An n-dimensional hybrid system embeds into a continuous vector field in m > 2n dimensions, enabling latent Neural ODEs with consistency losses to recover hybrid flows from time series.
Learning neural event functions for ordinary differential equations
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A symbolic decision tree method is introduced to simultaneously learn interpretable regime partitions and local governing equations using basis function parametrization and mixed-integer optimization.
RigidFormer learns mesh-free rigid dynamics from point clouds using object-centric anchors, Anchor-Vertex Pooling, Anchor-based RoPE, and differentiable Kabsch alignment to enforce rigidity.
GNOVA reconstructs and forecasts CDR-SB and MMSE scores with MAEs of 1.35 and 2.28 on 1727 ADNI patients over 10 years using only routine visit data, enabling interpolation, extrapolation, and uncertainty estimates.
Autoencoders enable nonlinear dimensionality reduction for parametric ODEs, with analysis of exact representation properties and convergence of the reduced model to the original.
citing papers explorer
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Embedding Hybrid Systems into Continuous Latent Vector Fields
An n-dimensional hybrid system embeds into a continuous vector field in m > 2n dimensions, enabling latent Neural ODEs with consistency losses to recover hybrid flows from time series.
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Learning regime-dependent governing equations: A symbolic decision tree approach
A symbolic decision tree method is introduced to simultaneously learn interpretable regime partitions and local governing equations using basis function parametrization and mixed-integer optimization.
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RigidFormer: Learning Rigid Dynamics using Transformers
RigidFormer learns mesh-free rigid dynamics from point clouds using object-centric anchors, Anchor-Vertex Pooling, Anchor-based RoPE, and differentiable Kabsch alignment to enforce rigidity.
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Reconstructing and forecasting disease trajectories of patients with Alzheimer's disease using routine data in resource-constrained settings
GNOVA reconstructs and forecasts CDR-SB and MMSE scores with MAEs of 1.35 and 2.28 on 1727 ADNI patients over 10 years using only routine visit data, enabling interpolation, extrapolation, and uncertainty estimates.
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Model reduction of parametric ordinary differential equations via autoencoders: representation properties and convergence analysis
Autoencoders enable nonlinear dimensionality reduction for parametric ODEs, with analysis of exact representation properties and convergence of the reduced model to the original.