6 papers
A transition-density-based operator learning method for Fokker-Planck equations with various initial conditions
Li Zeng, Xiaoliang Wan, Yaobin Wang +2
Solving Fokker-Planck equations (FPEs) for multiple initial conditions typically requires repeated computations, leading to substantial computational costs. In this work, we propos…
Neural Galerkin Normalizing Flows for Bayesian Inference of Diffusions with Inaccessible Boundaries
Riccardo Saporiti, Fabio Nobile
One of the primary challenges in Bayesian inference on the parameters of a diffusion model from discrete observations is the unavailability of an analytical expression for the tran…
Optimized multilevel Monte Carlo methods in Banach spaces
Kristin Kirchner, Fabio Nobile, Christoph Schwab +1
We present a theoretical and numerical analysis of Monte Carlo methods for the estimation of statistical moments of random variables taking values in a Banach sp…
Neural Galerkin Normalizing Flow for Transition Probability Density Functions of Diffusion Models
Riccardo Saporiti, Fabio Nobile
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Pl…
LAGO: A Local-Global Optimization Framework Combining Trust Region Methods and Bayesian Optimization
Eliott Van Dieren, Tommaso Vanzan, Fabio Nobile
We introduce LAGO, a LocAl-Global Optimization framework coupling Bayesian Optimization (BO) and gradient-based trust region local refinement through an adaptive competition mechan…
Function integration, reconstruction and approximation using rank-1 lattices
Frances Y. Kuo, Giovanni Migliorati, Fabio Nobile +1
We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fo…