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The long runtime of high-fidelity partial differential equation (PDE) solversmakes them unsuitable for time-critical applications. We propose to acceleratePDE solvers using reduced-order modeling (ROM). Whereas prior ROM approachesreduce the dimensionality of discretized vector fields, our continuousreduced-order modeling (CROM) approach builds a low-dimensional embedding ofthe continuous vector fields themselves, not their discretization. We representthis reduced manifold using continuously differentiable neural fields, whichmay train on any and all available numerical solutions of the continuoussystem, even when they are obtained using diverse methods or discretizations.We validate our approach on an extensive range of PDEs with training data fromvoxel grids, meshes, and point clouds. Compared to priordiscretization-dependent ROM methods, such as linear subspace proper orthogonaldecomposition (POD) and nonlinear manifold neural-network-based autoencoders,CROM features higher accuracy, lower memory consumption, dynamically adaptiveresolutions, and applicability to any discretization. For equal latent spacedimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencodermethods, respectively. Experiments demonstrate 109$\times$ and 89$\times$wall-clock speedups over unreduced models on CPUs and GPUs, respectively.Videos and codes are available on the project page: https://crom-pde.github.io

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