arXiv subjects

P. Kuberry

Publications and source records attributed to P. Kuberry.

3 recordsLinked to original sources

arXiv2021

First-Passage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS)

We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with drift-diffusion dynamics $d\mathbf{X}_t = a(\mathbf{X}_t)dt + \mathbf{b}(\mathbf{X}_t)d\mathbf{W}_t$. We formulate descriptions of Brownian motion and general drift-diffusion processes on surfaces. We consider statistics of the form $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\int_0^\tau g(\mathbf{X}_t)dt \right] + \mathbb{E}^{\mathbf{x}}\left[f(\mathbf{X}_\tau)\right]$ for a domain $\Omega$ and the exit stopping time $\tau = \inf_t \{t > 0 \; |\; \mathbf{X}_t \not\in \Omega\}$, where $f,g$ are general smooth functions. For computing these statistics, we develop high-order Generalized Moving Least Squares (GMLS) solvers for associated surface PDE boundary-value problems based on Backward-Kolmogorov equations. We focus particularly on the mean First Passage Times (FPTs) given by the case $f = 0,\, g = 1$ where $u(\mathbf{x}) = \mathbb{E}^{\mathbf{x}}\left[\tau\right]$. We perform studies for a variety of shapes showing our methods converge with high-order accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how statistics are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.

math.NA↗

arXiv2020

Development, Demonstration, and Validation of Data-driven Compact Diode Models for Circuit Simulation and Analysis

Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion of new physics (eg, radiation effects) into an existing compact model is not trivial and may require redevelopment from scratch. Machine Learning (ML) techniques have the potential to automate and significantly speed up the development of compact models. In addition, ML provides a range of modeling options that can be used to develop hierarchies of compact models tailored to specific circuit design stages. In this paper, we explore three such options: (1) table-based interpolation, (2)Generalized Moving Least-Squares, and (3) feed-forward Deep Neural Networks, to develop compact models for a p-n junction diode. We evaluate the performance of these "data-driven" compact models by (1) comparing their voltage-current characteristics against laboratory data, and (2) building a bridge rectifier circuit using these devices, predicting the circuit's behavior using SPICE-like circuit simulations, and then comparing these predictions against laboratory measurements of the same circuit.

cs.LG↗

arXiv2019

Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving Least-Squares (GMLS) Approach

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate incompressible hydrodynamic equations in the Stokesian regime and handle the divergence-free constraints via a generalized vector potential. This provides less coordinate-centric descriptions and enables the development of efficient numerical methods and splitting schemes for the fourth-order governing equations in terms of a system of second-order elliptic operators. Using a Hodge decomposition, we develop methods for manifolds having spherical topology. We show the methods exhibit high-order convergence rates for solving hydrodynamic flows on curved surfaces. The methods also provide general high-order approximations for the metric, curvature, and other geometric quantities of the manifold and associated exterior calculus operators. The approaches also can be utilized to develop high-order solvers for other scalar-valued and vector-valued problems on manifolds.

math.NA↗