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arxiv: 2606.26980 · v1 · pith:KJJSD3JZnew · submitted 2026-06-25 · 📊 stat.AP

Climate-Driven Mortality Forecasting Using Deep Learning

Kenrick So , Karim Barigou , Jens Robben This is my paper

Pith reviewed 2026-06-26 02:17 UTC · model grok-4.3

classification 📊 stat.AP
keywords climate-driven mortalityexcess mortalityLee-Carter modeldeep learning forecastingCNN-LSTMGNN-LSTMquantile LSTMmortality risk management
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The pith

Deep learning layers on top of Lee-Carter cut climate-driven mortality forecast errors by 24 percent relative to prior networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out a two-step approach that first applies a regional weekly Lee-Carter model to capture long-term trends and seasonal patterns, then feeds the residuals into either a CNN-LSTM or a GNN-LSTM network that ingests environmental and climate variables to predict excess mortality. On French regional data from 1990 to 2019 the two architectures each lower test mean squared error by roughly 24 percent compared with the earlier MortFCNet model, with the biggest gains appearing at the oldest ages where climate shocks produce the sharpest mortality spikes. The networks are further extended to a quantile LSTM that supplies time-varying prediction intervals. A reader would care because the resulting forecasts give a more realistic picture of tail risks that matter for health planning and for financial contracts tied to longevity.

Core claim

The central claim is that the CNN-LSTM and GNN-LSTM architectures, when added to a Lee-Carter baseline, successfully capture delayed and nonlinear associations between environmental extremes and excess mortality; both models outperform the Lee-Carter baseline and MortFCNet across all regions, each reducing test MSE by approximately 24 percent relative to MortFCNet, with particularly large gains at the oldest ages.

What carries the argument

The two-step framework that fits a regional weekly Lee-Carter model for baseline trends and seasonality, then applies CNN-LSTM or GNN-LSTM networks to the residual excess mortality driven by climate variables, extended via quantile LSTM to produce time-varying prediction intervals.

If this is right

  • Forecasts become more accurate for sudden mortality spikes triggered by climate extremes.
  • Time-varying prediction intervals supply a more realistic description of extreme climate-driven mortality risk.
  • Insurers and pension funds obtain a clearer basis for quantifying climate-related longevity exposure.
  • The spatial structure in the GNN-LSTM version accounts for how climate impacts can propagate across neighboring regions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same two-step structure could be applied to other countries that maintain weekly regional mortality and climate records to check whether the error reductions hold outside France.
  • Coupling the quantile outputs with downscaled climate projections would allow scenario-based longevity forecasts under different warming trajectories.
  • The graph-based spatial component suggests the model could be adapted to study cross-border transmission of climate mortality effects in densely connected regions.

Load-bearing premise

The mortality variation left after the Lee-Carter baseline is driven mainly by measurable climate and environmental factors rather than by other unmodeled influences or data issues.

What would settle it

Retraining the same architectures on post-2019 weekly data that includes documented heat waves and cold spells, then checking whether the 24 percent MSE reduction disappears or whether performance gains remain after climate variables are removed from the deep-learning inputs.

Figures

Figures reproduced from arXiv: 2606.26980 by Jens Robben, Karim Barigou, Kenrick So.

Figure 1
Figure 1. Figure 1: Estimated parameters of the weekly seasonal Lee-Carter model in metropolitan French [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Test MSE by NUTS 2 region, sorted in ascending order of Lee–Carter baseline error. The [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Weekly mortality rate forecasts in Alsace (FRF1), age group 90+, with training period [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Weekly mortality rate forecasts for region FRK2, age group 90+, with training period [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: CNN–LSTM regional embedding clusters. (A) PCA projection of the trained regional embedding vectors. Each point represents one NUTS 2 region; colours denote k-means cluster assignment (k = 4); line segments connect each region to its cluster centroid. (B) Geographic map of cluster assignments across French NUTS 2 regions [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: GNN–LSTM regional embedding clusters, using the same layout conventions as Figure [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Permutation feature importance of the top 15 climate predictors for the CNN–LSTM and [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Temperature response curves for the CNN–LSTM and GNN–LSTM in FRF1 and FRK2, [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: CNN–LSTM 90% prediction interval for the log mortality rate in region FRK2, age group [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: GNN–LSTM 90% prediction interval for the log mortality rate in region FRK2, age group [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗
read the original abstract

Climate extremes have become important drivers of mortality, producing sudden spikes that traditional mortality models fail to predict. To address this gap, we propose a two-step modelling framework that combines a regional weekly Lee-Carter baseline model that captures long-term mortality trends and overall seasonal patterns, with two complementary deep learning architectures designed to model excess mortality driven by environmental conditions and climate shocks. The first, a CNN-LSTM, captures region-specific temporal responses through convolutional filters. The second, a GNN-LSTM, replaces convolutions with graph-based representations to model spatial mortality dependencies and the propagation of climate-related impacts across regions. Both architectures are further extended to a quantile LSTM framework that produces time-varying prediction intervals. We evaluate our models against both the Lee-Carter baseline and MortFCNet (Zheng et al., 2025). Using French regional data over 1990-2019, our models capture delayed and nonlinear associations between environmental extremes and excess mortality. Both proposed architectures outperform the Lee-Carter baseline and MortFCNet across all regions, each reducing test MSE by approximately 24% relative to the MortFCNet, with particularly large gains at the oldest ages where climate-driven mortality spikes are most severe. From a risk management perspective, the proposed framework provides a more realistic characterization of extreme climate-driven mortality risk, with time-varying prediction intervals that offer a more informed basis for the assessment of climate-related longevity exposure by insurers and pension funds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes a two-step framework for forecasting climate-driven mortality: a regional weekly Lee-Carter model captures baseline trends and seasonality, while CNN-LSTM and GNN-LSTM architectures model excess mortality attributable to environmental and climate variables. The GNN-LSTM variant incorporates spatial dependencies across regions. Both are extended to quantile LSTM for time-varying prediction intervals. On French regional data 1990-2019, the models are claimed to reduce test MSE by ~24% relative to MortFCNet (and outperform Lee-Carter), with largest gains at oldest ages.

Significance. If the reported out-of-sample gains hold under rigorous validation, the work would demonstrate a practical way to incorporate nonlinear climate effects and spatial propagation into mortality models, improving tail-risk characterization for longevity products. The graph-based spatial component is a distinctive technical choice that could generalize to other multi-region forecasting problems.

major comments (2)
  1. [Abstract] Abstract and (presumably) §3/§4: the central claim of an approximately 24% test-MSE reduction is presented without any description of the train-test split (temporal cutoff, proportion, or stratification by region/age), hyperparameter search procedure, or regularization/overfitting diagnostics. These omissions make it impossible to verify that the numerical improvement reflects genuine generalization rather than in-sample fitting.
  2. [Abstract] Abstract: the attribution of performance gains specifically to the climate-variable inputs rests on the untested premise that residual mortality after the Lee-Carter baseline is driven primarily by the supplied environmental covariates; no ablation removing those covariates or comparison against non-climate residual models is mentioned.
minor comments (1)
  1. The citation Zheng et al. (2025) for MortFCNet appears to be a future or in-preparation reference; its status should be clarified or replaced with a published alternative if possible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the constructive comments, which identify key areas where additional transparency will strengthen the manuscript. We respond point by point to the major comments below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and (presumably) §3/§4: the central claim of an approximately 24% test-MSE reduction is presented without any description of the train-test split (temporal cutoff, proportion, or stratification by region/age), hyperparameter search procedure, or regularization/overfitting diagnostics. These omissions make it impossible to verify that the numerical improvement reflects genuine generalization rather than in-sample fitting.

    Authors: We agree that the abstract presents the performance claim without these details and that the manuscript body does not supply a complete account of the temporal split, hyperparameter procedure, or overfitting diagnostics. We will revise both the abstract (with a concise reference to the temporal split) and Sections 3/4 to describe the train-test split (1990–2014 training with internal validation, 2015–2019 test, stratified by region and age), the grid-search hyperparameter protocol, regularization (dropout and early stopping), and supporting diagnostics such as training/validation loss curves. These additions will allow readers to assess generalization directly. revision: yes

  2. Referee: [Abstract] Abstract: the attribution of performance gains specifically to the climate-variable inputs rests on the untested premise that residual mortality after the Lee-Carter baseline is driven primarily by the supplied environmental covariates; no ablation removing those covariates or comparison against non-climate residual models is mentioned.

    Authors: We agree that an explicit ablation removing the climate covariates would provide stronger evidence that the reported gains are attributable to the environmental inputs rather than to the flexibility of the DL architectures alone. The current manuscript does not contain such an ablation. We will add this analysis in the revision by retraining the CNN-LSTM and GNN-LSTM models without the climate covariates and reporting the resulting change in test MSE relative to the full models. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical test-set results are independent of model construction

full rationale

The paper presents a two-step framework (Lee-Carter baseline plus DL residual models) evaluated via held-out test MSE on French regional data 1990-2019. The central claim of ~24% MSE reduction versus MortFCNet is a direct numerical comparison on unseen data after training; no equation reduces the reported performance metric to a fitted parameter by definition, no self-citation supplies a uniqueness theorem or ansatz that forces the result, and the architectures are standard CNN-LSTM/GNN-LSTM variants whose outputs are not tautological with their inputs. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework rests on the assumption that climate variables explain the residual mortality after Lee-Carter fitting and that the deep-learning models can learn these relationships without severe overfitting; both are learned from data rather than derived.

free parameters (2)
  • Lee-Carter parameters
    Fitted to long-term trends and seasonal patterns on the 1990-2019 French data.
  • CNN-LSTM and GNN-LSTM weights and hyperparameters
    Numerous parameters trained to minimize excess-mortality prediction error.
axioms (1)
  • domain assumption Environmental extremes produce measurable excess mortality not captured by the Lee-Carter baseline
    Invoked when the authors attribute performance gains to the DL components that receive climate inputs.

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discussion (0)

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