5 papers · 1 filter
Neural Operators for Multi-Task Control and Adaptation
David Sewell, Xingjian Li, Stepan Tretiakov +2
Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely un…
Learning Generalizable Neural Operators for Inverse Problems
Adam J. Thorpe, Stepan Tretiakov, Dibakar Roy Sarkar +2
Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B${}^{-1}…
SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Sampling
Stepan Tretiakov, Xingjian Li, Krishna Kumar
Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assump…
MLPs and KANs for data-driven learning in physical problems: A performance comparison
Raghav Pant, Sikan Li, Xingjian Li +2
There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov…
Basis-to-Basis Operator Learning Using Function Encoders
Tyler Ingebrand, Adam J. Thorpe, Somdatta Goswami +2
We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We d…