We study identifiability of stochastic differential equations (SDE) under multiple interventions. Our results give the first provable bounds for unique recovery of SDE parameters given samples from their stationary distributions. We give tight bounds on the number of necessary interventions for linear SDEs, and upper bounds for nonlinear SDEs in the small noise regime. We experimentally validate the recovery of true parameters in synthetic data, and motivated by our theoretical results, demonstrate the advantage of parameterizations with learnable activation functions in application to gene regulatory dynamics.

翻译：我们研究了在多重干预下随机微分方程（SDE）的可辨识性问题。我们的结果为给定其平稳分布样本时唯一恢复SDE参数提供了首个可证明的边界。针对线性SDE，我们给出了所需干预数量的紧致边界；针对小噪声机制下的非线性SDE，我们给出了上界。我们在合成数据中实验验证了真实参数的恢复能力，并基于理论结果，展示了在基因调控动力学应用中采用可学习激活函数参数化的优势。