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We investigate the possibility of using proper orthogonal decomposition (POD) in reconstructing complete flow fields from gappy data. The incomplete fields are created from DNS snapshots of flow past… (More)

We present a new compact expansion of a random flow field into stochastic spatial modes, hence extending the proper orthogonal decomposition (POD) to noisy (noncoherent) flows. As a prototype… (More)

- Paris Perdikaris, Daniele Venturi, Johannes O. Royset, George Em Karniadakis
- Proceedings. Mathematical, physical, and…
- 2015

We propose a new framework for design under uncertainty based on stochastic computer simulations and multi-level recursive co-kriging. The proposed methodology simultaneously takes into account… (More)

- Daniele Venturi, Themistoklis P. Sapsis, Hae Jun Cho, G. E. Karniadakis
- Proceedings of the Royal Society A: Mathematical…
- 2011

By using functional integral methods, we determine a computable evolution equation for the joint response-excitation probability density function of a stochastic dynamical system driven by coloured… (More)

[1] Sensor placement at the extrema of empirical orthogonal functions (EOFs) is efficient and leads to accurate reconstruction of the ocean state from a limited number of measurements. In this paper,… (More)

- Paris Perdikaris, Daniele Venturi, George Em Karniadakis
- SIAM J. Scientific Computing
- 2016

We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the… (More)

- Daniele Venturi, Daniel M. Tartakovsky, Alexandre M. Tartakovsky, George Em Karniadakis
- J. Comput. Physics
- 2013

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive… (More)

- Daniele Venturi, G. E. Karniadakis
- Proceedings. Mathematical, physical, and…
- 2014

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging… (More)

- Daniele Venturi
- 2006

The connections between the random elements of a discrete random flow field and the uncertainty in the hierarchical set of its spatio-temporal scales, obtained by the symmetric version of the proper… (More)

Stochastic bifurcations and stability of natural convection within two-dimensional square enclosures are investigated by different stochastic modelling approaches. Deterministic stability analysis is… (More)