4 citations · 9 across the 11 of their papers we have counts for
11 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…
Mask-Based Deep Symbolic Regression
Zachary Bastiani, Robert M. Kirby, Jacob Hochhalter +1
Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress,…
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…
Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients
Zachary Bastiani, Robert M. Kirby, Jacob Hochhalter +1
We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the p…
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…
Streaming Factor Trajectory Learning for Temporal Tensor Decomposition
Shikai Fang, Xin Yu, Shibo Li +3
Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and…
Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data
Shikai Fang, Xin Yu, Zheng Wang +3
Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a…
Solving High Frequency and Multi-Scale PDEs with Gaussian Processes
Shikai Fang, Madison Cooley, Da Long +3
Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). How…
Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels
Da Long, Wei W. Xing, Aditi S. Krishnapriyan +3
Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data s…