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We introduce the Koopman-inspired Fourier Neural Operator (kFNO) for predicting complex flame instabilities governed by nonlinear PDEs. Leveraging Koopman theory to lift dynamics into a high-dimensional latent space, kFNO improves short-term accuracy and long-term statistical fidelity. We validate kFNO on synthesized flame fronts from re-scaled Sivashinsky equations (modeling hybrid Darrieus–Landa
