Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this gap and develop probabilistic ODE solvers that are both stable and scalable. We propose two complementary strategies. First, we develop a matrix-free update step that uses Jacobian-vector products, iterative linear solvers, and stochastic covariance...
| Authors | Nathanael Bosch |
|---|---|
| Primary category | math.NA |
| Published | 6 June 2026 |
| Last updated at source | 6 June 2026 |
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