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21 papers · 1 filter
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
Sifan Wang, Hanwen Wang, Paris Perdikaris
Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cas…
An overview on deep learning-based approximation methods for partial differential equations
Christian Beck, Martin Hutzenthaler, Arnulf Jentzen +1
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-b…
Relationship between changing malaria burden and low birth weight in sub-Saharan Africa: a difference-in-differences study via a pair-of-pairs approach
Siyu Heng, Wendy P. O'Meara, Ryan A. Simmons +1
Although interventional studies demonstrate that preventing malaria during pregnancy can reduce the low birth weight (i.e., child's birth weight 2,500 grams) rate, it remains u…
Multi-modal excitation to model the Quasi-Biennial Oscillation
Pierre Léard, Daniel Lecoanet, Michael Le Bars
The Quasi-Biennial Oscillation (QBO) of stratospheric winds is the most striking example of mean-flow generation and reversal by the non-linear interactions of internal waves. Prev…
Local SGD: Unified Theory and New Efficient Methods
Eduard Gorbunov, Filip Hanzely, Peter Richtárik
We present a unified framework for analyzing local SGD methods in the convex and strongly convex regimes for distributed/federated training of supervised machine learning models. W…
Weighted analyticity of Hartree-Fock eigenfunctions
Yvon Maday, Carlo Marcati
We prove analytic-type estimates in weighted Sobolev spaces on the eigenfunctions of a class of elliptic and nonlinear eigenvalue problems with singular potentials, which includes…