2 citations · 2 across the 12 of their papers we have counts for
10 papers · 1 filter
Two-Scale Localized PCA-Net: Coarse-Global and Local-Residual Representations for Artifact-Reduced PDE Operator Learning
Mrigank Dhingra, Jordan Stout, Omer San
Localized dimensionality reduction improves the scalability of operator learning for high-dimensional partial differential equations (PDEs), but independently decoded local patches…
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…
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…
SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolution
Muhammad Abid, Omer San
Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machi…
Stabilizing autoregressive forecasts in chaotic systems via multi-rate latent recurrence
Mrigank Dhingra, Omer San
Long-horizon autoregressive forecasting of chaotic dynamical systems remains challenging due to rapid error amplification and distribution shift: small one-step inaccuracies compou…
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…
Method of Manufactured Learning for Solver-free Training of Neural Operators
Arth Sojitra, Omer San
Training neural operators to approximate mappings between infinite-dimensional function spaces often requires extensive datasets generated by either demanding experimental setups o…
Localized PCA-Net Neural Operators for Scalable Solution Reconstruction of Elliptic PDEs
Mrigank Dhingra, Romit Maulik, Adil Rasheed +1
Neural operator learning has emerged as a powerful approach for solving partial differential equations (PDEs) in a data-driven manner. However, applying principal component analysi…
FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
Arth Sojitra, Mrigank Dhingra, Omer San
Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to par…