Learned dynamics graphs often fail to help inverse problems
Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems
Machine Learning
Summary
The paper finds that using learned relationships from data that simulates processes (dynamics) does not always help solve reverse problems, like finding the source of a leak, even when theory says it should. The authors show that learned graphs predicting dynamics often miss key connections needed for these tasks, which can make results worse. They propose a quick test to check if a learned structure will transfer well to such inverse problems. This warns against assuming any learned structure will help without checking.
What this means in practice
- •For computational fluid dynamics engineers: Avoid using learned dynamics-based graphs to locate sources like leaks, reducing errors compared to relying on physics-based or flexible models.
- •For sensor network designers: Use the proposed transferability test to evaluate learned graph structures before deploying them for source detection in complex environments.
Tested on simulated data.
Authors
Nicholas Tan Jerome, Fangnian Wang
Abstract
A natural strategy for inverse problems with scarce labelled data is to transfer relational structure learned from abundant forward-simulation data. We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help. We prove that approximate structure provides estimation-error benefits whenever the edge error satisfies $Δ< n^2 - kn$, reducing sample complexity from $O(n^2)$ to $O(kn+Δ)$. Structure learned via Neural Relational Inference (NRI) from dynamics prediction satisfies this condition, yet on a source-localisation task across 180 CFD-simulated hydrogen-leak scenarios and 180 acoustic scenarios, it degrades performance by 116% and 201% relative to a flexible, task-optimised attention baseline, while a physics-based prior (Green's function) degrades by only 69-72%. Four independent lines of evidence show this is not a tuning failure: NRI improves only 0.5% when given 18x more training data (versus 16.6% for the task-optimised baseline, $p<0.001$); performance is insensitive to the NRI edge threshold across a wide range; the dynamics-learned graph overlaps the task-optimal graph on only 6% of edges; and two further dynamics-derived structure estimators (correlation- and mutual-information-based) show no measurable benefit over a structure-free baseline, with the correlation-based estimator performing markedly worse. We formalise this gap as a statement about approximation error that the edge-accuracy condition cannot control, and we provide a lightweight transferability test (Jaccard similarity against a partially-observed target-task graph) that separates successful from failed transfer in all four domain/structure pairs we evaluate, using under an hour of computation and 15-20% of target-domain data; we present this as a heuristic calibrated on few cases, not a validated general threshold.