# Breaking the Black Box: Inherently Interpretable Physics-Constrained Machine Learning With Weighted Mixed-Effects for Imbalanced Seismic Data

arXiv: https://arxiv.org/abs/2508.19031 · HTML: https://mlsanity.com/paper/2508.19031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 26 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Curve Your Enthusiasm: Concurvity Regularization in Differentiable Generalized Additive Models](https://mlsanity.com/paper/2305.11475/) (2023)

## Abstract (arXiv)

Ground motion models (GMMs) are critical for seismic risk mitigation and infrastructure design. Machine learning (ML) is increasingly applied to GMM development due to expanding strong motion databases. However, existing ML-based GMMs operate as 'black boxes,' creating opacity that undermines confidence in engineering decisions. Moreover, seismic datasets exhibit severe imbalance, with scarce large-magnitude near-field records causing systematic underprediction of critical high-hazard ground motions. Despite these limitations, research addressing both interpretability and data imbalance remains limited. This study develops an inherently interpretable neural network employing independent additive pathways with novel HazBinLoss and concurvity regularization. HazBinLoss integrates physics-constrained weighting with inverse bin count scaling to address underfitting in sparse, high-hazard regions. Concurvity regularization enforces pathway orthogonality, reducing inter-pathway correlation. The model achieves robust performance: mean squared error = 0.6235, mean absolute error = 0.6230, and coefficient of determination = 88.48%. Pathway scaling corroborates established seismological behaviors. Weighted hierarchical Student-t mixed-effects analysis demonstrates unbiased residuals with physically consistent variance partitioning: sigma components range from 0.26-0.38 (inter-event), 0.12-0.41 (inter-region), 0.58-0.71 (intra-event), and 0.68-0.89 (total). The lower inter-event and higher intra-event components have implications for non-ergodic hazard analysis. Predictions exhibit strong agreement with NGA-West2 GMMs across diverse conditions. This interpretable framework advances GMMs, establishing a transparent, physics-consistent foundation for seismic hazard and risk assessment.