Generative modeling of time-dependent densities via optimal transport and projection pursuit

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MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation

A Thakur, S Chakraborty - arxiv preprint arxiv:2404.15731, 2024 - arxiv.org
We propose a neural operator framework, termed mixture density nonlinear manifold
decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation …
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Learning Density Evolution from Snapshot Data

R Yao, A Nitanda, X Chen, Y Yang - arxiv preprint arxiv:2502.17738, 2025 - arxiv.org
Motivated by learning dynamical structures from static snapshot data, this paper presents a
distribution-on-scalar regression approach for estimating the density evolution of a …
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Measure-Theoretic Time-Delay Embedding

J Botvinick-Greenhouse, M Oprea, R Maulik… - arxiv preprint arxiv …, 2024 - arxiv.org
The celebrated Takens' embedding theorem provides a theoretical foundation for
reconstructing the full state of a dynamical system from partial observations. However, the …
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