109 citations · 522 across the 51 of their papers we have counts for
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Approximate homogenization of convex nonlinear elliptic PDEs
Chris Finlay, Adam M. Oberman
We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal…
Approximate homogenization of fully nonlinear elliptic PDEs: estimates and numerical results for Pucci type equations
Chris Finlay, Adam M. Oberman
We are interested in the shape of the homogenized operator for PDEs which have the structure of a nonlinear Pucci operator. A typical operator is $H^{a_1,a_2}(Q,x)…
Stochastic Backward Euler: An Implicit Gradient Descent Algorithm for -means Clustering
Penghang Yin, Minh Pham, Adam Oberman +1
In this paper, we propose an implicit gradient descent algorithm for the classic -means problem. The implicit gradient step or backward Euler is solved via stochastic fixed-poin…
Deep Relaxation: partial differential equations for optimizing deep neural networks
Pratik Chaudhari, Adam Oberman, Stanley Osher +2
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation te…
Approximate Convex Hulls: sketching the convex hull using curvature
Robert Graham, Adam M. Oberman
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the com…