# Explicit Features Versus Implicit Spatial Relations in Geomorphometry: A Comparative Analysis for DEM Error Correction in Complex Geomorphological Regions

## TL;DR

This study compares complex deep learning models with traditional feature-based methods for correcting elevation data errors, finding that simpler physics-based approaches perform better and are more reliable.

## Contribution

The paper introduces a novel comparative framework showing that physics-based feature engineering outperforms geometric deep learning in DEM error correction under sparse supervision.

## Key findings

- Hybrid GNN models show negligible accuracy gains over XGBoost with much higher computational cost.
- XGBoost provides stable predictions using deterministic physical features, while GNNs show attribution instability.
- Sparse supervision favors explicit physical descriptors over complex geometric deep learning models.

## Abstract

What are the main findings?
Severe Scale Mismatch: GNN-XGBoost hybrid models yield negligible accuracy gains (<0.05 m) at a nearly 18-fold computational cost. The vast spatial baseline of ICESat-2 footprints (averaging ~485 m) severely violates the dense connectivity assumption of GNNs, inducing predictable “over-smoothing”.Mechanism Decoupling & ID Chaos: A critical divergence in decision logic is uncovered: XGBoost strictly isolates deterministic physical drivers (e.g., Aspect) with near-perfect stability (ρ > 0.97). Conversely, GNNs exhibit severe “Attribution Stochasticity” (ρ≈ 0.63–0.77), acting as opportunistic “residual-dependent latent feature learners” that fit local noise.

Severe Scale Mismatch: GNN-XGBoost hybrid models yield negligible accuracy gains (<0.05 m) at a nearly 18-fold computational cost. The vast spatial baseline of ICESat-2 footprints (averaging ~485 m) severely violates the dense connectivity assumption of GNNs, inducing predictable “over-smoothing”.

Mechanism Decoupling & ID Chaos: A critical divergence in decision logic is uncovered: XGBoost strictly isolates deterministic physical drivers (e.g., Aspect) with near-perfect stability (ρ > 0.97). Conversely, GNNs exhibit severe “Attribution Stochasticity” (ρ≈ 0.63–0.77), acting as opportunistic “residual-dependent latent feature learners” that fit local noise.

What are the implications of the main findings?
Physics Trumps Geometry: For geospatial regression tasks relying on sparse supervision, explicit physical feature engineering offers superior interpretability and transferability compared to “Black Box” geometric deep learning, challenging the “complexity is better” assumption.New Evaluation Standard: The identification of “stable prediction, drifting explanation” (Underspecification) underscores a critical imperative: Geo-AI research must prioritize “Explanatory Stability” as a prerequisite for scientific inference, rather than solely pursuing marginal accuracy gains.

Physics Trumps Geometry: For geospatial regression tasks relying on sparse supervision, explicit physical feature engineering offers superior interpretability and transferability compared to “Black Box” geometric deep learning, challenging the “complexity is better” assumption.

New Evaluation Standard: The identification of “stable prediction, drifting explanation” (Underspecification) underscores a critical imperative: Geo-AI research must prioritize “Explanatory Stability” as a prerequisite for scientific inference, rather than solely pursuing marginal accuracy gains.

Global Digital Elevation Models (DEMs) exhibit systematic biases constrained by acquisition geometry and surface penetration. This study aims to evaluate whether the increasing complexity of geometric deep learning (e.g., Graph Neural Networks, GNNs) is justified by performance gains over established feature engineering paradigms (e.g., XGBoost) under the constraints of sparse altimetry supervision. We established a rigorous comparative framework across four mainstream products—ALOS World 3D, Copernicus DEM, SRTM GL1, and TanDEM-X—using Sichuan Province, China, as a representative natural laboratory. Our results reveal a fundamental scale mismatch (where the ~485 m average spacing of sampled altimetry footprints dwarfs the local terrain resolution): despite their topological complexity, Hybrid GNN models fail to establish a statistically significant accuracy advantage over the systematically optimized XGBoost baseline, demonstrating RMSE parity. Mechanistically, we uncover a critical divergence in decision logic: XGBoost relies on a stable “Physics Skeleton” consistently dominated by deterministic features (terrain aspect and vegetation density), whereas GNNs exhibit severe “Attribution Stochasticity” (ρ ≈ 0.63–0.77). The GNN component acts as a residual-dependent latent feature learner rather than discovering universal topological laws. We conclude that for geospatial regression tasks relying on sparse supervision, “Physics Trumps Geometry.” A “Feature-First” paradigm that prioritizes robust, domain-knowledge-based physical descriptors outweighs the indeterminate complexity of “Black Box” architectures. This study underscores the imperative of prioritizing explanatory stability over marginal accuracy gains to foster trusted Geo-AI.