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Variational Autoencoding Neural Operators
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Variational Autoencoding Neural Operators
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Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.
Forward citations
Cited by 5 Pith papers
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NOFE - Neural Operator Function Embedding
NOFE learns continuous function-to-function embeddings via graph kernel operators, outperforming PCA, t-SNE, and UMAP in local structure preservation on function-valued datasets like ERA5 while remaining robust to sam...
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SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
SPAMoE reduces average MAE by 44.4% on OpenFWI datasets for full-waveform inversion via a spectral-preserving DINO encoder and dynamic frequency-band routing to specialized neural operators.
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SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion
SPAMoE reduces average MAE by 44.4% on ten OpenFWI sub-datasets via a spectral-preserving DINO encoder plus frequency-routed MoE of FNO, MNO and LNO experts.
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NOFE - Neural Operator Function Embedding
NOFE is a neural operator method for continuous dimensionality reduction using Graph Kernel Operators that outperforms PCA, t-SNE and UMAP on local structure preservation and sampling independence in datasets includin...
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Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling
DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.
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