1 citations · 1 across the 6 of their papers we have counts for
4 papers · 1 filter
Operator Learning at Machine Precision
Aras Bacho, Aleksei G. Sorokin, Xianjin Yang +6
Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing th…
A joint optimization approach to identifying sparse dynamics using least squares kernel collocation
Alexander W. Hsu, Ike Griss Salas, Jacob M. Stevens-Haas +3
We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed…
Understanding In-Context Learning on Structured Manifolds: Bridging Attention to Kernel Methods
Zhaiming Shen, Alexander Hsu, Rongjie Lai +1
While in-context learning (ICL) has achieved remarkable success in natural language and vision domains, its theoretical understanding-particularly in the context of structured geom…
Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis
Yasamin Jalalian, Juan Felipe Osorio Ramirez, Alexander Hsu +2
We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and am…