61 citations · 78 across the 9 of their papers we have counts for
9 papers
Generalized Adjoint Method
Andrew Zheng, Adam R. Stinchcombe
The adjoint method is an efficient way to numerically compute gradients in optimization problems with constraints, but is only formulated to differentiable cost and constraint func…
Walk-on-Interfaces: A Monte Carlo Estimator for an Elliptic Interface Problem with Nonhomogeneous Flux Jump Conditions and a Neumann Boundary Condition
Xinwen Ding, Adam R Stinchcombe
Elliptic interface problems arise in numerous scientific and engineering applications, modeling heterogeneous materials in which physical properties change discontinuously across i…
Evaluating singular and near-singular integrals on smooth surfaces with quadratic geometric approximation and closed form expressions
Andrew Zheng, Spyros Alexakis, Adam R Stinchcombe
Most Fredholm integral equations involve integrals with weakly singular kernels. Once the domain of integration is discretized into flat triangular elements, these weakly singular…
A boundary integral equation method for the complete electrode model in electrical impedance tomography with tests on experimental data
Teemu Tyni, Adam R Stinchcombe, Spyros Alexakis
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, whe…
A Multi-Scale Simulation of Retinal Physiology
Belal Abuelnasr, Adam R. Stinchcombe
We present a detailed physiological model of the retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical g…
Fast Computation of Electrostatic Potentials for Piecewise Constant Conductivities
Kyle Bower, Kirill Serkh, Spyros Alexakis +1
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ a…
Promoter methylation in a mixed feedback loop circadian clock model
Turner Silverthorne, Edward Saehong Oh, Adam R Stinchcombe
We introduce and analyze an extension of the mixed feedback loop model of François and Hakim. Our extension includes an additional promoter state and allows for reversible protein…
Solving Elliptic Equations with Brownian Motion: Bias Reduction and Temporal Difference Learning
Cameron Martin, Hongyuan Zhang, Julia Costacurta +2
The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time Markov processes. This connect…
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks
Jihun Han, Mihai Nica, Adam R Stinchcombe
We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network wh…