New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs. - Daniele Venturi 002; George E. Karniadakis (J. Comput. Phys., 2012)

Exact PDF equations and closure approximations for advective-reactive transport. - Daniele Venturi 002; Daniel M. Tartakovsky; Alexandre M. Tartakovsky; George E. Karniadakis (J. Comput. Phys., 2013)

Adaptive Discontinuous Galerkin Method for Response-Excitation PDF Equations. - Heyrim Cho; Daniele Venturi 002; George E. Karniadakis (SIAM J. Sci. Comput., 2013)

Algorithms for Propagating Uncertainty Across Heterogeneous Domains. - Heyrim Cho; Xiu Yang; Daniele Venturi 002; George E. Karniadakis (SIAM J. Sci. Comput., 2015)

Numerical methods for high-dimensional probability density function equations. - Heyrim Cho; Daniele Venturi 002; George E. Karniadakis (J. Comput. Phys., 2016)

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets. - Paris Perdikaris; Daniele Venturi 002; George E. Karniadakis (SIAM J. Sci. Comput., 2016)

Multi-fidelity Gaussian process regression for prediction of random fields. - Lucia Parussini; Daniele Venturi 002; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2017)

Parallel tensor methods for high-dimensional linear PDEs. - Arnout M. P. Boelens; Daniele Venturi 002; Daniel M. Tartakovsky (J. Comput. Phys., 2018)

Data-driven closures for stochastic dynamical systems. - Catherine Brennan; Daniele Venturi 002 (J. Comput. Phys., 2018)

Faber approximation of the Mori-Zwanzig equation. - Yuanran Zhu; Daniele Venturi 002 (J. Comput. Phys., 2018)

Generalized Langevin equations for systems with local interactions. - Yuanran Zhu; Daniele Venturi 002 (CoRR, 2019)

Spectral methods for nonlinear functionals and functional differential equations. - Daniele Venturi 002; Alec Dektor (CoRR, 2020)

Improving neural network predictions of material properties with limited data using transfer learning. - Schuyler Krawczuk; Daniele Venturi 002 (CoRR, 2020)

Step-truncation integrators for evolution equations on low-rank tensor manifolds. - Abram Rodgers; Daniele Venturi 002 (CoRR, 2020)

Tensor methods for the Boltzmann-BGK equation. - Arnout M. P. Boelens; Daniele Venturi 002; Daniel M. Tartakovsky (J. Comput. Phys., 2020)

Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs. - Alec Dektor; Daniele Venturi 002 (J. Comput. Phys., 2020)

A new scalable algorithm for computational optimal control under uncertainty. - Panos Lambrianides; Qi Gong; Daniele Venturi 002 (J. Comput. Phys., 2020)

Stability analysis of hierarchical tensor methods for time-dependent PDEs. - Abram Rodgers; Daniele Venturi 002 (J. Comput. Phys., 2020)

Dynamic tensor approximation of high-dimensional nonlinear PDEs. - Alec Dektor; Daniele Venturi 002 (J. Comput. Phys., 2021)

Rank-Adaptive Tensor Methods for High-Dimensional Nonlinear PDEs. - Alec Dektor; Abram Rodgers; Daniele Venturi 002 (J. Sci. Comput., 2021)

Implicit step-truncation integration of nonlinear PDEs on low-rank tensor manifolds. - Abram Rodgers; Daniele Venturi 002 (CoRR, 2022)

The Mori-Zwanzig formulation of deep learning. - Daniele Venturi 002; Xiantao Li (CoRR, 2022)

Adaptive Integration of Nonlinear Evolution Equations on Tensor Manifolds. - Abram Rodgers; Alec Dektor; Daniele Venturi 002 (J. Sci. Comput., 2022)

Coordinate-adaptive integration of PDEs on tensor manifolds. - Alec Dektor; Daniele Venturi 002 (CoRR, 2023)

Tensor rank reduction via coordinate flows. - Alec Dektor; Daniele Venturi 002 (J. Comput. Phys., 2023)

Implicit Integration of Nonlinear Evolution Equations on Tensor Manifolds. - Abram Rodgers; Daniele Venturi 002 (J. Sci. Comput., 2023)

Tensor approximation of functional differential equations. - Abram Rodgers; Daniele Venturi 002 (CoRR, 2024)

Malliavin-Bismut Score-based Diffusion Models. - Ehsan Mirafzali; Utkarsh Gupta; Patrick Wyrod; Frank Proske; Daniele Venturi 002; Razvan Marinescu (CoRR, 2025)

Uncertainty propagation in feed-forward neural network models. - Jeremy Diamzon; Daniele Venturi 002 (CoRR, 2025)

A Malliavin calculus approach to score functions in diffusion generative models. - Ehsan Mirafzali; Frank Proske; Utkarsh Gupta; Daniele Venturi 002; Razvan Marinescu (CoRR, 2025)