37 citations · 102 across the 10 of their papers we have counts for
10 papers
Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences
Panagiota Birmpa, Eric Joseph Hall
We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including -divergences, we prove…
Mutual Information for Explainable Deep Learning of Multiscale Systems
Søren Taverniers, Eric J. Hall, Markos A. Katsoulakis +1
Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically i…
Weak error rates for option pricing under linear rough volatility
Christian Bayer, Eric Joseph Hall, Raúl Tempone
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [Ba…
GINNs: Graph-Informed Neural Networks for Multiscale Physics
Eric J. Hall, Søren Taverniers, Markos A. Katsoulakis +1
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate fo…
Causality and Bayesian network PDEs for multiscale representations of porous media
Kimoon Um, Eric Joseph Hall, Markos A. Katsoulakis +1
Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the relationship between pr…
Robust information divergences for model-form uncertainty arising from sparse data in random PDE
Eric Joseph Hall, Markos A. Katsoulakis
We develop a novel application of hybrid information divergences to analyze uncertainty in steady-state subsurface flow problems. These hybrid information divergences are non-intru…
Uncertainty quantification for generalized Langevin dynamics
Eric Joseph Hall, Markos A. Katsoulakis, Luc Rey-Bellet
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these…
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
Eric Joseph Hall, Håkon Hoel, Mattias Sandberg +2
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting,…
Higher order spatial approximations for degenerate parabolic stochastic partial differential equations
Eric Joseph Hall
We consider an implicit finite difference scheme on uniform grids in time and space for the Cauchy problem for a second order parabolic stochastic partial differential equation whe…
Accelerated spatial approximations for time discretized stochastic partial differential equations
Eric Joseph Hall
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equatio…