用神经算子逆推微分方程参数，速度快且稳定。
Inverse Neural Operator for ODE Parameter Optimization
- 先用条件傅里叶网络重建完整轨迹，再用可学习速度场优化参数
- 在25和40参数系统上精度超基线，推理仅需0.23秒
- 适合需要快速高精度参数反演的复杂动力系统
我们提出逆向神经算子（INO），一种两阶段框架，用于从稀疏、不完整的观测中恢复隐藏的常微分方程（ODE）参数。第一阶段，带有交叉注意力的条件傅里叶神经算子（C-FNO）通过谱正则化抑制高频伪影，学习一个可微分代理模型，从任意稀疏输入重建完整轨迹。第二阶段，压缩漂移模型（ADM）在参数空间中学习加权速度场，将随机初始参数直接推向真实值，无需对代理模型反向传播，避免了刚性系统中基于梯度方法的雅可比不稳定性问题。在真实世界刚性大气化学基准（POLLU，25个参数）和合成基因调控网络（GRN，40个参数）上的实验表明，INO在参数恢复精度上优于基于梯度和压缩基线方法，且推理时间仅需0.23秒，相比迭代梯度下降提速487倍。
原文摘要 · Abstract (English)
We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a differentiable surrogate that reconstructs full ODE trajectories from arbitrary sparse inputs, suppressing high-frequency artifacts via spectral regularization. In Stage 2, an Amortized Drifting Model (ADM) learns a kernel-weighted velocity field in parameter space, transporting random parameter initializations toward the ground truth without backpropagating through the surrogate, avoiding the Jacobian instabilities that afflict gradient-based inversion in stiff regimes. Experiments on a real-world stiff atmospheric chemistry benchmark (POLLU, 25 parameters) and a synthetic Gene Regulatory Network (GRN, 40 parameters) show that INO outperforms gradient-based and amortized baselines in parameter recovery accuracy while requiring only 0.23s inference time, a 487x speedup over iterative gradient descent.
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