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108 papers · 1 filter
On the derivation of the homogeneous kinetic wave equation
Charles Collot, Pierre Germain
The nonlinear Schrödinger equation in the weakly nonlinear regime with random Gaussian fields as initial data is considered. The problem is set on the torus in any dimension greate…
Simulating sticky particles: A Monte Carlo method to sample a stratification
Miranda Holmes-Cerfon
Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bond…
Optimal experimental design under irreducible uncertainty for linear inverse problems governed by PDEs
Karina Koval, Alen Alexanderian, Georg Stadler
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here,…
Explicit computation of symmetric differentials and its application to quasi-hyperbolicity
Nils Bruin, Jordan Thomas, Anthony Várilly-Alvarado
We develop explicit techniques to investigate algebraic quasi-hyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods…
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
Elizabeth Qian, Boris Kramer, Benjamin Peherstorfer +1
We present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system's governing equa…
Iterative Construction of Gaussian Process Surrogate Models for Bayesian Inference
Leen Alawieh, Jonathan Goodman, John B. Bell
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems…