7 papers
Blow-up for energy supercritical defocusing nonlinear Schrödinger equations in dimensions three, four and five
Kevin Buck, Alvaro Carballeira, Javier Gómez-Serrano +1
We prove finite time blow-up from smooth, radial, compactly supported initial data for the energy supercritical defocusing nonlinear Schrödinger equation $i\partial_tu+Δu-|u|^{p-1}…
Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant
Kevin Buck, Charles L. Fefferman, Javier Gómez-Serrano +3
We prove the fixed-potential conjecture of Fefferman, Shapiro, and Weinstein for inversion-symmetric magnetic double wells. We construct a number and one smooth, compactly…
Auto-Adaptive PINNs with Applications to Phase Transitions
Kevin Buck, Woojeong Kim
We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which…
Convergence Properties of PINNs for the Navier-Stokes-Cahn-Hilliard System
Kevin Buck, Roger Temam
Approximating solutions to differential equations using neural networks has become increasingly popular and shows significant promise. In this paper, we propose a simplified framew…
Nonconvex optimization and convergence of stochastic gradient descent, and solution of asynchronous game
Kevin Buck, Jessica Babyak, Paolo Piersanti +3
We review convergence and behavior of stochastic gradient descent for convex and nonconvex optimization, establishing various conditions for convergence to zero of the variance of…
Sychronous vs. asynchronous coalitions in multiplayer games, with applications to guts poker
Jessica Babyak, Kevin Buck, Leah Dichter +2
We study the issue introduced by Buck-Lee-Platnick-Wheeler-Zumbrun of synchronous vs. asynchronous coalitions in multiplayer games, that is, the difference between coalitions with…
Continuous guts poker and numerical optimization of generalized recursive games
Kevin Buck, Jae Hwan Lee, Jacob Platnick +2
We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and v. coal…