28 citations · 34 across the 9 of their papers we have counts for
9 papers
Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography
Boyuan Deng, Kshitiz Upadhyay, Michael Shields
The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber complex. Inferring such fields from s…
Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
Cornelius Otchere, Michael Shields
Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundar…
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. Clas…
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…
Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators
Ponkrshnan Thiagarajan, Tamer A. Zaki, Michael D. Shields
Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demandi…
Neural Chaos: A Spectral Stochastic Neural Operator
Bahador Bahmani, Ioannis G. Kevrekidis, Michael D. Shields
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties,…
Neural Operators for Stochastic Modeling of Nonlinear Structural System Response to Natural Hazards
Somdatta Goswami, Dimitris G. Giovanis, Bowei Li +2
Traditionally, neural networks have been employed to learn the mapping between finite-dimensional Euclidean spaces. However, recent research has opened up new horizons, focusing on…
Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving
Varun Kumar, Somdatta Goswami, Katiana Kontolati +2
Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-ta…
A Resolution Independent Neural Operator
Bahador Bahmani, Somdatta Goswami, Ioannis G. Kevrekidis +1
The Deep Operator Network (DeepONet) is a powerful neural operator architecture that uses two neural networks to map between infinite-dimensional function spaces. This architecture…