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Patel, R.

Publications and source records attributed to Patel, R..

11 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

GMLS-Nets: A Framework for Learning from Unstructured Data

Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently been used in the literature for solving partial differential equations. By parameterizing the GMLS estimator, we obtain learning methods for operators with unstructured stencils. In GMLS-Nets the necessary calculations are local, readily parallelizable, and the estimator is supported by a rigorous approximation theory. We show how the framework may be used for unstructured physical data sets to perform functional regression to identify associated differential operators and to regress quantities of interest. The results suggest the architectures to be an attractive foundation for data-driven model development in scientific machine learning applications

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Protein kinase B/Akt activates c-Jun NH(2)-terminal kinase by increasing NO production in response to shear stress

Laminar shear stress activates c-Jun NH(2)-terminal kinase (JNK) by the mechanisms involving both nitric oxide (NO) and phosphatidylinositide 3-kinase (PI3K). Because protein kinase B (Akt), a downstream effector of PI3K, has been shown to phosphorylate and activate endothelial NO synthase, we hypothesized that Akt regulates shear-dependent activation of JNK by stimulating NO production. Here, we examined the role of Akt in shear-dependent NO production and JNK activation by expressing a dominant negative Akt mutant (Akt(AA)) and a constitutively active mutant (Akt(Myr)) in bovine aortic endothelial cells (BAEC). As expected, pretreatment of BAEC with the PI3K inhibitor (wortmannin) prevented shear-dependent stimulation of Akt and NO production. Transient expression of Akt(AA) in BAEC by using a recombinant adenoviral construct inhibited the shear-dependent stimulation of NO production and JNK activation. However, transient expression of Akt(Myr) by using a recombinant adenoviral construct did not induce JNK activation. This is consistent with our previous finding that NO is required, but not sufficient on its own, to activate JNK in response to shear stress. These results and our previous findings strongly suggest that shear stress triggers activation of PI3K, Akt, and endothelial NO synthase, leading to production of NO, which (along with O(2-), which is also produced by shear) activates Ras-JNK pathway. The regulation of Akt, NO, and JNK by shear stress is likely to play a critical role in its antiatherogenic effects.

Non-NASA Center↗
NASA NTRS1977

Modeling error analysis of stationary linear discrete-time filters

The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.

Patel, R.↗
NASA NTRS1976

Closed-loop stability of linear quadratic optimal systems in the presence of modeling errors

The well-known stabilizing property of linear quadratic state feedback design is utilized to evaluate the robustness of a linear quadratic feedback design in the presence of modeling errors. Two general conditions are obtained for allowable modeling errors such that the resulting closed-loop system remains stable. One of these conditions is applied to obtain two more particular conditions which are readily applicable to practical situations where a designer has information on the bounds of modeling errors. Relations are established between the allowable parameter uncertainty and the weighting matrices of the quadratic performance index, thereby enabling the designer to select appropriate weighting matrices to attain a robust feedback design.

Toda, M.↗