4 papers
BumpNet: A Sparse MLP Framework for Learning PDE Solutions
Shao-Ting Chiu, Ioannis G. Kevrekidis, Ulisses Braga-Neto
We introduce BumpNet, a sparse multilayer perceptron (MLP) framework for PDE numerical solution and operator learning. BumpNet is based on basis function expansion, which makes the…
Free-RBF-KAN: Kolmogorov-Arnold Networks with Adaptive Radial Basis Functions for Efficient Function Learning
Shao-Ting Chiu, Siu Wun Cheung, Ulisses Braga-Neto +2
Kolmogorov-Arnold Networks (KANs) offer a promising framework for approximating complex nonlinear functions, yet the original B-spline formulation suffers from significant computat…
In-Context Multi-Operator Learning with DeepOSets
Shao-Ting Chiu, Aditya Nambiar, Ali Syed +2
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linea…
DeepOSets: Non-Autoregressive In-Context Learning with Permutation-Invariance Inductive Bias
Shao-Ting Chiu, Junyuan Hong, Ulisses Braga-Neto
In-context learning (ICL) is the remarkable ability displayed by some machine learning models to learn from examples provided in a user prompt without any model parameter updates.…