On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks
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Abstract (arXiv)
Invertible neural networks (INNs) represent an important class of deep neural network architectures that have been widely used in several applications. The universal approximation properties of INNs have also been established recently. However, the approximation rate of INNs is largely missing. In this work, we provide an analysis of the capacity of a class of coupling-based INNs to approximate bi-Lipschitz continuous mappings on a compact domain, and the result shows that it can well approximate both forward and inverse maps simultaneously. Furthermore, we develop an approach for approximating bi-Lipschitz maps on infinite-dimensional spaces that simultaneously approximate the forward and inverse maps, by combining model reduction with principal component analysis and INNs for approximating the reduced map, and we analyze the overall approximation error of the approach. Preliminary numerical results show the feasibility of the approach for approximating the solution operator for parameterized second-order elliptic problems.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 41 of its 69 references that are in the map. First posted on arXiv 18 Aug 2023.
Builds on
41 of 69 references.
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29 more
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Citing papers per year: 2024: 1; 2025: 0; 2026: 1.
2 papers.