Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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k-contact geometry supplies explicit Hamiltonian descriptions for multiple dissipative PDEs including damped Klein-Gordon, Allen-Cahn, Fisher-KPP, and complex Ginzburg-Landau equations.
A new framework selects suboptimal delay embeddings via combinatorial optimization on in-sample error and combines forecasts to outperform prior methods on toy and flood datasets.
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Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows
Manifold-adapted anisotropic radial basis functions, shaped by clustering, yield a global explicit non-intrusive reduced vector field that recovers chaotic invariant measures competitively with intrusive and neural models.
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A Guide to Applications of $k$-Contact Geometry in Dissipative Field Equations
k-contact geometry supplies explicit Hamiltonian descriptions for multiple dissipative PDEs including damped Klein-Gordon, Allen-Cahn, Fisher-KPP, and complex Ginzburg-Landau equations.
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Forecasting high-dimensional dynamics exploiting suboptimal embeddings
A new framework selects suboptimal delay embeddings via combinatorial optimization on in-sample error and combines forecasts to outperform prior methods on toy and flood datasets.