4 papers · 1 filter
The Complexity of Sequential Prediction in Dynamical Systems
Vinod Raman, Unique Subedi, Ambuj Tewari
We study the problem of learning to predict the next state of a dynamical system when the underlying evolution function is unknown. Unlike previous work, we place no parametric ass…
Operator Learning: A Statistical Perspective
Unique Subedi, Ambuj Tewari
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator…
On the Benefits of Active Data Collection in Operator Learning
Unique Subedi, Ambuj Tewari
We study active data collection strategies for operator learning when the target operator is linear and the input functions are drawn from a mean-zero stochastic process with conti…
Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
Unique Subedi, Ambuj Tewari
We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main e…