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Relevant bibliographies by topics / Data approximation

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Academic literature on the topic 'Data approximation'

Author: Grafiati

Published: 7 December 2024

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Journal articles on the topic "Data approximation"

1

FROYLAND, GARY, KEVIN JUDD, ALISTAIR I. MEES, DAVID WATSON, and KENJI MURAO. "CONSTRUCTING INVARIANT MEASURES FROM DATA." International Journal of Bifurcation and Chaos 05, no. 04 (August 1995): 1181–92. http://dx.doi.org/10.1142/s0218127495000843.

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We present a method of approximating an invariant measure of a dynamical system from a finite set of experimental data. Our reconstruction technique automatically provides us with a partition of phase space, and we assign each set in the partition a certain weight. By refining the partition, we may make our approximation to an invariant measure of the reconstructed system as accurate as we wish. Our method provides us with both a singular and an absolutely continuous approximation, so that the most suitable representation may be chosen for a particular problem.

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Grubas, Serafim I., Georgy N. Loginov, and Anton A. Duchkov. "Traveltime-table compression using artificial neural networks for Kirchhoff-migration processing of microseismic data." GEOPHYSICS 85, no. 5 (August 19, 2020): U121—U128. http://dx.doi.org/10.1190/geo2019-0427.1.

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Massive computation of seismic traveltimes is widely used in seismic processing, for example, for the Kirchhoff migration of seismic and microseismic data. Implementation of the Kirchhoff migration operators uses large precomputed traveltime tables (for all sources, receivers, and densely sampled imaging points). We have tested the idea of using artificial neural networks for approximating these traveltime tables. The neural network has to be trained for each velocity model, but then the whole traveltime table can be compressed by several orders of magnitude (up to six orders) to the size of less than 1 MB. This makes it convenient to store, share, and use such approximations for processing large data volumes. We evaluate some aspects of choosing neural-network architecture, training procedure, and optimal hyperparameters. On synthetic tests, we find a reasonably accurate approximation of traveltimes by neural networks for various velocity models. A final synthetic test shows that using the neural-network traveltime approximation results in good accuracy of microseismic event localization (within the grid step) in the 3D case.

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STOJANOVIĆ, MIRJANA. "PERTURBED SCHRÖDINGER EQUATION WITH SINGULAR POTENTIAL AND INITIAL DATA." Communications in Contemporary Mathematics 08, no. 04 (August 2006): 433–52. http://dx.doi.org/10.1142/s0219199706002180.

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We consider linear Schrödinger equation perturbed by delta distribution with singular potential and the initial data. Due to the singularities appearing in the equation, we introduce two kinds of approximations: the parameter's approximation for potential and the initial data given by mollifiers of different growth and the approximation for the Green function for Schrödinger equation with regularized derivatives. These approximations reduce the perturbed Schrödinger equation to the family of singular integral equations. We prove the existence-uniqueness theorems in Colombeau space [Formula: see text], 1 ≤ p,q ≤ ∞, employing novel stability estimates (w.r.) to singular perturbations for ε → 0, which imply the statements in the framework of Colombeau generalized functions. In particular, we prove the existence-uniqueness result in [Formula: see text] and [Formula: see text] algebra of Colombeau.

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FRAHLING, GEREON, PIOTR INDYK, and CHRISTIAN SOHLER. "SAMPLING IN DYNAMIC DATA STREAMS AND APPLICATIONS." International Journal of Computational Geometry & Applications 18, no. 01n02 (April 2008): 3–28. http://dx.doi.org/10.1142/s0218195908002520.

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A dynamic geometric data stream is a sequence of m ADD/REMOVE operations of points from a discrete geometric space {1,…, Δ} d ?. ADD (p) inserts a point p from {1,…, Δ} d into the current point set P , REMOVE(p) deletes p from P . We develop low-storage data structures to (i) maintain ε-nets and ε-approximations of range spaces of P with small VC-dimension and (ii) maintain a (1 + ε)-approximation of the weight of the Euclidean minimum spanning tree of P . Our data structure for ε-nets uses [Formula: see text] bits of memory and returns with probability 1 – δ a set of [Formula: see text] points that is an e-net for an arbitrary fixed finite range space with VC-dimension [Formula: see text]. Our data structure for ε-approximations uses [Formula: see text] bits of memory and returns with probability 1 – δ a set of [Formula: see text] points that is an ε-approximation for an arbitrary fixed finite range space with VC-dimension [Formula: see text]. The data structure for the approximation of the weight of a Euclidean minimum spanning tree uses O ( log (1/δ)( log Δ/ε) O ( d )) space and is correct with probability at least 1 – δ. Our results are based on a new data structure that maintains a set of elements chosen (almost) uniformly at random from P .

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Chen, Jing-Bo, Hong Liu, and Zhi-Fu Zhang. "A separable-kernel decomposition method for approximating the DSR continuation operator." GEOPHYSICS 72, no. 1 (January 2007): S25—S31. http://dx.doi.org/10.1190/1.2399368.

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We develop a separable-kernel decomposition method for approximating the double-square-root (DSR) continuation operator in one-way migrations in this paper. This new approach is a further development of separable approximations of the single-square-root (SSR) operator. The separable approximation of the DSR operator generally involves solving a complicated nonlinear system of integral equations. Instead of solving this nonlinear system directly, our new method consists of repeatedly applying the separable-kernel technique developed for the two-variable SSR operator to the multivariable DSR operator. Numerical experiments demonstrate the efficiency of the proposed method. We illustrate the fast convergence of the obtained separable approximation. We also demonstrate the capability of this novel approximation for imaging an area with geologic complexities through synthetic data.

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Mardia, K. V., and I. L. Dryden. "Shape distributions for landmark data." Advances in Applied Probability 21, no. 4 (December 1989): 742–55. http://dx.doi.org/10.2307/1427764.

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The paper obtains the exact distribution of Bookstein's shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendall's uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Bookstein's result for three landmarks. The adequacy of these approximations is also studied.

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Mardia, K. V., and I. L. Dryden. "Shape distributions for landmark data." Advances in Applied Probability 21, no. 04 (December 1989): 742–55. http://dx.doi.org/10.1017/s0001867800019029.

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The paper obtains the exact distribution of Bookstein's shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendall's uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Bookstein's result for three landmarks. The adequacy of these approximations is also studied.

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Birch, A. C., and A. G. Kosovichev. "Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data." Symposium - International Astronomical Union 203 (2001): 180–82. http://dx.doi.org/10.1017/s0074180900219025.

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Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

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Dong, Bin, Zuowei Shen, and Jianbin Yang. "Approximation from Noisy Data." SIAM Journal on Numerical Analysis 59, no. 5 (January 2021): 2722–45. http://dx.doi.org/10.1137/20m1389091.

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Piegl, L. A., and W. Tiller. "Data Approximation Using Biarcs." Engineering with Computers 18, no. 1 (April 29, 2002): 59–65. http://dx.doi.org/10.1007/s003660200005.

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Dissertations / Theses on the topic "Data approximation"

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Ross, Colin. "Applications of data fusion in data approximation." Thesis, University of Huddersfield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247372.

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Deligiannakis, Antonios. "Accurate data approximation in constrained environments." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2681.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.
Thesis research directed by: Computer Science. Title from abstract of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Tomek, Peter. "Approximation of Terrain Data Utilizing Splines." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2012. http://www.nusl.cz/ntk/nusl-236488.

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Pro optimalizaci letových trajektorií ve velmi malé nadmorské výšce, terenní vlastnosti musí být zahrnuty velice přesne. Proto rychlá a efektivní evaluace terenních dat je velice důležitá vzhledem nato, že čas potrebný pro optimalizaci musí být co nejkratší. Navyše, na optimalizaci letové trajektorie se využívájí metody založené na výpočtu gradientu. Proto musí být aproximační funkce terenních dat spojitá do určitého stupne derivace. Velice nádejná metoda na aproximaci terenních dat je aplikace víceroměrných simplex polynomů. Cílem této práce je implementovat funkci, která vyhodnotí dané terenní data na určitých bodech spolu s gradientem pomocí vícerozměrných splajnů. Program by měl vyčíslit více bodů najednou a měl by pracovat v $n$-dimensionálním prostoru.

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Cao, Phuong Thao. "Approximation of OLAP queries on data warehouses." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00905292.

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We study the approximate answers to OLAP queries on data warehouses. We consider the relative answers to OLAP queries on a schema, as distributions with the L1 distance and approximate the answers without storing the entire data warehouse. We first introduce three specific methods: the uniform sampling, the measure-based sampling and the statistical model. We introduce also an edit distance between data warehouses with edit operations adapted for data warehouses. Then, in the OLAP data exchange, we study how to sample each source and combine the samples to approximate any OLAP query. We next consider a streaming context, where a data warehouse is built by streams of different sources. We show a lower bound on the size of the memory necessary to approximate queries. In this case, we approximate OLAP queries with a finite memory. We describe also a method to discover the statistical dependencies, a new notion we introduce. We are looking for them based on the decision tree. We apply the method to two data warehouses. The first one simulates the data of sensors, which provide weather parameters over time and location from different sources. The second one is the collection of RSS from the web sites on Internet.

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Lehman, Eric (Eric Allen) 1970. "Approximation algorithms for grammar-based data compression." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/87172.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.
Includes bibliographical references (p. 109-113).
This thesis considers the smallest grammar problem: find the smallest context-free grammar that generates exactly one given string. We show that this problem is intractable, and so our objective is to find approximation algorithms. This simple question is connected to many areas of research. Most importantly, there is a link to data compression; instead of storing a long string, one can store a small grammar that generates it. A small grammar for a string also naturally brings out underlying patterns, a fact that is useful, for example, in DNA analysis. Moreover, the size of the smallest context-free grammar generating a string can be regarded as a computable relaxation of Kolmogorov complexity. Finally, work on the smallest grammar problem qualitatively extends the study of approximation algorithms to hierarchically-structured objects. In this thesis, we establish hardness results, evaluate several previously proposed algorithms, and then present new procedures with much stronger approximation guarantees.
by Eric Lehman.
Ph.D.

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Hou, Jun. "Function Approximation and Classification with Perturbed Data." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618266875924225.

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Zaman, Muhammad Adib Uz. "Bicubic L1 Spline Fits for 3D Data Approximation." Thesis, Northern Illinois University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10751900.

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Univariate cubic L¹ spline fits have been successful to preserve the shapes of 2D data with abrupt changes. The reason is that the minimization of L¹ norm of the data is considered, as opposite to L² norm. While univariate L¹ spline fits for 2D data are discussed by many, bivariate L¹ spline fits for 3D data are yet to be fully explored. This thesis aims to develop bicubic L¹ spline fits for 3D data approximation. This can be achieved by solving a bi-level optimization problem. One level is bivariate cubic spline interpolation and the other level is L¹ error minimization. In the first level, a bicubic interpolated spline surface will be constructed on a rectangular grid with necessary first and second order derivative values estimated by using a 5-point window algorithm for univariate L¹ interpolation. In the second level, the absolute error (i.e. L¹ norm) will be minimized using an iterative gradient search. This study may be extended to higher dimensional cubic L¹ spline fits research.

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Cooper, Philip. "Rational approximation of discrete data with asymptotic behaviour." Thesis, University of Huddersfield, 2007. http://eprints.hud.ac.uk/id/eprint/2026/.

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This thesis is concerned with the least-squares approximation of discrete data that appear to exhibit asymptotic behaviour. In particular, we consider using rational functions as they are able to display a number of types of asymptotic behaviour. The research is biased towards the development of simple and easily implemented algorithms that can be used for this purpose. We discuss a number of novel approximation forms, including the Semi-Infinite Rational Spline and the Asymptotic Polynomial. The Semi-Infinite Rational Spline is a piecewise rational function, continuous across a single knot, and may be defined to have different asymptotic limits at ±∞. The continuity constraints at the knot are implicit in the function definition, and it can be fitted to data without the use of constrained optimisation algorithms. The Asymptotic Polynomial is a linear combination of weighted basis functions, orthogonalised with respect to a rational weight function of nonlinear approximation parameters. We discuss an efficient and numerically stable implementation of the Gauss-Newton method that can be used to fit this function to discrete data. A number of extensions of the Loeb algorithm are discussed, including a simple modification for fitting Semi- Infinite Rational Splines, and a new hybrid algorithm that is a combination of the Loeb algorithm and the Lawson algorithm (including its Rice and Usow extension), for fitting ℓp rational approximations. In addition, we present an extension of the Rice and Usow algorithm to include ℓp approximation for values p < 2. Also discussed is an alternative representation of a polynomial ratio denominator, that allows pole free approximations to be fitted to data with the use of unconstrained optimisation methods. In all cases we present a large number of numerical applications of these methods to illustrate their usefulness.

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Schmid, Dominik. "Scattered data approximation on the rotation group and generalizations." Aachen Shaker, 2009. http://d-nb.info/995021562/04.

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McQuarrie, Shane Alexander. "Data Assimilation in the Boussinesq Approximation for Mantle Convection." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/6951.

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Many highly developed physical models poorly approximate actual physical systems due to natural random noise. For example, convection in the earth's mantle—a fundamental process for understanding the geochemical makeup of the earth's crust and the geologic history of the earth—exhibits chaotic behavior, so it is difficult to model accurately. In addition, it is impossible to directly measure temperature and fluid viscosity in the mantle, and any indirect measurements are not guaranteed to be highly accurate. Over the last 50 years, mathematicians have developed a rigorous framework for reconciling noisy observations with reasonable physical models, a technique called data assimilation. We apply data assimilation to the problem of mantle convection with the infinite-Prandtl Boussinesq approximation to the Navier-Stokes equations as the model, providing rigorous conditions that guarantee synchronization between the observational system and the model. We validate these rigorous results through numerical simulations powered by a flexible new Python package, Dedalus. This methodology, including the simulation and post-processing code, may be generalized to many other systems. The numerical simulations show that the rigorous synchronization conditions are not sharp; that is, synchronization may occur even when the conditions are not met. These simulations also cast some light on the true relationships between the system parameters that are required in order to achieve synchronization. To conclude, we conduct experiments for two closely related data assimilation problems to further demonstrate the limitations of the rigorous results and to test the flexibility of data assimilation for mantle-like systems.

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Books on the topic "Data approximation"

1

Iske, Armin. Approximation Theory and Algorithms for Data Analysis. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7.

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Motwani, Rajeev. Lecture notes on approximation algorithms. Stanford, CA: Dept. of Computer Science, Stanford University, 1992.

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C, Mason J., and Cox M. G, eds. Algorithms for approximation II: Based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988. London: Chapman and Hall, 1990.

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Franke, Richard. Recent advances in the approximation of surfaces from scattered data. Monterey, Calif: Naval Postgraduate School, 1987.

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Ivanov, Viktor Vladimirovich. Metody vychisleniĭ na ĖVM: Spravochnoe posobie. Kiev: Nauk. dumka, 1986.

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Franke, Richard H. Least squares surface approximation to scattered data using multiquadric functions. Monterey, Calif: Naval Postgraduate School, 1993.

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Molchanov, I. N. Mashinnye metody reshenii͡a︡ prikladnykh zadach algebra, priblizhenie funkt͡s︡iĭ. Kiev: Nauk. dumka, 1987.

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K, Ray Bimal, ed. Polygonal approximation and scale-space analysis. Oakville, Ont: Apple Academic Press, 2013.

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C, Mason J., Cox M. G, and Institute of Mathematics and Its Applications., eds. Algorithms for approximation: Based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985. Oxford [Oxfordshire]: Clarendon Press, 1987.

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Eitan, Tadmor, Institute for Computer Applications in Science and Engineering., and Langley Research Center, eds. Recovering pointwise values of discontinuous data within spectral accuracy. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1985.

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Book chapters on the topic "Data approximation"

1

Shekhar, Shashi, and Hui Xiong. "Data Approximation." In Encyclopedia of GIS, 203. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-35973-1_237.

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Hutchings, Matthew, and Bertrand Gauthier. "Local Optimisation of Nyström Samples Through Stochastic Gradient Descent." In Machine Learning, Optimization, and Data Science, 123–40. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-25599-1_10.

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AbstractWe study a relaxed version of the column-sampling problem for the Nyström approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nyström samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nyström approximation accuracy; in this setting, we discuss how Nyström samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nyström samples with improved Nyström approximation accuracy in terms of trace, Frobenius and spectral norms.

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Markovsky, Ivan. "From Data to Models." In Low-Rank Approximation, 37–70. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89620-5_2.

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Deng, Shaobo, Huihui Lu, Sujie Guan, Min Li, and Hui Wang. "Approximation Relation for Rough Sets." In Data Mining and Big Data, 402–17. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7502-7_38.

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Rengaswamy, Raghunathan, and Resmi Suresh. "Function Approximation Methods." In Data Science for Engineers, 175–252. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/b23276-6.

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Iske, Armin. "Euclidean Approximation." In Approximation Theory and Algorithms for Data Analysis, 103–38. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_4.

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Iske, Armin. "Chebyshev Approximation." In Approximation Theory and Algorithms for Data Analysis, 139–84. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_5.

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Markovsky, Ivan. "Data-Driven Filtering and Control." In Low-Rank Approximation, 161–72. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89620-5_6.

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Adir, Allon, Ehud Aharoni, Nir Drucker, Ronen Levy, Hayim Shaul, and Omri Soceanu. "Approximation Methods Part II: Approximations of Standard Functions." In Homomorphic Encryption for Data Science (HE4DS), 125–47. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65494-7_6.

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Wu, Weili, Yi Li, Panos M. Pardalos, and Ding-Zhu Du. "Data-Dependent Approximation in Social Computing." In Approximation and Optimization, 27–34. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12767-1_3.

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Conference papers on the topic "Data approximation"

1

Ma, Guanqun, David Lenz, Tom Peterka, Hanqi Guo, and Bei Wang. "Critical Point Extraction from Multivariate Functional Approximation." In 2024 IEEE Topological Data Analysis and Visualization (TopoInVis), 12–22. IEEE, 2024. http://dx.doi.org/10.1109/topoinvis64104.2024.00006.

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Sahrom, Nor Ashikin, Mohammad Izat Emir Zulkifly, and Siti Nur Idara Rosli. "Interval-Valued Fuzzy Bézier Surface Approximation." In 2024 5th International Conference on Artificial Intelligence and Data Sciences (AiDAS), 1–5. IEEE, 2024. http://dx.doi.org/10.1109/aidas63860.2024.10730727.

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Barbas, Petros, Aristidis G. Vrahatis, and Sotiris K. Tasoulis. "RLAC: Random Line Approximation Clustering." In 2021 IEEE International Conference on Big Data (Big Data). IEEE, 2021. http://dx.doi.org/10.1109/bigdata52589.2021.9671596.

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Zhao, Danfeng, Zhou Huang, Feng Zhou, Antonio Liotta, and Dongmei Huang. "An Approximation Method for Large Graph Similarity." In 2020 IEEE International Conference on Big Data (Big Data). IEEE, 2020. http://dx.doi.org/10.1109/bigdata50022.2020.9378447.

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Das, Abhinandan, Johannes Gehrke, and Mirek Riedewald. "Approximation techniques for spatial data." In the 2004 ACM SIGMOD international conference. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1007568.1007646.

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Freedman, Daniel, and Pavel Kisilev. "Fast Data Reduction via KDE Approximation." In 2009 Data Compression Conference (DCC). IEEE, 2009. http://dx.doi.org/10.1109/dcc.2009.47.

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Panda, Biswanath, Mirek Riedewald, Johannes Gehrke, and Stephen B. Pope. "High-Speed Function Approximation." In Seventh IEEE International Conference on Data Mining (ICDM 2007). IEEE, 2007. http://dx.doi.org/10.1109/icdm.2007.107.

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Huang, Zhou, and Feng Zhou. "An Approximation Method for Querying Similar Large Graphs." In 2022 IEEE International Conference on Big Data (Big Data). IEEE, 2022. http://dx.doi.org/10.1109/bigdata55660.2022.10020310.

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Shahcheraghi, Maryam, Trevor Cappon, Samet Oymak, Evangelos Papalexakis, Eamonn Keogh, Zachary Zimmerman, and Philip Brisk. "Matrix Profile Index Approximation for Streaming Time Series." In 2021 IEEE International Conference on Big Data (Big Data). IEEE, 2021. http://dx.doi.org/10.1109/bigdata52589.2021.9671484.

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Kannan, Ramakrishnan, Mariya Ishteva, and Haesun Park. "Bounded Matrix Low Rank Approximation." In 2012 IEEE 12th International Conference on Data Mining (ICDM). IEEE, 2012. http://dx.doi.org/10.1109/icdm.2012.131.

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Reports on the topic "Data approximation"

1

Franke, Richard, Hans Hagen, and Gregory M. Nielson. Least Squares Surface Approximation to Scattered Data Using Multiquadric Functions. Fort Belvoir, VA: Defense Technical Information Center, December 1992. http://dx.doi.org/10.21236/ada259804.

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Ray, Jaideep, Matthew Barone, Stefan Domino, Tania Banerjee, and Sanjay Ranka. Verification of Data-Driven Models of Physical Phenomena using Interpretable Approximation. Office of Scientific and Technical Information (OSTI), September 2021. http://dx.doi.org/10.2172/1821318.

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Baraniuk, Richard, Ronald DeVore, Sanjeev Kulkarni, Andrew Kurdila, Stanley Osher, Guergana Petrova, Robert Sharpley, Richard Tsai, and Hongkai Zhao. Model Classes, Approximation, and Metrics for Dynamic Processing of Urban Terrain Data. Fort Belvoir, VA: Defense Technical Information Center, January 2013. http://dx.doi.org/10.21236/ada586168.

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Franke, Richard. Using Legendre Functions for Spatial Covariance Approximation and Investigation of Radial Nonisotrophy for NOGAPS Data. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada389396.

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Wu, Yan, Sonia Fahmy, and Ness B. Shroff. On the Construction of a Maximum-Lifetime Data Gathering Tree in Sensor Networks: NP-Completeness and Approximation Algorithm. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada517885.

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Shah, Rajiv R. High-Level Adaptive Signal Processing Architecture with Applications to Radar Non-Gaussian Clutter. Volume 2. A New Technique for Distribution Approximation of Random Data. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada300902.

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Gorton, O., and J. Escher. Cross Sections for Neutron-Induced Reactions from Surrogate Data: Assessing the Use of the Weisskopf-Ewing Approximation for (n,n') and (n,2n) Reactions. Office of Scientific and Technical Information (OSTI), September 2020. http://dx.doi.org/10.2172/1668500.

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Guan, Jiajing, Sophia Bragdon, and Jay Clausen. Predicting soil moisture content using Physics-Informed Neural Networks (PINNs). Engineer Research and Development Center (U.S.), August 2024. http://dx.doi.org/10.21079/11681/48794.

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Environmental conditions such as the near-surface soil moisture content are valuable information in object detection problems. However, such information is generally unobtainable at the necessary scale without active sensing. Richards’ equation is a partial differential equation (PDE) that describes the infiltration process of unsaturated soil. Solving the Richards’ equation yields information about the volumetric soil moisture content, hydraulic conductivity, and capillary pressure head. However, Richards’ equation is difficult to approximate due to its nonlinearity. Numerical solvers such as finite difference method (FDM) and finite element method (FEM) are conventional in approximating solutions to Richards’ equation. But such numerical solvers are time-consuming when used in real-time. Physics-informed neural networks (PINNs) are neural networks relying on physical equations in approximating solutions. Once trained, these networks can output approximations in a speedy manner. Thus, PINNs have attracted massive attention in the numerical PDE community. This project aims to apply PINNs to the Richards’ equation to predict underground soil moisture content under known precipitation data.

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Bunn, M. I., T. R. Carter, H. A. J. Russell, and C. E. Logan. A semiquantitative representation of uncertainty for the 3D Paleozoic bedrock model of Southern Ontario. Natural Resources Canada/CMSS/Information Management, 2023. http://dx.doi.org/10.4095/331658.

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The southern Ontario bedrock model is a valuable resource for researchers and practitioners, but its application is subject to uncertainty. To address this issue a semi-quantitative approach to visualize the relative effects of data sparsity for each layer, identify regions where a lack of data support reduces model confidence, and quantify potential errors in data collection and model construction is presented. This analysis summarizes several sources of error, including cartesian position error, error in the vertical position of the formation contact, error between the modelled topographic surface and recorded collar elevations, and error between the modelled formation top surface and formation top picks. Where data is present, these errors are added to provide an approximation of total uncertainty. Where data are not present, uncertainty is approximated as 50% of the range in formation top variation, with an average value of 27.5 m across all layers. The results show that data availability strongly influences the average total error for each layer, with deeper layers exhibiting higher total error due to lower data density. However, this analysis also suggests that the modelled surfaces likely carry errors of less than 5 to 10 m in most regions.

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Rofman, Rafael, Joaquín Baliña, and Emanuel López. Evaluating the Impact of COVID-19 on Pension Systems in Latin America and the Caribbean. The Case of Argentina. Inter-American Development Bank, October 2022. http://dx.doi.org/10.18235/0004508.

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This paper presents a first approximation to assess the impact of the COVID-19 outbreak on Argentinas pension system in both the short and medium/long-term. To this end, we have used the Pension Projection Model of the Inter-American Development Bank (IDB) to design and analyze possible scenarios and outcomes, based on alternative scenarios. According to the data analyzed and the projections, the impact of COVID-19 on Argentinas pension system in the short run seems to have been limited, particularly given the rapid recovery during the last months of 2021. The long-term impact is harder to predict. Given the macroeconomic effects of the efforts made by authorities to protect the system and pensioners during the pandemic on the one hand; and the effects of COVID-19 within the labor market on the other, overall consequences are still to be fully understood.

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