为神经网络动态模型提供安全误差边界，确保其在关键系统中的可靠使用。
Certified Neural Approximations of Nonlinear Dynamics
- 基于认证一阶模型构建可并行的自适应验证方法
- 给出神经近似与真实系统间的严格误差界，支持安全替代
- 适用于压缩网络和轨迹预测等复杂场景，优于现有方法
神经网络在非线性动力系统近似方面潜力巨大，但安全关键场景中需对近似精度提供形式化保证。为此，本文提出一种新型、自适应且可并行的验证方法，基于认证一阶模型，为神经动力系统近似提供形式化误差边界。该误差边界可被解释为作用于近似动态的有界扰动，从而允许将神经近似安全用作替代模型。我们在一系列文献基准上验证了该方法的有效性与可扩展性，结果表明其显著优于当前最先进方法。此外，框架还能成功处理以往方法难以应对的场景，包括神经网络压缩以及基于自编码器的深度学习架构训练柯普曼算子以实现轨迹预测。
原文摘要 · Abstract (English)
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system. To address this fundamental challenge, we propose a novel, adaptive, and parallelizable verification method based on certified first-order models. Our approach provides formal error bounds on the neural approximations of dynamical systems, allowing them to be safely employed as surrogates by interpreting the error bound as bounded disturbances acting on the approximated dynamics. We demonstrate the effectiveness and scalability of our method on a range of established benchmarks from the literature, showing that it significantly outperforms the state of the art. Furthermore, we show that our framework can successfully address additional scenarios previously intractable for existing methods -- neural network compression and an autoencoder-based deep learning architecture for training Koopman operators for the purpose of trajectory prediction.
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