7 papers
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
Matthew Lowery, John Turnage, Zachary Morrow +4
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for…
Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots
Branden Frieden, James M. Ferguson, Alan Kuntz +1
Continuum robots enable dexterous manipulation in constrained environments, but require accurate and efficient models for real-time manipulation and control. Traditional physics-ba…
Deep Gaussian Processes for Functional Maps
Matthew Lowery, Zhitong Xu, Da Long +5
Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including…
HyResPINNs: A Hybrid Residual Physics-Informed Neural Network Architecture Designed to Balance Expressiveness and Trainability
Madison Cooley, Robert M. Kirby, Shandian Zhe +1
Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that…
An Optimal Weighted Least-Squares Method for Operator Learning
John Turnage, Matthew Lowery, John Jakeman +3
We consider the problem of learning an unknown, possibly nonlinear operator between separable Hilbert spaces from supervised data. Inputs are drawn from a prescribed probability me…
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases
Madison Cooley, Varun Shankar, Robert M. Kirby +1
Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs…