Density functionals for surface science: Exchange-correlation model development with Bayesian error estimation
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Neural networks are increasingly integrated into scientific discovery, where input data reduction and model quantization play a key role in accelerating inference. However, understanding and mitigating the impact of these techniques on output error is critical for ensuring reliable results, particularly in tasks demanding high numerical precision. This paper introduces a comprehensive framework for optimizing neural network inference in scientific computing by combining data reduction and weight quantization while maintaining error-controlled outcomes. We develop theoretical analyses to bound error propagation under these reductions and propose a framework that balances computational performance with error constraints. Evaluation on real-world learning-based combustion simulations and satellite image classification demonstrates that our derived error bounds accurately predict observed errors while enabling significant computational speedup under our framework. This work highlights the potential for further leveraging advancements in modern lossy compression algorithms and hardware accelerators that support lower-precision formats.
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Tetrahedral finite element workflows have the potential to drastically reduce time to solution for computational solid mechanics simulations when compared to traditional hexahedral finite element analogues. A recently developed, higher-order composite tetrahedral element has shown promise in the space of incompressible computational plasticity. Mesh adaptivity has the potential to increase solution accuracy and increase solution robustness. In this work, we demonstrate an initial strategy to perform conformal mesh adaptivity for this higher-order composite tetrahedral element using well-established mesh modification operations for linear tetrahedra. We propose potential extensions to improve this initial strategy in terms of robustness and accuracy.
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Satellite-to-satellite tracking and orbit computation accuracy is evaluated on the basis of data obtained from near earth spacecraft via the geostationary ATS-6. The near earth spacecraft involved are Apollo-Soyuz, GEOS-3, and NIMBUS-6. In addition ATS-6 is being tracked by a new scheme wherein a single ground transmitter interrogates several ground based transponders via ATS-6 to achieve the precision geostationary orbits essential in satellite-to-satellite orbit computation. Also one way Doppler data is being recorded aboard NIMBUS-6 to determine the position of meteorological platforms. Accuracy assessments associated with the foregoing mission related experiments are discussed.
Methods of efficiently generating and classifying samples with specified multivariate normal distributions were discussed. Conservative confidence tables for sample sizes are given for selective sampling. Simulation results are compared with classified training data. Techniques for comparing error and separability measure for two normal patterns are investigated and used to display the relationship between the error and the Chernoff bound.
A method of optimum orbital averaging was employed to study the long range accuracy potential of polar orbiting applications satellites. This approach involved the determination of the boundary conditions of one set of differential equations of motion by adjusting the initial conditions in a least square sense with the use of data generated by another set of differential equations of motion.
This paper outlines the application of various estimation approaches to the problem of static shape determination for large antenna systems. The problem consists of estimating the shape of an antenna surface from measurements of its static deflection. The estimation schemes are based on any one of the modeling options of a single PDE for early insight and understanding, coarse-resolution multiple-PDE models for parametric studies and fine-resolution piecewise-continuum models for detailed design. For any one of these three models, estimator design can be developed using an infinite-dimensional approach, where the necessary finite-element truncation and approximation is conducted after the analytical design has taken place, or it can be based on a finite-dimensional approach, where the model is truncated before the estimation problem is formulated. One of the main objectives of the paper is to develop both approaches while simultaneously investigating their differences and similarities. Simulation results of an application of the finite-dimensional approach to a large parabolic reflector are presented.
The conduction of the Earth Radiation Budget Experiment (ERBE) will involve the utilization of three sets of instruments. Each set consists of a nonscanning package and a scanning radiometer. The instruments will fly on the NOAA F and G operational satellites and on a dedicated spacecraft, the Earth Radiation Budget Satellite (ERBS). The ERBS will be in a 57 deg inclination orbit and will precess around the earth to provide sampling of the diurnal cycle of regions between + or - 57 deg latitude. The primary function of the scanning radiometer is to provide measurements for the calculation of the earth-emitted and absorbed solar radiation at the top of the earth-atmosphere system, averaged over 250 x 250 km regions. The present paper is concerned with errors found in these regional averages. Attention is given to details regarding the problem, scene identification probabilities, scene identification error effects, total pixel error, and errors due to regional averaging.
The results of initial studies to determine the key parameters influencing the performance of a computer-based measurement system are presented. The system components were modeled, and a representative intensity pattern was chosen and deformed by known amounts. The effect of varying different model parameters in the model was analyzed numerically. The most significant parameters were found to be: (1) the number of quantization levels in the digitization process, (2) the ratio of the frequency of the signal to the frequency of the sampling, and (3) the form of the intensity interpolation function.
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