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

• DOI: 10.48550/arxiv.2206.02607
• Publication Date: 2022-01-01
• Authors: Peter Yichen Chen; Jinxu Xiang; Dong Heon Cho; Chang Yue; G A Pershing; Henrique Teles Maia; Maurizio M. Chiar...; Kevin Carlberg; Eitan Grinspun
• Keywords: Manifold (fluid mechanics)

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality discretized vector fields, our continuous (CROM) approach builds a low-dimensional embedding fields themselves, not their discretization. represent this reduced manifold continuously differentiable neural which may train on any and all available numerical solutions system, even when they are obtained diverse methods or discretizations. validate an extensive range PDEs with training data from voxel grids, meshes, point clouds. Compared discretization-dependent methods, such as linear subspace proper orthogonal decomposition (POD) nonlinear neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, applicability For equal latent space dimension, exhibits 79$\times$ 49$\times$ better 39$\times$ 132$\times$ smaller footprint, than POD autoencoder respectively. Experiments demonstrate 109$\times$ 89$\times$ wall-clock speedups over unreduced models CPUs GPUs, Videos codes project page: https://crom-pde.github.io