---
title: "When Does Jacobian Fine-Tuning Stabilize Neural PDE Emulators?"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.42013v1"
permalink: "https://feed.astralor.com/items/itm_439ca4a35012bb6e7d901504"
published: "2026-10-30T16:49:56.000Z"
score: 54
channel: "tech"
tags: ["When Does Jacobian","Fine-Tuning Stabilize Neural","PDE Emulators","Neural","PDEs","Jacobian-based"]
---

# When Does Jacobian Fine-Tuning Stabilize Neural PDE Emulators?

## At a glance

Neural emulators of chaotic PDEs are trained on one-step prediction but deployed autoregressively, where their errors compound. Jacobian-based regularisers aim to curb this growth, but in a chaotic system part of the gr…

## Key points

- Neural emulators of chaotic PDEs are trained on one-step prediction but deployed autoregressively, where their errors compound.
- Jacobian-based regularisers aim to curb this growth, but in a chaotic system part of the growth is physical and cannot be trained away.
- We separate the two sources of this error with a first-order decomposition.

## Full text

Neural emulators of chaotic PDEs are trained on one-step prediction but deployed autoregressively, where their errors compound. Jacobian-based regularisers aim to curb this growth, but in a chaotic system part of the growth is physical and cannot be trained away. We separate the two sources of this error with a first-order decomposition. We compare the emulator's error with a counterfactual that propagates the same one-step mistakes through the solver's Jacobian, giving an amplification ratio: the factor by which the model's own dynamics amplify its errors. We study 21 configurations across four PDEs, five architectures and two model sizes (8-10k and 33k parameters), with errors measured at one Lyapunov time. Jacobian fine-tuning reduced the error by more than 10% for 1 of 34 seeds whose amplification ratio was at most 1.25, and for all 20 seeds whose ratio was at least four; for the latter, the error fell by a factor of 8 (small models) and 55 (33k models) in geometric mean over seeds. The gain approximately equals the one-step accuracy cost of fine-tuning divided by the amplification ratio. Matching the solver's Jacobian along the model's own error direction (EDJM) outperformed random directions at the same cost on 28 of 35 seeds; input-noise injection performed comparably to EDJM.

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