TL;DR
It is demonstrated that DMD via ensembling can recover the spectra of the linearized dynamics, corresponding to the Koopman operator, restricted to linear observables of nonlinear PDEs in the neighborhood of their equilibria with good accuracy.
Dynamic mode decomposition (DMD) is a data-driven method that computes the best linear approximation of the underlying dynamical system and decomposes the dynamics into a superposition of characteristic spatiotemporal patterns. Originally introduced by the fluid dynamics community, DMD and its extensions have found wid...
The Dynamic Mode Decomposition (DMD) has been consolidated as a basic tool for data-driven analysis of dynamical systems, allowing simultaneous identification of coherent structures and their dynamics from time-resolved measurements. However, with a linear regression at its core, DMD is unable to produce accurate model...
Correlation-Basis enhanced DMD is introduced, a data-driven method whose goal is to learn an effective autonomous linear operator for periodic nonlinear dynamics, used to absorb nonlinear components that cannot be represented by the learned linear operator.
This work proposes the local gradient neural operator (LGNO) as a lightweight and interpretable alternative for field temporal evolution prediction and source identification in typical mechanical problems and exhibits wide applicability to mechanical problems including diffusion, flow, and quantum phenomena.
Variational modeling is highlighted as a complementary approach to robust long-horizon neural PDE dynamics by introducing latent Markov dynamics, which combines spatially resolved latent fields, structured Gaussian perturbations, and a neural-operator transition.
Across five well-established PDE benchmarks spanning steady-state prediction and time-dependent dynamics, Transolver$ achieves state-of-the-art with a benchmark-averaged relative error reduction of 33.4% over the strongest baseline for each metric, while consistently improving autoregressive rollout over single-operato...
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