Excluding the Target Domain Improves Extrapolation: Deconfounded Hierarchical Physics Constraints

TL;DR

This paper introduces the Deconfounded Hierarchical Gate (DHG), a method that improves physics-based extrapolation by removing confounding effects and leveraging hierarchical physical constraints, leading to significant performance gains.

Contribution

The paper presents DHG, a novel mechanism combining counterfactual estimation and hierarchical gating to address confounding and improve out-of-distribution physics extrapolation.

Findings

Excluding target domain data during pretraining improves extrapolation by 39%.

DHG achieves a 46% RMSE reduction on battery temperature extrapolation.

Hierarchical physical constraints enhance transferability and robustness.

Abstract

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).