6 papers · 1 filter
From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models
Conor Rowan
Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displac…
On the definition and importance of interpretability in scientific machine learning
Conor Rowan, Alireza Doostan
Though neural networks trained on large datasets have been successfully used to describe and predict many physical phenomena, there is a sense among scientists that, unlike traditi…
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…
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…