6 citations · 11 across the 7 of their papers we have counts for
7 papers · 1 filter
Localized Operator Learning with Adaptive Partition-of-Unity Mixture-of-Expert Networks
Madison Cooley, Ramansh Sharma, Shandian Zhe +2
Operator learning methods such as DeepONets and FNOs often struggle with PDE families featuring sharp interfaces, heterogeneous coefficients, and localized multiscale structures. W…
The Frame Kernel Method for Multiscale Operator Learning
Branden Frieden, Ryan Whitehead, M. Keith Ballard +2
We present a natively multiscale operator learning method for the surrogate modeling of (numerical solvers for) multiscale partial differential equations (PDEs). The primary novelt…
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…
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…
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…
Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
Madison Cooley, Shandian Zhe, Robert M. Kirby +1
We present polynomial-augmented neural networks (PANNs), a novel machine learning architecture that combines deep neural networks (DNNs) with polynomial expansions. PANNs combine t…