10 citations · 18 across the 9 of their papers we have counts for
9 papers
Shock solutions for the one-dimensional information geometric regularization of compressible flow
William Barham, Brian K. Tran, Ben S. Southworth +1
The information geometric regularization (IGR) is an inviscid regularization of the compressible Euler equations that alters the geometry of Lagrangian characteristics to prevent t…
Hamiltonian Information Geometric Regularization of the Compressible Euler Equations
William Barham, Brian K. Tran, Ben S. Southworth +1
The recently proposed information geometric regularization (IGR) was the first inviscid regularization of the multi-dimensional compressible Euler equations, which enabled the simu…
Information geometric regularization of unidimensional pressureless Euler equations yields global strong solutions
Ruijia Cao, Florian Schäfer
Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower,…
Asymptotic properties of Vecchia approximation for Gaussian processes
Myeongjong Kang, Florian Schäfer, Joseph Guinness +1
Vecchia approximation has been widely used to accurately scale Gaussian-process (GP) inference to large datasets, by expressing the joint density as a product of conditional densit…
InRank: Incremental Low-Rank Learning
Jiawei Zhao, Yifei Zhang, Beidi Chen +2
The theory of greedy low-rank learning (GLRL) aims to explain the impressive generalization capabilities of deep learning. It proves that stochastic gradient-based training implici…
Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes
Yifan Chen, Houman Owhadi, Florian Schäfer
In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, G…
Competitive Physics Informed Networks
Qi Zeng, Yash Kothari, Spencer H. Bryngelson +1
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural netwo…
Polymatrix Competitive Gradient Descent
Jeffrey Ma, Alistair Letcher, Florian Schäfer +2
Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which…
Competitive Mirror Descent
Florian Schäfer, Anima Anandkumar, Houman Owhadi
Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that…