4 papers · 1 filter
Physics-informed diffusion models in spectral space
Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito +1
We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions o…
INEUS: Iterative Neural Solver for High-Dimensional PIDEs
Jean-Loup Dupret, Davide Gallon, Patrick Cheridito
In this paper, we introduce INEUS, a meshfree iterative neural solver for partial integro-differential equations (PIDEs). The method replaces the explicit evaluation of nonlocal ju…
SAD Neural Networks: Divergent Gradient Flows and Asymptotic Optimality via o-minimal Structures
Julian Kranz, Davide Gallon, Steffen Dereich +1
We study gradient flows for loss landscapes of fully connected feedforward neural networks with commonly used continuously differentiable activation functions such as the logistic,…
An overview of diffusion models for generative artificial intelligence
Davide Gallon, Arnulf Jentzen, Philippe von Wurstemberger
This article provides a mathematically rigorous introduction to denoising diffusion probabilistic models (DDPMs), sometimes also referred to as diffusion probabilistic models or di…