Learning Physics-Based Reduced-Order Models from Data Using Quadratic Manifolds

Explore a novel approach for learning data-driven quadratic manifolds and their application in deriving efficient physics-based reduced-order models in this 55-minute talk from the Alan Turing Institute. Delve into the challenges of computer simulations for complex physical and chemical processes, and discover how reduced-order models can make computationally demanding applications more tractable. Examine the limitations of traditional model reduction techniques and learn about a new method that combines quadratic manifold approximation with the operator inference method. Understand the key components of this approach, including the polynomial mapping between high-dimensional states and low-dimensional embeddings, and how it incorporates both linear subspace representation and a quadratic component. Gain insights into the scalability and non-intrusive nature of this technique, and see its practical application in transport-dominated systems of partial differential equations, demonstrating the significant efficiency gains over linear subspace approximations.