Wikipedia Easy Search

Machine learning and data mining
Part of a series on
Paradigms Supervised learning Unsupervised learning Semi-supervised learning Self-supervised learning Reinforcement learning Meta-learning Online learning Batch learning Curriculum learning Rule-based learning Neuro-symbolic AI Neuromorphic engineering Quantum machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association rules Semantic analysis Structured prediction Feature engineering Feature learning Learning to rank Grammar induction Ontology learning Multimodal learning
Supervised learning (classification • regression) Apprenticeship learning Decision trees Ensembles Bagging Boosting Random forest k-NN Linear regression Naive Bayes Artificial neural networks Logistic regression Perceptron Relevance vector machine (RVM) Support vector machine (SVM)
Clustering BIRCH CURE Hierarchical k-means Fuzzy Expectation–maximization (EM) DBSCAN OPTICS Mean shift
Dimensionality reduction Factor analysis CCA ICA LDA NMF PCA PGD t-SNE SDL
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov
Anomaly detection RANSAC k-NN Local outlier factor Isolation forest
Artificial neural network Autoencoder Deep learning Feedforward neural network Recurrent neural network LSTM GRU ESN reservoir computing Boltzmann machine Restricted GAN Diffusion model SOM Convolutional neural network U-Net LeNet AlexNet DeepDream Neural radiance field Transformer Vision Mamba Spiking neural network Memtransistor Electrochemical RAM (ECRAM)
Reinforcement learning Q-learning SARSA Temporal difference (TD) Multi-agent Self-play
Learning with humans Active learning Crowdsourcing Human-in-the-loop RLHF
Model diagnostics Coefficient of determination Confusion matrix Learning curve ROC curve
Mathematical foundations Kernel machines Bias–variance tradeoff Computational learning theory Empirical risk minimization Occam learning PAC learning Statistical learning VC theory
Journals and conferences ECML PKDD NeurIPS ICML ICLR IJCAI ML JMLR
Related articles Glossary of artificial intelligence List of datasets for machine-learning research List of datasets in computer vision and image processing Outline of machine learning
v t e

The proper orthogonal decomposition is a numerical method that enables a reduction in the complexity of computer intensive simulations such as computational fluid dynamics and structural analysis (like crash simulations). Typically in fluid dynamics and turbulences analysis, it is used to replace the Navier–Stokes equations by simpler models to solve.^[1]

It belongs to a class of algorithms called model order reduction (or in short model reduction). What it essentially does is to train a model based on simulation data. To this extent, it can be associated with the field of machine learning.

^ Berkooz, G; Holmes, P; Lumley, J L (January 1993). "The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows". Annual Review of Fluid Mechanics. 25 (1): 539–575. Bibcode:1993AnRFM..25..539B. doi:10.1146/annurev.fl.25.010193.002543. ISSN 0066-4189.

Proper orthogonal decomposition