13 papers
Nonlinear elliptic homogenization with the parametric Deep Ritz method
Conor Rowan
Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales. When these small scale features have rapid, periodic fluctuations…
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…
Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization
Grant Norman, Conor Rowan, Kurt Maute +1
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems.…
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-…
Solving engineering eigenvalue problems with neural networks using the Rayleigh quotient
Conor Rowan, John Evans, Kurt Maute +1
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue…
A thermoelastic plate model for shot peen forming metal panels based on effective torque
Conor Rowan
A common technique used in factories to shape metal panels is shot peen forming. The impacts between the hard steel shot and the softer metal of the panel cause localized plastic d…
Physics-informed solution reconstruction in elasticity and heat transfer using the explicit constraint force method
Conor Rowan, Kurt Maute, Alireza Doostan
One use case of ``physics-informed neural networks'' (PINNs) is solution reconstruction, which aims to estimate the full-field state of a physical system from sparse measurements.…
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…