no code implementations • 20 Mar 2023 • Joseph Hart, Mamikon Gulian, Indu Manickam, Laura Swiler
In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable.
no code implementations • 22 Apr 2022 • Ravi G. Patel, Indu Manickam, Myoungkyu Lee, Mamikon Gulian
We propose error-in-variables (EiV) models for two operator regression methods, MOR-Physics and DeepONet, and demonstrate that these new models reduce bias in the presence of noisy independent variables for a variety of operator learning problems.
no code implementations • 7 Jul 2021 • Nat Trask, Mamikon Gulian, Andy Huang, Kookjin Lee
We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based minimization of a maximum likelihood loss.
no code implementations • 22 Dec 2020 • Mamikon Gulian, Ari Frankel, Laura Swiler
The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary conditions, but for which only scattered observations of the source term are available.
no code implementations • 16 Jun 2020 • Laura Swiler, Mamikon Gulian, Ari Frankel, Cosmin Safta, John Jakeman
Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources.
no code implementations • 17 May 2020 • Huaiqian You, Yue Yu, Nathaniel Trask, Mamikon Gulian, Marta D'Elia
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori.
no code implementations • 2 Aug 2018 • Mamikon Gulian, Maziar Raissi, Paris Perdikaris, George Karniadakis
We extend this framework to linear space-fractional differential equations.