Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Learning vector fields of differential equations on manifolds with geometrically constrained operator-valued kernels
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Learns vector fields of ODEs on smooth manifolds using a geometrically constrained operator-valued kernel that represents tangent-bundle vector fields.
Problem
Learning ordinary differential equations on manifolds; existing neural network methods are computationally expensive.
Approach
A geometrically constrained operator-valued kernel that imposes the manifold's geometry so vector fields on tangent bundles are represented directly, offering a lighter alternative to neural ODE approaches.
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