RNC-LM extends geodesic-accelerated Levenberg-Marquardt to arbitrary-order Riemann normal coordinate corrections, reusing the LM matrix factorization for all orders and achieving large speedups on PINN and potential-fitting benchmarks.
A note on Riemann normal coordinates
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abstract
The goal of this note is to provide a recursive algorithm that allows one to calculate the expansion of the metric tensor up to the desired order in Riemann normal coordinates. We test our expressions up to fourth order and predict results up to sixth order. For an arbitrary number of symmetric partial derivatives acting on the components of the metric tensor subtle treatment is required since the degree of complication increases rapidly.
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cs.LG 1years
2026 1verdicts
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Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates
RNC-LM extends geodesic-accelerated Levenberg-Marquardt to arbitrary-order Riemann normal coordinate corrections, reusing the LM matrix factorization for all orders and achieving large speedups on PINN and potential-fitting benchmarks.