Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems
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Abstract (arXiv)
The recently introduced class of architectures known as Neural Operators has emerged as highly versatile tools applicable to a wide range of tasks in the field of Scientific Machine Learning (SciML), including data representation and forecasting. In this study, we investigate the capabilities of Neural Implicit Flow (NIF), a recently developed mesh-agnostic neural operator, for representing the latent dynamics of canonical systems such as the Kuramoto-Sivashinsky (KS), forced Korteweg-de Vries (fKdV), and Sine-Gordon (SG) equations, as well as for extracting dynamically relevant information from them. Finally we assess the applicability of NIF as a dimensionality reduction algorithm and conduct a comparative analysis with another widely recognized family of neural operators, known as Deep Operator Networks (DeepONets).
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 9 of its 20 references that are in the map. First posted on arXiv 26 Apr 2024.
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9 of 20 references.
References · 9
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
- 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 89
- 2021Improved architectures and training algorithms for deep operator networkscited by 86
- 2022Learning two-phase microstructure evolution using neural operators and autoencoder architecturescited by 72
- 2021Data-driven discovery of intrinsic dynamicscited by 45
- 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
- 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
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