Abstract
We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling. SKINNs define a class of M-estimators that are consistent and asymptotically normal with root-N convergence, sandwich covariance, and recovery of pseudo-true parameters under misspecification. We establish identification of structural parameters under joint flexibility, derive generalization and target-risk bounds under distributional shift in a convex proxy, and provide a restricted-optimal characterization of the weighting parameter that governs the bias-variance tradeoff. In an illustrative financial application to option pricing, SKINNs improve out-of-sample valuation and hedging performance, particularly at longer horizons and during high-volatility regimes, while recovering economically interpretable structural parameters with improved stability relative to conventional calibration. More broadly, SKINNs provide a general econometric framework for combining model-based reasoning with high-dimensional, data-driven estimation.
Abstract (translated)
我们开发了结构化知识感知神经网络（SKINNs），这是一种统一的估计框架，可将理论、模拟、先验学习或跨领域洞见作为可微约束嵌入到灵活的神经函数逼近器中。SKINNs在单一优化问题中联合估计神经网络参数与经济意义明确的结构参数，不仅通过配点法在观测数据上，更在更广泛的输入域内 enforce 理论一致性，从而统一了函数型GMM、贝叶斯更新、迁移学习、物理信息神经网络及代理模型等方法。SKINNs定义了一类M估计量，在设定错误时仍具有一致性、渐近正态性、根N收敛率、三明治协方差估计及伪真值参数恢复等性质。我们证明了在联合灵活性下结构参数的可识别性，在凸代理中推导了分布偏移下的泛化与目标风险界，并提供了控制偏差-方差权衡的加权参数的受限最优刻画。在期权定价的金融应用示例中，SKINNs提升了样本外估值与对冲表现，尤其在长期预测与高波动 regimes 中，同时相比传统校准方法能恢复更具经济解释性且稳定性更高的结构参数。更广泛地，SKINNs为结合基于模型的推理与高维数据驱动估计提供了通用计量框架。
URL
https://arxiv.org/abs/2604.00987
