Optimal prediction and the Mori-Zwanzig representation of irreversible processes.

By Alexandre J. Chorin, Ole H. Hald, Raz Kupferman. Proceedings of the National Academy of Sciences of the United States of America, 2000

343 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f599b55c2dd05f588dfd4efaaa46aa4370b21645

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. G. Em Karniadakis
2. Paris Perdikaris
3. Maizar Raissi
4. Igor Mezi'c
5. Yibo Yang
6. Liu Yang
7. Ioannis G. Kevrekidis
8. Dongkun Zhang

In Statistical and Nonlinear Physics

1. G. Em Karniadakis
2. Maizar Raissi
3. Paris Perdikaris
4. Steven L. Brunton
5. Igor Mezi'c
6. Ioannis G. Kevrekidis
7. Michael Ghil
8. J. Nathan Kutz

Citations in the corpus

• Inferring solutions of differential equations using noisy multi-fidelity data (2016, background): “Some specific non-linear equations can be transformed into systems of linear equations – albeit in high-dimensions [21, 22, 23] – that can be solved with extensions of the current framework. variance of u , while the smaller top right panel shows the corresponding error against the exact solution.”
• Machine learning of linear differential equations using Gaussian processes (2017, background): “However, some specific non-linear operators can be addressed with extensions of the current framework by transforming such equations into systems of linear equations [53,9] – albeit in high dimensions.”
• Data-driven non-Markovian closure models (2014, background): “the conditional expectation of ηt remains zero as t evolves, so that ηt is uncorrelated with any function of v [43, 121].”
• Mathematical and physical ideas for climate science (2013, methodology): “There are the short and long memory approximations made in the method of optimal prediction (Bernstein, 2007; Chorin and Stinis, 2006; Chorin and Hald , 2013; Chorin et al., 1998, 2000, 2002, 2006; Defrasne, 2004; Hald and Kupferman, 2001; Park et al., 2007).”
• Equation-free: The computer-aided analysis of complex multiscale systems (2004, methodology): “…quasi-continuum methods of Phillips and coworkers (Phillips, 2001; Ortiz and Phillips (1999)); optimal prediction methods of Chorin and coworkers (Chorin et al., 1998, 2000); coupling of continuum fields with stochastic evolution by Oettinger and coworkers (Oettinger, 1996; Laso and Oettinger,…”
• Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging (2009, methodology): “Another idea is to treat fast variables by conditioning; here, we refer the reader to optimal prediction [28, 27, 29] that has also been used for model reduction.”
• Non-equilibrium glass transitions in driven and active matter (2013, neutral): “Since our study was performed within a particular theoretical framework, it would be interesting to check the robustness of our findings beyond the realm of schematic glassy models, for instance using nonequilibrium mode-coupling types of approximations [37, 38].”
• Spectral Properties of Dynamical Systems, Model Reduction and Decompositions (2005, methodology): “There has been a substantial interest recently in improving the projection methods for obtaining low-dimensional models of formally infinite-dimensional systems by introducing stochastic terms to account for neglected modes [13, 7, 28, 21, 4, 15, 8] .”
• Optimal prediction with memory (2002, methodology): “The discrepancy between the two curves is due to the omission of the memory, see [7,6].”