Ecological Momentary Assessment (EMA) studies enable the collection of high-frequency self-reports of suicidal thoughts and behaviors (STBs) via smartphones. Latent stochastic differential equations (SDEs) are a promising model class for EMA data, as it is irregularly sampled, noisy, and partially observed. But SDE-based models suffer from two key limitations. (a) These models often violate domain constraints, undermining scientific validity and clinical trust of the model. (b) Training is numerically unstable without ad hoc fixes (e.g. oversimplified dynamics) that are ill-suited for high-stakes applications. Here, we develop a novel class of expressive SDEs whose solutions are provably confined to a prescribed compact polyhedral state space, matching the domains of EMA data. In this work, (1) we show why chain-rule based constructions of SDEs on compact domains fail, theoretically and empirically; (2) we derive constraints on drift and diffusion for general and stationary SDEs so their solutions remain in the desired state space; and (3), we introduce a parameterization that maps arbitrary (neural or expert-given) dynamics into constraint-satisfying SDEs. On several real EMA datasets, including a large suicide-risk study, our parameterization improves forecasts and optimization dynamics over standard latent neural SDE baselines. These contributions pave the way for principled, trustworthy continuous-time models of suicide risk and other clinical time series and extend applications of SDE-based methods (e.g. diffusion models) to domains with hard state constraints.

翻译：生态瞬时评估（EMA）研究通过智能手机实现了对自杀想法与行为（STBs）高频自我报告的数据收集。潜变量随机微分方程（SDEs）是处理EMA数据的一类有前景的模型框架，因其数据呈现非规则采样、含噪声且部分可观测的特点。然而，基于SDE的模型面临两个关键局限：（a）此类模型常违反状态空间约束，削弱了模型的科学有效性与临床可信度；（b）在没有特定修正（如过度简化的动力学假设）时训练过程数值不稳定，这种临时性方法不适用于高风险应用场景。为此，我们开发了一类新型具有表达力的SDE，其解可被严格限定在预定义的紧致多面体状态空间中，完美匹配EMA数据的域约束。本研究（1）从理论与实证角度揭示了为何基于链式法则的紧致域SDE构建方法存在根本缺陷；（2）推导了一般性与平稳SDE的漂移项与扩散项约束条件，确保其解始终维持在目标状态空间内；（3）提出一种参数化方法，可将任意动力学（神经网络或专家定义）映射为满足约束条件的SDE。在多个真实EMA数据集（包括大规模自杀风险研究）上，我们的参数化方法相较于标准潜变量神经SDE基线模型，显著提升了预测精度与优化动力学表现。这些成果为基础化、可信赖的自杀风险及其他临床时间序列连续时间模型铺平了道路，并将基于SDE的方法（如扩散模型）扩展至具有严格状态约束的领域。