CROM: Continuous reduced-order modeling of PDEs using implicit neural representations

Abstract

We propose CROM (Continuous Reduced-Order Modeling), a framework for model reduction of PDEs using implicit neural representations. By leveraging coordinate-based neural networks, CROM represents the solution manifold continuously in both space and time, enabling super-resolution queries and analytical computation of spatiotemporal derivatives. This approach combines the approximation power of neural networks with the mathematical rigor of projection-based model reduction, offering significant advantages for scientific computing and real-time simulation applications.