9 papers
Visualizing the loss landscapes of physics-informed neural networks
Conor Rowan, Finn Murphy-Blanchard
Training a neural network requires navigating a high-dimensional, non-convex loss surface to find parameters that minimize this loss. In many ways, it is surprising that optimizers…
Boundary condition enforcement with PINNs: a comparative study and verification on 3D geometries
Conor Rowan, Kai Hampleman, Kurt Maute +1
Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in phys…
On the failure of ReLU activation for physics-informed machine learning
Conor Rowan
Physics-informed machine learning uses governing ordinary and/or partial differential equations to train neural networks to represent the solution field. Like any machine learning…
Finding geodesics with the Deep Ritz method
Conor Rowan
Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout…
Nonlinear discretizations and Newton's method: characterizing stationary points of regression objectives
Conor Rowan
Second-order methods are emerging as promising alternatives to standard first-order optimizers such as gradient descent and ADAM for training neural networks. Though the advantages…
Variational volume reconstruction with the Deep Ritz Method
Conor Rowan, Sumedh Soman, John A. Evans
We present a novel approach to variational volume reconstruction from sparse, noisy slice data using the Deep Ritz method. Motivated by biomedical imaging applications such as MRI-…