CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations

Understand

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications.

• We propose to accelerate PDE solvers using reduced-order modeling (ROM).
• Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a low-dimensional embedding of the continuous vector fields themselves, not their discretization.
• We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations.