Publications

Journal Preprints

  1. A. Rodgers and D. Venturi, ``Tensor approximation of functional differential equations'', ArXiv: 2403.04946, 2024, pp. 1-16 (PDF)

Journal Publications (Google Scholar)

  1. A. Dektor and D. Venturi, ``Coordinate-adaptive integration of PDEs on tensor manifolds'', Comm. Appl. Math. Comput., 2024, pp. 1-18 (PDF)
  2. A. Rodgers and D. Venturi, ``Implicit integration of nonlinear evolutions on tensor manifolds'', J. Sci. Comput., 2023, 97, pp. 1-27 (PDF)
  3. A. Dektor and D. Venturi, ``Tensor rank reduction via coordinate flows'', J. Comput. Phys., 2023, 491, pp. 112378 (PDF)
  4. D. Venturi and X. Li, ``The Mori-Zwanzig formulation of deep learning'', Research in the Mathematical Sciences, 2023, 10 (23), pp. 1-47 (PDF)
  5. A. Rodgers, A. Dektor and D. Venturi, ``Adaptive integration of nonlinear evolution equations on tensor manifolds'', J. Sci. Comput., 2022, 92 (39), pp. 1-31 (PDF)
  6. Y. Zhu and D. Venturi, ``Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations'', J. Math. Phys., 62, 2021, p. 1035051 (PDF)
  7. A. Dektor, A. Rodgers and D. Venturi, ``Rank-adaptive tensor methods for high-dimensional nonlinear PDEs'', J. Sci. Comput.,  2021, 88 (36), pp. 1-27 (PDF)
  8. D. Venturi and A. Dektor, ``Spectral methods for nonlinear functionals and functional differential equations'', Research in the Mathematical Sciences, 2021, 8 (27), pp. 1-39 (PDF)
  9. A. Dektor and D. Venturi, `` Dynamic tensor approximation of high-dimensional nonlinear PDEs'', J. Comput. Phys., 2021, 437, p. 110295 (PDF)
  10. S. Krawczuk and D. Venturi, ``Improving neural network predictions of material properties with limited data using transfer learning'', Journal of Machine Learning for Modeling and Computing, 2020, 2, p. 31-47 (PDF)
  11. A. Boelens, D. Venturi and D. Tartakovsky, ``Tensor methods for the Botzmann-BGK equation'', J. Comput. Phys. , 2020, 421, p. 109744 (PDF)
  12. P. Lambrianides, Q. Gong and D. Venturi, ``A new scalable algorithm for computational optimal control under uncertainty'', J. Comput. Phys. , 2020, 420, p. 109710 (PDF)
  13. A. Rodgers and D. Venturi, ``Stability analysis of hierarchical tensor methods for time-dependent PDEs'', J. Comput. Phys., 2020, 409, p. 109341 (PDF)
  14. Y. Zhu and D. Venturi, ``Generalized Langevin equations for systems with local interactions'', J. Stat. Phys., 2020, 178 (5), pp. 1217-1247 (PDF)
  15. A. Dektor and D. Venturi, ``Dynamically orthogonal tensor methods for high-dimensional nonlinear PDEs'', J. Comput. Phys., 2020, 404, p. 103501 (PDF)
  16. Y. Zhu, J. Dominy, and D. Venturi, ``On the estimation of the Mori-Zwanzig memory integral'', J. Math. Phys., 2018, 59, pp. 103501(1-39) (PDF)
  17. A. Boelens, D. Venturi and D. Tartakovsky, ``Parallel tensor methods for high-dimensional linear PDEs'', J. Comp. Phys., 2018, 375, pp. 519-539 (PDF)
  18. Y. Zhu and D. Venturi, ``Faber approximation of the Mori-Zwanzig equation'' J. Comp. Phys., 2018, 372, pp. 694-718. (PDF)
  19. C. Brennan and D. Venturi, ``Data-driven closures for stochastic dynamical systems'', J. Comp. Phys., 2018, 372, pp. 281-298. (PDF)
  20. D. Venturi, ``The numerical approximation of nonlinear functionals and functional differential equations'',  Physics Reports, 2018, 732, pp. 1-102. (PDF)
  21. J. Dominy and D. Venturi, ``Duality and conditional expectations in the Nakajima-Mori-Zwanzig formulation'', J. Math Phys., 2017,  58, pp. 082701(1-26). (PDF)
  22. L. Parussini, D. Venturi, P. Perdikaris and G. E. Karniadakis, ``Multi-fidelity Gaussian process regression for prediction of random fields'', J. Comput. Phys., 2017, 336, pp. 35-50. (PDF)
  23. P. Perdikaris, D. Venturi, and G. E. Karniadakis, ``Multi-fidelity information fusion algorithms for high dimensional systems and massive data-sets'', SIAM J. Sci. Comput., 2016, 38(4), B521–B538. (PDF)
  24. H. Cho, X. Yang, D. Venturi and G. E. Karniadakis, ``Numerical methods for propagating uncertainty across heterogeneous domains'', SIAM J. Sci. Comput., 2015, 37(6), A3030–A3054. (PDF)
  25. H. Cho, D. Venturi and G. E. Karniadakis, ``Numerical methods for high-dimensional probability density function equations'', J. Comput. Phys., 2016, 315, pp. 817-837. (PDF)
  26. P. Perdikaris, D. Venturi, J. Royset and G. E. Karniadakis, ``Multi-fidelity modeling via recursive co-kriging and Gaussian Markov random fields'', Proc. R. Soc. A, 2015, 471 (2179), pp. 1-22. (PDF)
  27. H. Cho, D. Venturi and G. E. Karniadakis, ``Statistical analysis and simulation of random shocks in stochastic Burgers equation'', Proc. R. Soc. A, 2014, 470 (2171), pp. 1-21. (PDF)
  28. D. Venturi and G. E. Karniadakis, ``Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems'', Proc. R. Soc. A, 2014, 470 (2166), pp. 1-20. (PDF)
  29. D. Venturi, ``Conjugate flow action functionals'', J. Math. Phys., 2013, 54, pp. 113502(1-19). (PDF)
  30. H. Cho, D. Venturi and G. E. Karniadakis, ``Karhunen-Loève expansion for multiple correlated stochastic processes'', Prob. Eng. Mech., 2013, 34, pp. 157-167. (PDF)
  31. D. Venturi, X. Wan, R. Mikulevicius, B. L. Rozovskii and G. E. Karniadakis, ``Wick-Malliavin approximation to nonlinear stochastic PDEs: Analysis and Simulation'', Proc. R. Soc. A, 2013, 469  (2158), pp. 1-20. (PDF)
  32. H. Cho, D. Venturi and G. E. Karniadakis, ``Adaptive discontinuous Galerkin method for response-excitation PDF equations'', SIAM J. Sci. Comput., 2013, 35(4), pp. B890-B911. (PDF)
  33. D. Venturi, D. M. Tartakovsky, A. M. Tartakovsky and G. E. Karniadakis, ``Exact PDF equations and closure approximations for advective-reactive transport'', J. Comput. Phys., 2013, 243, pp. 323-343. (PDF)
  34. D. Venturi and G. E. Karniadakis, ``New evolution equations for the joint response-excitation probability density function of stochastic solutions to first-order nonlinear PDEs'', J. Comput. Phys., 2012, 231, pp. 7450-7474. (PDF)
  35. D. Venturi, M. Choi and G. E. Karniadakis, ``Supercritical quasi-conduction states in stochastic Rayleigh-Bénard convection'', Int. J. Heat and Mass Transf., 2012, 55, pp. 3732-3743. (PDF)
  36. D. Venturi, T. P. Sapsis, H. Cho and G. E. Karniadakis, ``A computable evolution equation for the joint response-excitation probability density function of stochastic dynamical systems'', Proc. R. Soc. A, 2011, 468, pp. 759-783. (PDF)
  37. D. Venturi and G. E. Karniadakis, ``Differential constraints for the probability density function of stochastic solutions to the wave equation'', Int. J. for UQ, 2011, 2, pp. 131-150. (PDF)
  38. X. Yang, D. Venturi, C. Chen, C. Chryssostomidis and G. E. Karniadakis ``EOF-based constrained sensor placement and field reconstruction from noisy ocean measurements: Application to Nantucket Sound'', Journal of Geophysical Research - Oceans, 2010, 115, C12072, pp. 1-16. (PDF)
  39. D. Venturi, ``A fully symmetric nonlinear biorthogonal decomposition theory for random fields'', Physica D, 2010, 240, pp. 415-425. (PDF)
  40. D. Venturi, X. Wan and G. E. Karniadakis, ``Stochastic bifurcation analysis of Rayleigh-Bénard convection'', J. Fluid Mech., 2010, 650, pp. 391-413. (PDF)

     

  41. D. Venturi, ``Convective derivatives and Reynolds transport in curvilinear time-dependent coordinate systems'', J. Phys. A: Math. Gen., 2009, 42, 125203(1-16). (PDF)

     

  42. D. Venturi, X. Wan and G. E. Karniadakis, ``Stochastic low-dimensional modeling of a random laminar wake past a circular cylinder'', J. Fluid Mech., 2008, 606, pp. 339-367. (PDF)

  43. D. Venturi, ``On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate'', J. Fluid Mech., 2006, 559, pp. 215-254. (PDF)
  44. D. Venturi and G.E. Karniadakis, ``Gappy data and reconstruction procedures for flow past a cylinder'', J. Fluid Mech., 2004, 519, pp. 315-336. (PDF)

Book Chapters

  1. H. Cho, D. Venturi and G. E. Karniadakis, ``Numerical methods for high-dimensional kinetic equations'', 2017,  in SEMA-SIMAI Springer series book Uncertainty quantification for kinetic and hyperbolic equations (PDF),  pp. 93-125. (preprint PDF)
  2. D. Venturi, H. Cho and G. E. Karniadakis, ``Mori-Zwanzig approach to uncertainty quantification'', Springer Handbook on Uncertainty Quantification, 2016, pp.1-36. (PDF)

Research Reports  

  1. DARPA report on physics-informed data-driven computational optimal control for stochastic nonlinear systems, 2019, pp. 1-116. (PDF)
  2. AFOSR report on the Mori-Zwanzig formulation of deterministic and stochastic dynamical systems, 2020, pp. 1-88. (PDF) 

Lecture Notes and Textbooks

  1. D. Venturi, ``Lecture notes on fluid dynamics, thermodynamics and heat transfer'', pp. 1-241 (in Italian), University of Bologna, 2008. (PDF)
  2. AM 10, ``Mathematical Methods for Engineers I'', 2021 (PDF)
  3. AM 213B, ``Numerical methods for differential equations, 2022 (PDF) 
  4. AM 238, ``Fundamentals of uncertainty quantification in computational science and engineering'', 2022 (PDF) 
  5. AM 114-214, ``Nonlinear dynamical systems'', 2023 (PDF-Part_1, PDF-Part_2, PDF-Part_3)

Refereed Conference Proceedings

  1. D. Venturi, B. Pulvirenti, A. Lazari, M. Zucchini and S. Salvigni, ``Applicazione della tecnologia del vuoto a processi di deumidificazione e raffreddamento industriale'' (``An application of vacuum processes to dehydration and cooling''), Atti del XXV congresso nazionale dell'Unione Italiana di Termofluidodinamica (UIT), Trieste (Italy), June 18-20, 2007, pp. 393-398. (PDF)
  2. D. Venturi and S. Salvigni, ``Stochastic natural convection in square enclosures with horizontal isothermal walls'', Atti del XXV congresso nazionale dell'Unione Italiana di Termofluidodinamica(UIT), Trieste (Italy) June 18-20, 2007, pp. 277-282. (PDF)
  3. D. Venturi and S. Salvigni, ``The stochastic modeling of a random laminar wake past a circular cylinder'',Atti del XXV congresso nazionale dell'Unione Italiana di Termofluidodinamica (UIT), Trieste (Italy), June 18-20, 2007, pp. 599-604. (PDF)
  4. D. Venturi, B. Pulvirenti and S. Salvigni, ``Direct numerical simulation of natural convection over horizontal plates'', Atti del XXIII congresso nazionale dell'Unione Italiana di Termofluidodinamica (UIT)}, Parma (Italy), June 20-22, 2005, pp. 365-370. (PDF)
  5. B. Pulvirenti, D. Venturi, M. Lorenzini, G. L. Morini and S. Salvigni, ``Turbulent flow past two tandem cylinders: experimental and numerical study'', Atti del XXIV congresso nazionale dell'Unione Italiana di Termofluidodinamica (UIT), Napoli (Italy), June 21-23, 2006, pp. 247-252.
  6. B. Pulvirenti, D. Venturi, P. Proli and S. Salvigni, ``Ricostruzione di dati mancanti in misure PIV di un flusso intorno ad un cilindro'' (``Data reconstruction in PIV measurements of flow past cylinder''), Atti del XXII congresso nazionale dell'Unione Italiana di Termofluidodinamica (UIT), Genova (Italy), June 21-23, 2004, pp. 151-156.