Tensor-Train Operator Inference

Abstract: In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches: full--order tensor--train operator inference, full--order quantized tensor--train operator inference, and reduced--order tensor--train operator inference. In each case, snapshot data is represented in tensor--train format--either through compression or cross interpolation--enabling the efficient handling of extremely large datasets with significantly reduced computational effort compared to standard methods. The effectiveness of each approach is demonstrated through numerical experiments related to Computational Fluid Dynamics and benchmarked against the standard reduced--order operator inference method, highlighting the advantages of the tensor--train representations in both accuracy and scalability.