12 papers
Iterative Refinement Diffusion for Super-Resolved Data Assimilation of Multiscale Physical Systems
Mrigank Dhingra, Ramchandran Muthukumar, Rebecca Willett +1
Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation. Classical data assimilation…
Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation
Muhammad Abid, Omer San
Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial d…
WLNO: Wavelet-Laplace Neural Operator for Solving Partial Differential Equations
Muhammad Abid, Arth Sojitra, Omer San
This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-resi…
The impact of observation density on Bayesian inversion of latent dynamics in shock-dominated flows
Bipin Tiwari, Muhammad Abid, Omer San
Inferring unknown initial states in shock-dominated compressible flows from sparse and noisy measurements is a challenging ill-posed inverse problem due to nonlinear wave interacti…
Digital Twins in Coronary Artery Disease: A Mathematical Roadmap
Alessandro Veneziani, Annalisa Quaini, Marco Tezzele +2
The combination of data and models, enhanced by AI methodologies, leads to the paradigm called Digital Twins. This concept is expected to bring unprecedented support to personalize…
Hyperfastrl: Hypernetwork-based reinforcement learning for unified control of parametric chaotic PDEs
Anil Sapkota, Omer San
Spatiotemporal chaos in fluid systems exhibits severe parametric sensitivity, rendering classical adjoint-based optimal control intractable because each operating regime requires r…