Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
Short-horizon accuracy does not ensure that a learned chaotic system has correct long-time dynamics. Trajectory (zeroth-order) matching constrains vector-field values, and Jacobian (first-order) matching constrains local tangent dynamics, but neither determines how the Jacobian varies away from supervised states, so a model can be locally accurate while drifting toward spurious attractors and distorting long-time statistics. We show that second-order supervision mitigates these failures. Because forming full Hessian tensors is computationally prohibitive in high dimensions, we propose model-constrained randomized Jacobian matching, which compares the Jacobians of the true and learned vect...
| Authors | Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh |
|---|---|
| Primary category | math.NA |
| Published | 1 June 2026 |
| Last updated at source | 4 September 2026 |
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