Model-based design of experiments (MBDOE) is essential for efficient parameter estimation in nonlinear dynamical systems. However, conventional adaptive MBDOE requires costly posterior inference and design optimization between each experimental step, precluding real-time applications. We address this by combining Deep Adaptive Design (DAD), which amortizes sequential design into a neural network policy trained offline, with differentiable mechanistic models. For dynamical systems with known governing equations but uncertain parameters, we extend sequential contrastive training objectives to handle nuisance parameters and propose a transformer-based policy architecture that respects the temporal structure of dynamical systems. We demonstrate the approach on four systems of increasing complexity: a fed-batch bioreactor with Monod kinetics, a Haldane bioreactor with uncertain substrate inhibition, a two-compartment pharmacokinetic model with nuisance clearance parameters, and a DC motor for real-time deployment.

翻译：模型实验设计（MBDOE）对于非线性动力系统中的高效参数估计至关重要。然而，传统的自适应MBDOE需要在每个实验步骤之间进行昂贵的后验推断和设计优化，这阻碍了实时应用。我们通过将深度自适应设计（DAD）与可微分机理模型相结合来解决这一问题，其中DAD将序列设计摊销为离线训练的神经网络策略。针对具有已知控制方程但参数不确定的动力系统，我们扩展了序列对比训练目标以处理冗余参数，并提出了一种基于Transformer的策略架构，该架构尊重动力系统的时间结构。我们在四个复杂度递增的系统上验证了该方法：具有Monod动力学的补料分批生物反应器、具有不确定底物抑制的Haldane生物反应器、带有冗余清除参数的两房室药代动力学模型，以及用于实时部署的直流电机。