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math.NA2025
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…
math.NA2025
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…
math.OC2025
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…