, tools that help us understand how ESMs succeed and fail at representing these dynamics are crucial, particularly in relation to the observed system. Furthermore, the computational and memory constraints on ESM data output motivate in situ analysis of ESM dynamics, including automatic detection of dynamical shifts. Also, of key importance are procedures that leverage ESMs to optimize observational campaigns for improving process representation, reducing structural uncertainty and improving model skill.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

An Observation-Driven Framework for Modeling Post-Fire Hydrologic Response: Evaluation for Two Central California Case Studies

In a warming climate, wildfires are becoming increasingly common, especially in semi-arid environments. Wildfires can disrupt forest ecosystems and induce changes to the land surface. Collectively, these impacts can alter the hydrologic response of a catchment following a fire, resulting in increased potential for surface runoff, reduced evapotranspiration, and, ultimately, a higher risk for flash flooding and mass wasting. The timescale for post-fire recovery of hydrological processes to return to pre-fire conditions is not well established due to the lack of ground measurements. Accurate characterization of fire impacts on hydrologic response is also challenging to simulate, given the complex interplay of various processes. Here, we present a generalized framework to quantify wildfire impacts on runoff generation. We consider the vegetation and soil disturbances as the primary contributors to post-fire floods. Using an ensemble modeling structure to account for parameter uncertainty and consider model sensitivity, remotely sensed leaf area index (LAI) is assimilated into a land surface model (LSM) to simulate vegetation disturbance, and the maximum land surface saturation LSM parameter is decreased to parameterize the soil disturbance following observed fires. We evaluated the impacts of fire-induced changes to LAI and soil saturation on hydrologic states like runoff and evapotranspiration. Analysis of two events in central California shows that 1) the LAI assimilation has a greater impact on water balance; and 2) the soil scheme captures a range of outcomes, with substantial impacts on surface runoff for some ensemble members, which could affect flood potential.

Timothy M Lahmers↗
DOE OSTI2023

Generalized Aerosol/Chemistry Interface (GIANT): A Community Effort to Advance Collaborative Science across Weather and Climate Models

Atmospheric aerosol and chemistry modules are key elements in Earth system models (ESMs), as they predict air pollutant concentrations and properties that can impact human health, weather, and climate. The current uncertainty in climate projections is partly due to the inaccurate representation of aerosol direct and indirect forcing. Aerosol/chemistry parameterizations used within ESMs and other atmospheric models span large structural and parameter uncertainties that are difficult to assess independently of their host models. Moreover, there is a strong need for a standardized interface between aerosol/chemistry modules and the host model to facilitate portability of aerosol/chemistry parameterizations from one model to another, allowing not only a comparison between different parameterizations within the same modeling framework, but also quantifying the impact of different model frameworks on aerosol/chemistry predictions. To address this need, we have initiated a new community effort to coordinate the construction of a Generalized Aerosol/Chemistry Interface (GIANT) for use across weather and climate models. We aim to organize a series of community workshops and hackathons to design and build GIANT, which will serve as the interface between a range of aerosol/chemistry modules and the physics and dynamics components of atmospheric host models. GIANT will leverage ongoing efforts at the U.S. modeling centers focused on building next-generation ESMs and the international AeroCom initiative to implement this common aerosol/chemistry interface. GIANT will create transformative opportunities for scientists and students to conduct innovative research to better characterize structural and parametric uncertainties in aerosol/chemistry modules, and to develop a common set of aerosol/chemistry parameterizations.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRSDate not supplied

Cavitation Effects on the Structural Dynamics of Turbomachinery Components

The structural integrity of inducer and impeller blades in rocket engine turbomachinery must be evaluated in the face of complex excitation mechanisms including fluctuating pressures due to cavitation. Cavitation occurs when the local fluid pressure drops below the vapor pressure, causing the formation of vapor-filled bubbles. Cavitation can exist to various extents within the typical operating range of rocket engine turbopumps. Despite recent progress towards reducing uncertainties in structural dynamic models of turbomachinery components, the extent to which pump cavitation affects the structural dynamic properties (i.e., natural frequencies, damping, and mode shapes) of inducer and impeller blades remains largely unknown. To study the structural dynamic effects of cavitating flows, experiments are conducted in a high-speed water tunnel. The test articles mimic a single inducer blade that is unwrapped from the hub, thus resembling a low aspect ratio cantilevered plate. To induce cavitation, the plates are oriented at a non-zero angle of attack and have rough strips near their leading edges. To control the extent of cavitation, the static pressure of the water tunnel is controlled between roughly 0.5 and 1.5 atm. A high-speed camera is used to quantify the coverage of the cavitations heet. The sheet coverage is then correlated to changes in fluid-added mass and hydroelstic damping. In addition, a corresponding two-way coupled CFD/FE model is under development for test/analysis correlation.

Ben Davis↗
NASA NTRSDate not supplied

Cavitation Effects on the Structural Dynamics of Turbomachinery Components

The structural integrity of inducer and impeller blades in rocket engine turbomachinery must be evaluated in the face of complex excitation mechanisms including fluctuating pressures due to cavitation. Cavitation occurs when the local fluid pressure drops below the vapor pressure, causing the formation of vapor-filled bubbles. Cavitation can exist to various extents within the typical operating range of rocket engine turbopumps. Despite recent progress towards reducing uncertainties in structural dynamic models of turbomachinery components, the extent to which pump cavitation affects the structural dynamic properties (i.e., natural frequencies, damping, and mode shapes) of inducer and impeller blades remains largely unknown. To study the structural dynamic effects of cavitating flows, experiments are conducted in a high-speed water tunnel. The test article is a low aspect ratio cantilevered plate, thus mimicing a single inducer blade that is unwrapped from its hub. The test article is oriented at zero angle of attack and has a triangular trip at its leading edge to induce cavitation. To change the extent of cavitation, the static pressure of the water tunnel is controlled. A high-speed camera is used to quantify the coverage of the cavitation sheet.

Fluid-Structure Interaction↗
NASA NTRSDate not supplied

Cavitation Effects on the Structural Dynamics of Turbomachinery Components

The structural integrity of inducer and impeller blades in rocket engine turbo machinery must be evaluated in the face of complex excitation mechanisms including fluctuating pressures due to cavitation. Cavitation occurs when the local fluid pressure drops below the vapor pressure, causing the formation of vapor-filled bubbles. Cavitation can exist to various extents within the typical operating range of rocket engine turbo pumps. Despite recent progress towards reducing uncertainties in structural dynamic models of turbo machinery components, the extent to which pump cavitation affects the structural dynamic properties (i.e., natural frequencies, damping, and mode shapes) of inducer and impeller blades remains largely unknown. To study the structural dynamic effects of cavitating flows, experiments are conducted in a high-speed water tunnel. The test article is a low aspect ratio cantilevered plate, thus mimicing a single inducer blade that is unwrapped from its hub. The test article is oriented at zero angle of attack and has a triangular trip at its leading edge to induce cavitation. To change the extent of cavitation, the static pressure of the water tunnel is controlled. A high-speed camera is used to quantify the coverage of the cavitation sheet.

Structural Dynamics↗
NASA NTRS2000

Parameterization of Model Validating Sets for Uncertainty Bound Optimizations

Given measurement data, a nominal model and a linear fractional transformation uncertainty structure with an allowance on unknown but bounded exogenous disturbances, easily computable tests for the existence of a model validating uncertainty set are given. Under mild conditions, these tests are necessary and sufficient for the case of complex, nonrepeated, block-diagonal structure. For the more general case which includes repeated and/or real scalar uncertainties, the tests are only necessary but become sufficient if a collinearity condition is also satisfied. With the satisfaction of these tests, it is shown that a parameterization of all model validating sets of plant models is possible. The new parameterization is used as a basis for a systematic way to construct or perform uncertainty tradeoff with model validating uncertainty sets which have specific linear fractional transformation structure for use in robust control design and analysis. An illustrative example which includes a comparison of candidate model validating sets is given.

Lim, K. B.↗
NASA NTRS1996

Uncertainty and Intelligence in Computational Stochastic Mechanics

Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.

Ayyub, Bilal M.↗
DOE OSTI2020

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗
DOE OSTI2026

Contrasting Parametric Sensitivities in Two Global Vegetation Models Using Parameter Perturbation Ensembles

Uncertainty in land model projections remains high and the roles of parametric and structural uncertainty are difficult to disentangle. To compare parametric sensitivity across model structures we present two parameter perturbation ensembles using the Community Land Model (CLM) operating in satellite phenology mode. The ensembles contrast two vegetation modules: (a) the default CLM vegetation module and (b) the Functionally Assembled Terrestrial Ecosystem Simulator (CLM-FATES). We perturbed over 300 parameters and quantified their effects on biophysical fluxes globally and across biomes. Most parameters have minimal impact on biophysical fluxes, with only a few substantially influencing results. While both models exhibit similar parameter sensitivity for some fluxes, CLM-FATES shows larger spread in gross primary productivity (GPP), driven by strong sensitivity to carboxylation rate. CLM-FATES also shows a weaker GPP response to soil hydrology parameters and exhibits higher water use efficiency (WUE). Cross-model comparisons reveal similar sensitivities for some parameters (e.g., leaf dimension) but divergent responses to others (e.g., stomatal intercept), highlighting underlying structural differences. Differences in WUE and sensitivity to hydrology and stomatal conductance parameters underscore how model structure fundamentally alters parametric sensitivity. The data sets generated from these ensembles can be used to identify influential parameters and guide future calibration efforts.

Foster, A. C. [NSF National Center for Atmospheric↗
NASA NTRS1993

Parametric uncertainty modeling for application to robust control

Viewgraphs and a paper on parametric uncertainty modeling for application to robust control are included. Advanced robust control system analysis and design is based on the availability of an uncertainty description which separates the uncertain system elements from the nominal system. Although this modeling structure is relatively straightforward to obtain for multiple unstructured uncertainties modeled throughout the system, it is difficult to formulate for many problems involving real parameter variations. Furthermore, it is difficult to ensure that the uncertainty model is formulated such that the dimension of the resulting model is minimal. A procedure for obtaining an uncertainty model for real uncertain parameter problems in which the uncertain parameters can be represented in a multilinear form is presented. Furthermore, the procedure is formulated such that the resulting uncertainty model is minimal (or near minimal) relative to a given state space realization of the system. The approach is demonstrated for a multivariable third-order example problem having four uncertain parameters.

Belcastro, Christine M.↗
DOE OSTI2024

Regional climate change: consensus, discrepancies, and ways forward

Climate change has emerged across many regions. Some observed regional climate changes, such as amplified Arctic warming and land-sea warming contrasts have been predicted by climate models. However, many other observed regional changes, such as changes in tropical sea surface temperature and monsoon rainfall are not well simulated by climate model ensembles even when taking into account natural internal variability and structural uncertainties in the response of models to anthropogenic radiative forcing. This suggests climate model predictions may not fully reflect what our future will look like. The discrepancies between models and observations are not well understood due to several real and apparent puzzles and limitations such as the “signal-to-noise paradox” and real-world record-shattering extremes falling outside of the possible range predicted by models. Addressing these discrepancies, puzzles and limitations is essential, because understanding and reliably predicting regional climate change is necessary in order to communicate effectively about the underlying drivers of change, provide reliable information to stakeholders, enable societies to adapt, and increase resilience and reduce vulnerability. The challenges of achieving this are greater in the Global South, especially because of the lack of observational data over long time periods and a lack of scientific focus on Global South climate change. To address discrepancies between observations and models, it is important to prioritize resources for understanding regional climate predictions and analyzing where and why models and observations disagree via testing hypotheses of drivers of biases using observations and models. Gaps in understanding can be discovered and filled by exploiting new tools, such as artificial intelligence/machine learning, high-resolution models, new modeling experiments in the model hierarchy, better quantification of forcing, and new observations. Conscious efforts are needed toward creating opportunities that allow regional experts, particularly those from the Global South, to take the lead in regional climate research. This includes co-learning in technical aspects of analyzing simulations and in the physics and dynamics of regional climate change. Finally, improved methods of regional climate communication are needed, which account for the underlying uncertainties, in order to provide reliable and actionable information to stakeholders and the media.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2021

Earth system modeling: can we stay ahead of what's actually happening?

Over the last forty years, Earth System Models have become more and more comprehensive and detailed. They have assimilated previously independent modeling efforts in ocean circulation, atmospheric composition, the stratosphere, land surface, and the cryosphere, and are today demonstrably more skillful than earlier efforts. Yet the structural uncertainty in the latest model projections is actually increasing. Meanwhile, impacts of climate change on, for instance, wildfires, tropical cyclones and sea level, appear to be increasing faster than we have been able to predict. I will address some of the current issues at the bleeding edges of model development and the continuing importance of model evaluation.

Gavin A Schmidt↗
DOE OSTI2025

Data and scripts from: “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”

This data package includes data and scripts from the manuscript “Denoising autoencoder for reconstructing sensor observation data and predicting evapotranspiration: noisy and missing values repair and uncertainty quantification”.The study addressed common challenges faced in environmental sensing and modeling, including uncertain input data, missing sensor observations, and high-dimensional datasets with interrelated but redundant variables. Point-scaled meteorological and soil sensor observations were perturbed with noises and missing values, and denoising autoencoder (DAE) neural networks were developed to reconstruct the perturbed data and further predict evapotranspiration. This study concluded that (1) the reconstruction quality of each variable depends on its cross-correlation and alignment to the underlying data structure, (2) uncertainties from the models were overall stronger than those from the data corruption, and (3) there was a tradeoff between reducing bias and reducing variance when evaluating the uncertainty of the machine learning models.This package includes:(1) Four ipython scripts (.ipynb): “DAE_train.ipynb” trains and evaluates DAE neural networks, “DAE_predict.ipynb” makes predictions from the trained DAE models, “ET_train.ipynb” trains and evaluates ET prediction neural networks, and “ET_predict.ipynb” makes predictions from trained ET models.(2) One python file (.py): “methods.py” includes all user-defined functions and python codes used in the ipython scripts.(3) A “sub_models” folder that includes five trained DAE neural networks (in pytorch format, .pt), which could be used to ingest input data before being fed to the downstream ET models in ‘ET_train.ipynb” or ‘ET_predict.ipynb’.(4) Two data files (.csv). Daily meteorological, vegetation, and soil data is in “df_data.csv”, where “df_meta.csv” contains the location and time information of “df_data.csv”. Each row (index) in “df_meta.csv” corresponds to each row in “df_data.csv”. These data files are formatted to follow the data structure requirements and be directly used in the ipython scripts, and they have been shuffled chronologically to train machine learning models. The meteorological and soil data was collected using point sensors between 2019-2023 at(4.a) Three shrub-dominated field sites in East River, Colorado (named “ph1”, “ph2” and “sg5” in “df_meta.csv”, where “ph1” and “ph2” were located at PumpHouse Hillslopes, and “sg5” was at Snodgrass Mountain meadow) and(4.b) One outdoor, mesoscale, and herbaceous-dominated experiment in Berkeley, California (named “tb” in “df_meta.csv”, short for Smartsoils Testbed at Lawrence Berkeley National Lab).- See "df_data_dd.csv" and "df_meta_dd.csv" for variable descriptions and the Methods section for additional data processing steps. See "flmd.csv" and "README.txt" for brief file descriptions.- All ipython scripts and python files are written in and require PYTHON language software.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Uncertainty-Aware, Structure-Preserving Machine Learning Approach for Domain Shift Detection From Nonlinear Dynamic Responses of Structural Systems

Complex structural systems deployed for aerospace, civil, or mechanical applications must operate reliably under varying operational conditions. Structural health monitoring (SHM) systems help ensure the reliability of these systems by providing continuous monitoring of the state of the structure. SHM relies on synthesizing measured data with a predictive model to make informed decisions about structural states. However, these models—which may be thought of as a form of a digital twin—need to be updated continuously as structural changes (e.g., due to damage) arise. We propose an uncertainty-aware machine learning model that enforces distance preservation of the original input state space and then encodes a distance-aware mechanism via a Gaussian process (GP) kernel. The proposed approach leverages the spectral-normalized neural GP algorithm to combine the flexibility of neural networks with the advantages of GP, subjected to structure-preserving constraints, to produce an uncertainty-aware model. This model is used to detect domain shift due to structural changes that cannot be observed directly because they may be spatially isolated (e.g., inside a joint or localized damage). This work leverages detection theory to detect domain shift systematically given statistical features of the prediction variance produced by the model. The proposed approach is demonstrated on a nonlinear structure being subjected to damage conditions. In conclusion, it is shown that the proposed approach is able to rely on distances of the transformed input state space to predict increased variance in shifted domains while being robust to normative changes.

Algorithms↗
DOE OSTI2025

Denoising Autoencoder for Reconstructing Sensor Observation Data and Predicting Evapotranspiration: Noisy and Missing Values Repair and Uncertainty Quantification

Abstract Machine learning (ML) methods applied in scientific research often deal with interrelated features in high‐dimensional data. Reducing data noise and redundancy is needed to increase prediction accuracy and efficiency especially when dealing with data from field sensors. We explored an unsupervised learning method, the denoising autoencoder (DAE), to extract the underlying data structure from noisy raw data in the context of predicting hydrologic quantities from multiple field sensors. These sensors have intrinsic instrumental noise and occasional malfunctions that cause missing values. Our DAE neural network reconstructed meteorological sensor data containing noise and missing values to predict evapotranspiration in a mountainous watershed. The DAE reconstructed the sensor variables with a mean coefficient of determination value of 0.77 across 15 dimensions representing individual sensors. It reduced variance and bias uncertainties compared to a classical autoencoder model. The reconstruction quality varied across dimensions depending on their cross‐correlation and alignment with the underlying data structure. Uncertainties arising from the model structure were overall higher than those resulting from data corruption. We attached the DAE structure to a downstream ET‐prediction neural network in three formats and achieved reasonably accurate ET predictions . The use of the DAE notably reduced variance uncertainty in ET prediction. However, excessive variance reduction may be accompanied by an increase in bias due to the intrinsic bias‐variance tradeoff. Our method of evaluating and reducing uncertainties in aggregated data from different sources can be used to improve predictive models, process understanding, and uncertainty quantification for better water resource management. Plain Language Summary We present a machine learning method, namely the denoising autoencoder, which reduces the effects of data noise and missing values typically present in scientific data sets collected through sensor measurements. This method selects the most relevant information from noisy raw data collected by the instruments and fills in missing values. To demonstrate the effectiveness of our method, we applied it to predict evapotranspiration, a hydrologic variable that represents the water moved from the land surface to the atmosphere through a combination of evaporation and plant water use (transpiration). We also used a random sampling technique (the Monte Carlo method) to compare the uncertainty in the predictions when using the raw and noisy data versus the reconstructed data. The denoising process produced more accurate predictions of evapotranspiration with less uncertainty. Improved predictions of evapotranspiration can lead to a better understanding and accounting of water budgets. This ML approach is broadly suitable for a wide variety of applications that involve noisy sensor data with missing values. Key Points We used a denoising autoencoder (DAE) neural network to reduce noise in meteorological and soil sensor observations by on average We used Monte Carlo sampling to estimate the bias and variance of all model outputs, including uncertainty sources from data and the model We attached the DAE component to a downstream neural network to predict ET with the variance reduced by , compared to that without the DAE

denoising autoencoder↗
DOE OSTI2024

a priori uncertainty quantification of reacting turbulence closure models using Bayesian neural networks

While many physics-based closure model forms have been posited for the sub-filter scale (SFS) in large eddy simulation (LES), vast amounts of data available from direct numerical simulations (DNS) create opportunities to leverage data-driven modeling techniques. Albeit flexible, data-driven models still depend on the dataset and the functional form of the model chosen. Increased adoption of such models requires reliable uncertainty estimates both in the data-informed and out-of-distribution regimes. Here, in this work, we employ Bayesian neural networks (BNNs) to capture both epistemic and aleatoric uncertainties in a reacting flow model. In particular, we model the filtered progress variable scalar dissipation rate which plays a key role in the dynamics of turbulent premixed flames. We demonstrate that BNN models can provide unique insights about the structure of uncertainty of the data-driven closure models. We also propose a method for the incorporation of out-of-distribution information in a BNN, which can be used for out-of-distribution query detection. The efficacy of the model is demonstrated by a priori evaluation on a dataset consisting of a variety of flame conditions and fuels.

97 MATHEMATICS AND COMPUTING↗