Benjamin Peherstorfer   |   Courant Institute of Mathematical Sciences, New York University

Sampling strategy for empirical interpolation and gappy proper orthogonal decomposition

Implements a strategy for selecting sampling points for (discrete) empirical interpolation.

Download Matlab code on GitHub https://github.com/pehersto/odeim.

References:

[1] Peherstorfer, B., Drmac, Z. & Gugercin, S. Stability of discrete empirical interpolation and gappy proper orthogonal decomposition with randomized and deterministic sampling points.
SIAM Journal on Scientific Computing, 42:A2837-A2864, 2020.
[Abstract] [BibTeX]

Operator Inference (OpInf)

Implements a data-driven model reduction method that builds on operator inference. Code by Elizabeth Qian (MIT).

Download from Elizabeth's GitHub page https://github.com/elizqian/operator-inference.

References:

[1] Peherstorfer, B. & Willcox, K. Data-driven operator inference for nonintrusive projection-based model reduction.
Computer Methods in Applied Mechanics and Engineering, 306:196-215, 2016.
[Abstract] [BibTeX]
[2] Qian, E., Kramer, B., Marques, A.N. & Willcox, K.E. Transform & Learn: A data-driven approach to nonlinear model reduction.
In AIAA Aviation 2019 Forum, AIAA, 2019.
[BibTeX]

Multifidelity Monte Carlo

Implements the multifidelity Monte Carlo (MFMC) method for uncertainty propagation. The implementation demonstrates MFMC on a toy example with five models.

Download from GitHub https://github.com/pehersto/mfmc.

References:

[1] Peherstorfer, B., Willcox, K. & Gunzburger, M. Optimal model management for multifidelity Monte Carlo estimation.
SIAM Journal on Scientific Computing, 38(5):A3163-A3194, 2016.
[Abstract] [BibTeX]

Online adaptive discrete empirical interpolation method

The online adaptive discrete empirical interpolation method (ADEIM) constructs reduced models that are adapted online. Updates to the DEIM basis are computed from sparse samples of the full model residual. This code demonstrates ADEIM on a time-dependent problem.

Download from GitHub https://github.com/pehersto/adeim.

References:

[1] Peherstorfer, B. & Willcox, K. Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates.
SIAM Journal on Scientific Computing, 37(4):A2123-A2150, 2015.
[Abstract] [BibTeX]

SG++ sparse grid toolbox

I have contributed to the SG++ project, which is a universal toolbox for spatially adaptive sparse grid methods and the combination technique.

Download from SG++ website http://sgpp.sparsegrids.org/.

References:

[1] Peherstorfer, B., Zimmer, S., Zenger, C. & Bungartz, H.J. A Multigrid Method for Adaptive Sparse Grids.
SIAM Journal on Scientific Computing, 37(5):S51-S70, 2015.
[Abstract] [BibTeX]
[2] Pflüger, D., Peherstorfer, B. & Bungartz, H.J. Spatially adaptive sparse grids for high-dimensional data-driven problems.
Journal of Complexity, 26(5):508-522, 2010.
[Abstract] [BibTeX]