Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations

Understand

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations.

• We consider systems described by Partial Differential Equations (PDEs) discretized with structured or unstructured grids.
• The framework integrates multi-level information to generate high fidelity time sequences of the system dynamics.
• We demonstrate the effectiveness and versatility of our framework with two case studies in incompressible, two dimensional, low Reynolds cylinder flow on an unstructured mesh and incompressible turbulent channel flow on a structured mesh, both parameterized by the Reynolds number.