Regime-adaptive partial differential equations for interpretable multi-ethnic urban modeling
Bibliographic record
Abstract
Machine learning models for societal applications often sacrifice interpretability for accuracy. We present the Multi-Ethnic Spatial Mixture of Experts (MESMoE), an interpretable framework integrating physics-informed modeling with specialized neural experts to predict urban population dynamics across ethnic groups. MESMoE addresses the challenge of capturing heterogeneous mechanisms that vary by ethnicity, spatial context, and temporal period through a learnable router that directs predictions to specialized experts for distinct demographic regimes (colonization, jump process, decline, and PDE-based diffusion). This approach achieves robust performance (R 2 values of 0.76–0.81 for 5-year forecasts, 0.71 for 10-year forecasts) while substantially outperforming seven baseline models (45–70% improvement in R 2 ) and maintaining full interpretability through physics-informed parameterization. Using Toronto census data spanning two decades, our model reveals previously undetectable patterns including cross-ethnic influence networks and systematic differences in settlement strategies across ethnic groups. Our findings demonstrate that incorporating domain knowledge through regime-specific, physics-informed modeling can simultaneously enhance predictive accuracy and interpretability—challenging the perceived trade-off in machine learning for complex social systems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".