Excluding the Target Domain Improves Extrapolation: Deconfounded Hierarchical Physics Constraints

2026-05-08

AI Summary

This work addresses the challenge of out-of-distribution extrapolation in physics-constrained deep generative models, which often suffer from missing hierarchical physical structures and confounding effects such as temperature variations. To overcome these limitations, the authors propose a Deconfounded Hierarchical Gating (DHG) mechanism that integrates counterfactual do-operators with backdoor adjustment to eliminate confounding bias, while guiding the generation process through coarse-to-fine hierarchical physical constraints. Notably, the study reveals that excluding target-domain data during pretraining substantially enhances extrapolation performance, underscoring the importance of learning domain-invariant physical patterns. Evaluated on lithium-ion battery temperature extrapolation, DHG achieves an RMSE of 0.215, representing a 46% improvement over an unconstrained baseline; further excluding target-domain data during pretraining reduces the error by an additional 39%, lowering RMSE from 0.324 to 0.224.

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).

Problem

• extrapolation
• physics-constrained models
• confounding variables
• hierarchical physical laws
• out-of-distribution

Innovation

• Deconfounded Hierarchical Gate
• physics-constrained generative models
• counterfactual estimation
• out-of-distribution extrapolation
• backdoor adjustment