# Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning

@inproceedings{Goyal2021LearningLQ, title={Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning}, author={Pawan Goyal and Peter Benner}, year={2021} }

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or first principles are onerous or infeasible. Moreover, these models are high-dimensional but spatially correlated. It is, however, observed that the dynamics of high-fidelity models often evolve in low-dimensional manifolds. Furthermore, it is also known that…

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Operator inference for non-intrusive model reduction with nonlinear manifolds

- Mathematics, Computer ScienceArXiv
- 2022

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing the quadRatic manifold to derive eﬃcient physics-based reduced-order models, using a polynomial mapping between high- dimensional states and a low-dimensional embedding.

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