用神经微分方程建模空调系统，速度快且精度高。
Scalable Physics-Informed Neural Differential Equations and Data-Driven Algorithms for HVAC Systems
- 用物理约束的神经网络学部件动态，自动满足能量质量守恒。
- 系统级模拟速度提升数倍，误差低于百分之几，支持16组压缩机-冷凝器。
- 适合做大规模暖通系统仿真优化，尤其看重效率与真实性的场景。
我们提出一种可扩展的数据驱动仿真框架，用于大型暖通空调（HVAC）系统，将物理信息神经常微分方程（PINODE）与微分代数方程（DAE）求解器结合。在部件层面，采用隐式PINODE学习换热器动态，输出制冷剂质量 $M_r$ 与内能 $E_ ext{hx}$，通过自动微分实现物理约束训练。通过门控结构与层归一化实现梯度稳定，支持长期预测。在系统层面，将学习到的部件与IDA和DASSL等DAE求解器集成，显式强制节点约束（压力平衡与流量一致），并使用贝叶斯优化调参以平衡精度与效率。为减少系统级残差偏差，引入轻量校正网络，在短轨迹上训练。在双压缩机及扩大的网络实验中，该方法相比高保真仿真实现多倍加速，误差保持极低（MAPE低于百分之几），并可扩展至包含最多16组压缩机-冷凝器的系统。
原文摘要 · Abstract (English)
We present a scalable, data-driven simulation framework for large-scale heating, ventilation, and air conditioning (HVAC) systems that couples physics-informed neural ordinary differential equations (PINODEs) with differential-algebraic equation (DAE) solvers. At the component level, we learn heat-exchanger dynamics using an implicit PINODE formulation that predicts conserved quantities (refrigerant mass $M_r$ and internal energy $E_\text{hx}$) as outputs, enabling physics-informed training via automatic differentiation of mass/energy balances. Stable long-horizon prediction is achieved through gradient-stabilized latent evolution with gated architectures and layer normalization. At the system level, we integrate learned components with DAE solvers (IDA and DASSL) that explicitly enforce junction constraints (pressure equilibrium and mass-flow consistency), and we use Bayesian optimization to tune solver parameters for accuracy--efficiency trade-offs. To reduce residual system-level bias, we introduce a lightweight corrector network trained on short trajectory segments. Across dual-compressor and scaled network studies, the proposed approach attains multi-fold speedups over high-fidelity simulation while keeping errors low (MAPE below a few percent) and scales to systems with up to 16 compressor-condenser pairs.
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