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Physics-Informed Neural Networks for Climate-Aware Digital Twins
US & West ·
This study evaluates a physics-informed neural network for potential-temperature forecasting under incomplete thermal observations, constrained by a pressure-coordinate advection-source equation and a diabatic-source closure frozen after the preceding 12 hours. Validation uses hourly ERA5 reanalysis at three pressure levels for one-, two- and three-hour horizons against persistence, local-trend, and two neural baselines.
Why it matters
The approach shows how physical constraints complement data in short-horizon forecasting, which is relevant for climate-aware digital twins of cities and regions.
The paper develops collective tube MPC, where the calibrated uncertainty object is the entire finite-horizon prediction-error trajectory rather than separate events combined by a union bound. A reusable trajectory tube is calibrated offline, its cross-sections define online Pontryagin tightenings, and the certified violation event is a fresh prediction-error trajectory leaving the tube.
A trust-region formulation is proposed for sampling-based model predictive control algorithms such as MPPI, constraining updates of the proposal distribution via a KL divergence bound and, optionally, an entropy lower bound. This replaces heuristic tuning of temperature or momentum with values optimal with respect to the underlying Lagrangian.
Observed control leverages the duality between state estimation and model predictive control to compute control actions with linear scalability in prediction horizon length. The algorithms provide adaptive horizon lengths and early termination criteria, using Kalman smoothers as the backend. A separate formulation splits linear MPC into purely reactive and anticipatory components.