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math.OC2026
Strong error analysis for the stochastic momentum optimizer
Davide Gallon, Arnulf Jentzen
Stochastic gradient descent (SGD) optimization schemes are the methods of choice for the optimization of deep neural networks (DNNs) in artificial intelligence (AI) systems. Often…
cs.LG2026
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…
cs.LG2026
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…