Excluding the Target Domain Improves Extrapolation: Deconfounded Hierarchical Physics Constraints
For researchers applying physics-constrained generative models to real-world systems with distribution shifts, this work provides a principled method to handle confounding variables and improve extrapolation, though the evaluation is limited to a single domain (battery temperature).
The paper tackles out-of-distribution extrapolation in physics-constrained deep generative models by introducing a Deconfounded Hierarchical Gate (DHG) that removes temperature confounding and applies hierarchical physical constraints. The method achieves a 46% improvement in RMSE (0.215 vs. 0.397) on a lithium-ion battery temperature extrapolation benchmark, and shows that excluding target-domain data from pretraining improves performance by 39%.
Extrapolation to out-of-distribution conditions is a fundamental challenge for physics-constrained deep generative models. Existing methods apply physical constraints as a single static regularization term uniformly across the generation process, and address neither the hierarchical structure of physical laws and the confounding variable problem. We propose the Deconfounded Hierarchical Gate (DHG), which serves as a diagnostic and control mechanism: it identifies when and how strongly temperature confounding contaminates each constraint level, so that hierarchical gates reflect intrinsic physical inconsistency rather than spurious temperature effects. DHG combines counterfactual estimation via the do-operator with backdoor adjustment to remove confounding, then applies Coarse-to-Fine physical constraints progressively. We report a counter-intuitive finding in pretraining: excluding the target-domain data from pretraining outperforms including it by 39% in extrapolation performance (RMSE 0.224 vs. 0.324). This occurs because FNO learns domain-agnostic physical patterns that transfer more effectively when the target domain is withheld. On a lithium-ion battery temperature extrapolation benchmark (trained at 24 degrees Celsius, evaluated at 4.0--43.0 degrees Celsius), our method achieves RMSE = 0.215, a 46% improvement over the unconstrained baseline (Pure CFM: 0.397).