提出Deceptron模块，让物理反问题求解更快更稳。
Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion
- 用可学习的局部逆映射替代传统迭代方法
- 在热传导和阻尼振子问题上迭代次数减少2-20倍
- 适合需要快速稳定求解物理反问题的研究者
物理科学中的反问题通常在输入空间中病态，导致步长敏感。我们提出Deceptron，一种轻量级双向模块，用于学习可微前向代理的局部逆。训练结合监督拟合、正反向一致性、轻量级谱惩罚、软偏置约束以及雅可比复合惩罚（JCP），通过JVP/VJP探针强制满足 $J_g(f(x)) J_f(x) approx I$。求解时，D-IPG（Deceptron反向预处理梯度）在输出空间进行下降，经由 $g$ 拉回并按基线规则回溯与停止。在1维热传导初始条件恢复和阻尼振子反问题上，D-IPG在热传导问题上迭代次数减少约20倍，在振子问题上减少2-3倍，迭代次数和计算成本与高斯-牛顿法相当。诊断显示JCP显著降低复合误差并追踪迭代增益。我们还展示了单尺度2D版本DeceptronNet（v0），在严格公平协议下学习几步修正，表现出显著快速收敛。
原文摘要 · Abstract (English)
Inverse problems in the physical sciences are often ill-conditioned in input space, making progress step-size sensitive. We propose the Deceptron, a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Training combines a supervised fit, forward-reverse consistency, a lightweight spectral penalty, a soft bias tie, and a Jacobian Composition Penalty (JCP) that encourages $J_g(f(x))\,J_f(x)\!\approx\!I$ via JVP/VJP probes. At solve time, D-IPG (Deceptron Inverse-Preconditioned Gradient) takes a descent step in output space, pulls it back through $g$, and projects under the same backtracking and stopping rules as baselines. On Heat-1D initial-condition recovery and a Damped Oscillator inverse problem, D-IPG reaches a fixed normalized tolerance with $\sim$20$\times$ fewer iterations on Heat and $\sim$2-3$\times$ fewer on Oscillator than projected gradient, competitive in iterations and cost with Gauss-Newton. Diagnostics show JCP reduces a measured composition error and tracks iteration gains. We also preview a single-scale 2D instantiation, DeceptronNet (v0), that learns few-step corrections under a strict fairness protocol and exhibits notably fast convergence.
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