Model order reduction

March 23, 2015 — April 21, 2023

feature construction
functional analysis
linear algebra
machine learning
networks
neural nets
PDEs
physics
probability
sparser than thou
statistics
statmech
surrogate
topology
Figure 1

The traditional means of emulating a complicated model is to find an approximation to it in the sense of using some kind of dominant subspace to summarise the behaviour of the model.

A highly-developed, powerful field with dense jargon.

1 References

Amsallem, Zahr, and Farhat. 2012. “Nonlinear Model Order Reduction Based on Local Reduced-Order Bases.” International Journal for Numerical Methods in Engineering.
Ghattas, and Willcox. 2021. “Learning Physics-Based Models from Data: Perspectives from Inverse Problems and Model Reduction.” Acta Numerica.
Gladish, Pagendam, Peeters, et al. 2018. “Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models.” Journal of Agricultural, Biological and Environmental Statistics.
Peherstorfer, and Willcox. 2015. “Dynamic Data-Driven Reduced-Order Models.” Computer Methods in Applied Mechanics and Engineering.
Pestourie, Mroueh, Rackauckas, et al. 2022. “Physics-Enhanced Deep Surrogates for PDEs.”
Siade, Cui, Karelse, et al. 2020. “Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory.” Water Resources Research.
Zahr, and Farhat. 2015. “Progressive Construction of a Parametric Reduced-Order Model for PDE-Constrained Optimization.” International Journal for Numerical Methods in Engineering.