Spectral Deferred Correction methods achieve at least order p after p iterations when viewed as Runge-Kutta methods, with order jumps of two possible for collocation methods using specific implicit error discretizations.
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Introduces the first explicit near-reversible integrator for neural SDEs on Lie groups by extending EES schemes with Bazavov's commutator-free lift, achieving better stability and up to 10x memory reduction on manifold benchmarks.
The authors introduce Explicit and Effectively Symmetric (EES) Runge-Kutta schemes by minimizing the antisymmetric component of B-series methods via new order conditions, yielding explicit methods with near-symmetric properties that outperform standard explicit schemes in tests.
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Spectral Deferred Corrections in the framework of Runge-Kutta methods
Spectral Deferred Correction methods achieve at least order p after p iterations when viewed as Runge-Kutta methods, with order jumps of two possible for collocation methods using specific implicit error discretizations.
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Explicit and Effectively Symmetric Schemes for Neural SDEs on Lie Groups
Introduces the first explicit near-reversible integrator for neural SDEs on Lie groups by extending EES schemes with Bazavov's commutator-free lift, achieving better stability and up to 10x memory reduction on manifold benchmarks.
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Explicit and Effectively Symmetric Runge-Kutta Methods
The authors introduce Explicit and Effectively Symmetric (EES) Runge-Kutta schemes by minimizing the antisymmetric component of B-series methods via new order conditions, yielding explicit methods with near-symmetric properties that outperform standard explicit schemes in tests.