CONFIDE: Contextual Finite Differences Modelling of PDEs
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Abstract (arXiv)
We introduce a method for inferring an explicit PDE from a data sample generated by previously unseen dynamics, based on a learned context. The training phase integrates knowledge of the form of the equation with a differential scheme, while the inference phase yields a PDE that fits the data sample and enables both signal prediction and data explanation. We include results of extensive experimentation, comparing our method to SOTA approaches, together with ablation studies that examine different flavors of our solution.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 21 of its 50 references that are in the map. First posted on arXiv 28 Mar 2023.
Builds on
21 of 50 references.
References · 21
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- 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 73
9 more
- 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 58
- 2022Generalizing to New Physical Systems via Context-Informed Dynamics Modelcited by 50
- 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
- 2022Learning differentiable solvers for systems with hard constraintscited by 34
- 2020Generative ODE Modeling with Known Unknownscited by 24
- 2021Multiple shooting for training neural differential equations on time seriescited by 17
- 2022Latent Neural ODEs with Sparse Bayesian Multiple Shootingcited by 17
- 2022Learning-informed parameter identification in nonlinear time-dependent PDEscited by 7
- 2020Optimization with learning-informed differential equation constraints and its applicationscited by 4
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Citing papers per year: 2026: 2.
2 papers.