Neural Implicit Flow: A Mesh-Agnostic Dimensionality Reduction Paradigm for Spatio-Temporal Data
Shaowu Pan, Steven L. Brunton, J. Nathan Kutz; 24(41):1−60, 2023.
Abstract
High-dimensional spatio-temporal dynamics often have a low-dimensional subspace representation. In engineering applications, dimensionality reduction is crucial for making solutions computationally feasible in real time. Existing paradigms, such as the singular value decomposition (SVD) and convolutional autoencoders (CAE), are limited in efficiently representing the complexity associated with spatio-temporal data, which may involve variable geometry, non-uniform grid resolution, adaptive meshing, and parametric dependencies. To address these challenges, we propose Neural Implicit Flow (NIF), a mesh-agnostic framework that enables a low-rank representation of large-scale, parametric, spatio-temporal data. NIF consists of two modified multilayer perceptrons (MLPs): ShapeNet, which isolates and represents spatial complexity, and ParameterNet, which handles other input complexities like parametric dependencies, time, and sensor measurements. We demonstrate the usefulness of NIF in parametric surrogate modeling, providing an interpretable representation and compression of complex spatio-temporal dynamics, efficient many-spatial-query tasks, and improved generalization performance for sparse reconstruction.
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