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Uncertainty Quantification and Sensitivity Analysis of Low-Dimensional Manifold via Co-Kurtosis PCA in Combustion Modeling

Balakrishnan, Uma; Kolla, Hemanth

For multi-scale multi-physics applications e.g., the turbulent combustion code Pele, robust and accurate dimensionality reduction is crucial to solving problems at exascale and beyond. A recently developed technique, Co-Kurtosis based Principal Component Analysis (CoK-PCA) which leverages principal vectors of co-kurtosis, is a promising alternative to traditional PCA for complex chemical systems. To improve the effectiveness of this approach, we employ Artificial Neural Networks for reconstructing thermo-chemical scalars, species production rates, and overall heat release rates corresponding to the full state space. Our focus is on bolstering confidence in this deep learning based non-linear reconstruction through Uncertainty Quantification (UQ) and Sensitivity Analysis (SA). UQ involves quantifying uncertainties in inputs and outputs, while SA identifies influential inputs. One of the noteworthy challenges is the computational expense inherent in both endeavors. To address this, we employ the Monte Carlo methods to effectively quantify and propagate uncertainties in our reduced spaces while managing computational demands. Our research carries profound implications not only for the realm of combustion modeling but also for a broader audience in UQ. By showcasing the reliability and robustness of CoK-PCA in dimensionality reduction and deep learning predictions, we empower researchers and decision-makers to navigate complex combustion systems with greater confidence.

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Shorter function summaries for finite state machine-based high consequence systems using logic synthesis and tautologies (Final Report LDRD 24-1302)

Amon, Tod T.

Computer programs are often viewed as collections of functions – each function has parameters (inputs) and computes a return value, and each has potential side effects that modify program state (outputs). In this research, a Sandia symbolic execution tool designed to support “human-in-the-loop” analysis was modified to automatically create “function summaries,” and a new tool, “diaboolical,” was created to support enhancing readability of the summary using a novel approach to bit-vector simplification that leverages logic synthesis and tautologies. For this effort, students at Auburn University created several finite state machines (FSMs) to serve as exemplars for high-consequence systems. Function summaries for each of the machines were obtained, and then portions of the summaries were simplified using both diaboolical and the simplification procedure of a popular SMT solver. A comparison of the results shows that diaboolical can often produce smaller function summaries, with expression length improvements over the unsimplified function summaries ranging from 0% to 90% for diaboolical and 0% to 65% for the SMT solver, though diaboolical had a significantly greater cost in time. Diaboolical was evaluated against a collection of “arbitrary” C-code as well as FSM exemplars, and for both datasets it achieved an approximately 10% improvement in expression length compared to simplifications that could be obtained using existing techniques. Function summaries can assist assurance efforts that evaluate existing systems and their executable code. A smaller function summary is likely easier for humans to understand and could thus increase the ability and efficacy of assurance practices centered around the analysis of executable artifacts.

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FY24 Advancements in PFLOTRAN Development for GDSA Framework

Park, Heeho D.; Fukuyama, David E.; Leone, Rosemary C.; Paul, Matthew J.; Bays, Nathan R.; Madsen, Calvin F.; Rechard, Robert P.

The Spent Fuel & Waste Science and Technology (SFWST) Campaign of the Office of Spent Fuel & Waste Disposition of U.S. Department of Energy Office of Nuclear Energy (DOE-NE) is conducting research and development on geologic disposal of spent nuclear fuel (SNF) and high-level nuclear waste (HLW). This report describes fiscal year 2024 accomplishments in the Geologic Disposal Safety Assessment (GDSA) PFLOTRAN Development work package, which is charged with developing subsurface simulation software for postclosure performance assessment of deep geologic disposal of SNF and HLW.

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FIRST-PRINCIPLES DERIVATION OF THE EFFECTIVE VISCOSITY FOR FLUXON PROPAGATION DUE TO QUASIPARTICLE TUNNELING IN LONG JOSEPHSON JUNCTIONS AND ASSOCIATED STOPPING DISTANCE

Lewis, Rupert M.; Frank, Michael P.; Kaplan, Steven B.

Poster to be presented at the Applied Superconductivity Conference, 2024 in Salt Lake City, Utah in September. This poster details our calculations on the propagation of ballistic fluxon solitons in long Josephson junctions.

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Adaptive Methods for Radial Basis Functions

Torchinsky, Jason L.; Actor, Jonas A.; Bosler, Peter A.; Salinger, Andrew G.

Radial basis functions (RBFs) are a powerful tool for constructing high-order accurate reduced representations of scattered data in arbitrary dimension and on manifolds. We present a method of constructing data approximations in which we utilize a functional tail to capture a global background profile and a RBF neural network (NN) to capture the smaller-scale features. In the RBF NN the RBF centers, matrix shape parameters were selected adaptively for each RBF. We also utilized a geodesic notion of distance on the manifold on which the data lies, e.g., the spherical geodesic for data on the sphere. Although each of these ideas have been been investigated separately in previous works, their combination into a single algorithm is novel. We defined a machine learning problem in which these properties are learned to minimize the data reduction error. We demonstrate the algorithm for applications of scattered data reduction in the plane and on the sphere.

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Strategic Petroleum Reserve Cavern Leaching Monitoring CY23

Zeitler, Todd; Maurer, Hannah G.

The effects of raw water leaching at the U.S. SPR were modeled using SANSMIC. In addition to 18 caverns identified in previous leaching reports, six caverns have been identified for further monitoring based on the results of this report. SANSMIC continues to serve as a useful tool for monitoring changes in cavern shape. However, some caverns where string cuts were made in the middle of drawdowns are showing overprediction in the SANSMIC model when compared with recent sonars.

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Interpreting test temperature and loading rate effects on the fracture toughness of polymer-metal interfaces via time–temperature superposition

International Journal of Fracture

Delrio, Frank W.; Huber, Todd; Jaramillo, Rex K.; Reedy, E.D.; Grutzik, Scott J.

In this letter, we present interfacial fracture toughness data for a polymer-metal interface where tests were conducted at various test temperatures T and loading rates δ˙. An adhesively bonded asymmetric double cantilever beam (ADCB) specimen was utilized to measure toughness. ADCB specimens were created by bonding a thinner, upper adherend to a thicker, lower adherend (both 6061 T6 aluminum) using a thin layer of epoxy adhesive, such that the crack propagated along the interface between the thinner adherend and the epoxy layer. The specimens were tested at T from 25 to 65 °C and δ˙ from 0.002 to 0.2 mm/s. The measured interfacial toughness Γ increased as both T and δ˙ increased. For an ADCB specimen loaded at a constant δ˙, the energy release rate G increases as the crack length a increases. For this reason, we defined rate effects in terms of the rate of change in the energy release rate G˙. Although not rigorously correct, a formal application of time–temperature superposition (TTS) analysis to the Γ data provided useful insights on the observed dependencies. In the TTS-shifted data, Γ decreased and then increased for monotonically increasing G˙. Thus, the TTS analysis suggests that there is a minimum value of Γ. This minimum value could be used to define a lower bound in Γ when designing critical engineering applications that are subjected to T and δ˙ excursions.

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Symbolic diagnostics to interpret and analyze neural network models

Robertson, Connor; Parish, Eric; Ray, Jaideep

Embedded machine-learned models (EMLMs) have the promise to improve the predictive accuracy of engineering simulators in environments of national interest. EMLMs often comprise complex input-output maps (e.g., neural networks), which make them unamenable to rigorous analysis and generally difficult to interpret. In the face of decades of theory, this lack of interpretability is a significant barrier to building confidence in these models. This work outlines an approach to interpret EMLMs using sparse polynomial regression for comparison with theoretical understanding. To do so, we build on the concept of Locally Interpretable Model-agnostic Explanations (LIME) using physics-informed clustering, prototype selection, and library construction. While general, we demonstrate our method on tensor-basis neural networks used in Reynolds-Averaged Navier-Stokes simulations of hypersonic fluid flows. Results are presented for a simulated toy model and for direct numerical simulations (DNS) of turbulent flows over a flat plate.

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Results 1076–1100 of 101,000
Results 1076–1100 of 101,000
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