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This work explores the physics-driven machine learning technique OperatorInference (OpInf) for predicting the state of chaotic dynamical systems. OpInfprovides a non-intrusive approach to infer approximations of polynomialoperators in reduced space without having access to the full order operatorsappearing in discretized models. Datasets for the physics systems are generatedusing conventional numerical solvers and then projected to a low-dimensionalspace via Principal Component Analysis (PCA). In latent space, a least-squaresproblem is set to fit a quadratic polynomial operator, which is subsequentlyemployed in a time-integration scheme in order to produce extrapolations in thesame space. Once solved, the inverse PCA operation is applied to reconstructthe extrapolations in the original space. The quality of the OpInf predictionsis assessed via the Normalized Root Mean Squared Error (NRMSE) metric fromwhich the Valid Prediction Time (VPT) is computed. Numerical experimentsconsidering the chaotic systems Lorenz 96 and the Kuramoto-Sivashinsky equationshow promising forecasting capabilities of the OpInf reduced order models withVPT ranges that outperform state-of-the-art machine learning methods such asbackpropagation and reservoir computing recurrent neural networks [1], as wellas Markov neural operators [2].

Non-Intrusive Reduced Models based on Operator Inference for Chaotic Systems