3 papers
math.NA2026
Hard-constrained Physics-informed Neural Networks for Interface Problems
Seung Whan Chung, Stephen T. Castonguay, Sumanta Roy +3
Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challe…
cs.CE2026
DeepONet: A Discontinuity Capturing Neural Operator
Sumanta Roy, Stephen T. Castonguay, Pratanu Roy +1
We present DeepONet, a physics-informed neural operator designed to learn mappings between function spaces that may contain discontinuities or exhibit non-smooth behavior. Cla…
cs.LG2025
A Physics-informed Multi-resolution Neural Operator
Sumanta Roy, Bahador Bahmani, Ioannis G. Kevrekidis +1
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial am…