Parsimonious representation of nonlinear dynamical systems through manifold learning: a chemotaxis case study

DOI10.1016/j.acha.2015.06.008zbMath1390.68523arXiv1505.06118OpenAlexW2962824627MaRDI QIDQ1742825

Ronen Talmon, Carmeline J. Dsilva, Ronald R. Coifman, Ioannis G. Kevrekidis

Publication date: 12 April 2018

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.06118

zbMATH Keywords

chemotaxisdiffusion mapsrepeated eigendirections

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Factor analysis and principal components; correspondence analysis (62H25) Learning and adaptive systems in artificial intelligence (68T05) Biochemistry, molecular biology (92C40)

Related Items (16)

Numerical bifurcation analysis of PDEs from lattice Boltzmann model simulations: a parsimonious machine learning approach ⋮ Data-Driven Reduction for a Class of Multiscale Fast-Slow Stochastic Dynamical Systems ⋮ Spectral Discovery of Jointly Smooth Features for Multimodal Data ⋮ Grassmannian diffusion maps based surrogate modeling via geometric harmonics ⋮ A geometric heat-flow theory of Lagrangian coherent structures ⋮ Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data ⋮ Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data ⋮ Manifold learning for accelerating coarse-grained optimization ⋮ Double diffusion maps and their latent harmonics for scientific computations in latent space ⋮ Data-driven control of agent-based models: an equation/variable-free machine learning approach ⋮ Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian ⋮ Manifold learning for organizing unstructured sets of process observations ⋮ Unnamed Item ⋮ Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling ⋮ Kernel-based parameter estimation of dynamical systems with unknown observation functions ⋮ Deep learning models for global coordinate transformations that linearise PDEs

Uses Software

• EMD
• ScatNet

Cites Work

• Hölder-Lipschitz norms and their duals on spaces with semigroups, with applications to earth mover's distance
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• Group Invariant Scattering
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• Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors
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• Manifold Learning for Latent Variable Inference in Dynamical Systems
• Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Graph Laplacian Tomography From Unknown Random Projections
• Image Completion by Diffusion Maps and Spectral Relaxation
• All of Nonparametric Statistics

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