Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of candidate functions chosen via available domain knowledge. In contrast, deep learning can demonstrably model systems of broad complexity with high fidelity, but black-box function approximation typically fails to yield explicit descriptive or disentangled representations revealing the structure of a system. We develop a novel identifiability theorem, leveraging causal representation learning, to uncover disentangled representations of system parameters without structural assumptions. We derive a graphical criterion specifying when system parameters can be uniquely disentangled from raw trajectory data, up to permutation and diffeomorphism. Crucially, our analysis demonstrates that global causal structures provide a lower bound on the disentanglement guarantees achievable when considering local state-dependent causal structures. We instantiate system parameter identification as a variational inference problem, leveraging a sparsity-regularised transformer to uncover state-dependent causal structures. We empirically validate our approach across four synthetic domains, demonstrating its ability to recover highly disentangled representations that baselines fail to recover. Corroborating our theoretical analysis, our results confirm that enforcing local causal structure is often necessary for full identifiability.

翻译：参数化系统辨识方法从数据中估计显式定义物理系统的参数。然而，这些方法仍受限于需提供显式函数空间——通常通过预定义的候选函数库（依据可用领域知识选取）来实现。相比之下，深度学习能够以高保真度建模复杂程度各异的系统，但黑箱函数逼近通常难以生成能揭示系统结构的显式描述性或解耦表征。我们提出了一种新的可辨识性定理，借助因果表征学习，在无需结构假设的前提下揭示系统参数的解耦表征。我们推导出一个图论判据，用于指明系统参数何时能够从原始轨迹数据中唯一解耦（仅允许置换和微分同胚）。关键的是，我们的分析表明，全局因果结构为仅考虑局部状态依赖因果结构时可实现的解耦保证提供了下界。我们将系统参数辨识问题转化为变分推断问题，利用稀疏正则化Transformer来发现状态依赖的因果结构。我们在四个合成领域上进行了实证验证，证明了我们的方法能够恢复基线方法无法恢复的高度解耦表征。与理论分析一致，我们的结果证实，实施局部因果结构对于完全可辨识性往往是必要的。