6 papers · 1 filter
Is Zero-Shot Super-Resolution Possible in Operator Learning?
Unique Subedi, Ambuj Tewari
Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grid…
Operator Learning for Schrödinger Equation: Unitarity, Error Bounds, and Time Generalization
Yash Patel, Unique Subedi, Ambuj Tewari
We consider the problem of learning the evolution operator for the time-dependent Schrödinger equation, where the Hamiltonian may vary with time. Existing neural network-based sur…
Learning to Choose or Choosing to Learn: Best-of-N vs. Supervised Fine-Tuning for Bit String Generation
Seamus Somerstep, Vinod Raman, Unique Subedi +1
Using the bit string generation problem as a case study, we theoretically compare two standard methods for adapting large language models to new tasks. The first, referred to as su…
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…