Multi-fidelity surrogate modeling using long short-term memory networks

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face trade-off between accuracy and efficiency. Especially for parametrized, time dependent problems in engineering computations, it is often case acceptable computational budgets limit availability high-fidelity, accurate simulation data. Multi-fidelity surrogate modeling has emerged as an effective strategy overcome this difficulty. Its key idea leverage many low-fidelity data, less but much faster compute, improve approximations with limited high-fidelity In work, introduce a novel data-driven framework multi-fidelity time-dependent using long short-term memory (LSTM) networks, enhance output predictions both unseen parameter values forward simultaneously - task known be particularly challenging models. We demonstrate wide applicability proposed approaches variety high- data generated through fine versus coarse meshes, small large steps, or finite element full-order deep learning reduced-order Numerical results show LSTM networks not only single-fidelity regression significantly, also outperform models based feed-forward neural networks.