结构动力学图世界模型：统一建模、约束展开与可解释校准

中文摘要 AI 辅助

复杂系统的状态演化由对象规律、关系传播、域守恒及未建模误差共同产生。将所有来源强制纳入一个黑箱会导致机制归因和约束保存无法审计；将每个机制强制纳入一个方程族则会丢弃成熟的域求解器。我们提出SD-GWM（结构动力学图世界模型）作为可执行的结构契约：节点声明自动力学S，边声明邻居图耦合动力学N——二者均为固定形式的机制资产（规则、常微分方程、求解器），仅校准授权参数。可选的有界残差R集中可学习性，而全局投影将状态映射到可行性，在不保证精度提升的情况下强制约束。在8个预注册研究问题上，SD-GWM实现：（i）异构集成：规则和求解器可原生插入；（ii）语义保真：禁用R可逐位保留源语义，有4个理论属性处于显式证明/经验边界下；（iii）可审计治理：逐步轨迹支持反事实故障定位（Top-1=1.0），无需事后近似。在半合成洪水测试平台和USGS河流流量任务中，SD-GWM在分析测试中将约束违规降至浮点容差，在半合成和真实数据案例中降至零。平稳时期，持续性模型与SD-GWM表现相当，但在254天极端洪水转变期间，持续性模型和所有神经基线均崩溃（90分钟均方根误差为892-3007立方英尺/秒），而SD-GWM保持在108立方英尺/秒（提升8-28倍）。仅在骨干网络存在偏差时，有界残差可将均方根误差降低约50%。我们将SD-GWM定位为可验证的底物，而非通用的最优预测器，用于可审计、约束安全的时空挖掘。

英文摘要

The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error. Forcing all sources into one black box makes mechanism attribution and constraint preservation unauditable; forcing every mechanism into one equation family discards mature domain solvers. We propose SD-GWM, a Structural Dynamics Graph World Model as an executable structural contract: nodes declare self-dynamics S, edges declare neighbor graph-coupled dynamics N---both fixed-form mechanism assets (rules, ODEs, solvers) calibrating only authorized parameters. An optional bounded residual R concentrates learnability, while a global projection maps states to feasibility, enforcing constraints without guaranteeing accuracy gains. On eight pre-registered research questions, SD-GWM delivers (i) heterogeneous integration: rules and solvers plug in natively; (ii) semantic fidelity: disabling R preserves source semantics bit-for-bit, with four theory properties under explicit proof/empirical boundaries; (iii) auditable governance: stepwise traces enable counterfactual fault localization (top-1 = 1.0) without post-hoc approximations. On a semi-synthetic flood testbed and USGS streamflow, SD-GWM reduces constraint violations to floating-point tolerance in analytical tests and to zero in semi-synthetic and real-data cases. Persistence matches SD-GWM in calm periods, but during a 254-day extreme-flood shift persistence and all neural baselines collapse (90-min RMSE 892-3007 cfs) while SD-GWM holds at 108 cfs (8-28x gain). The bounded residual cuts RMSE ~50% only under backbone bias. We position SD-GWM not as a universally superior forecaster, but as a verifiable substrate for auditable, constraint-safe spatiotemporal mining.

发表机构

• Sobey（Sobey公司）

机构由 AI 辅助整理，请以论文原文为准。