Hypothesis

Integrating Physics-Informed Neural Networks with Transformer Survival Models to Capture Non-Proportional Hazard Dynamics in Biological Aging

Recent transformer‑based survival models (TTSurv, SurLonFormer, pathway‑centered transformers) achieve C‑indices of 0.77‑0.78 on high‑dimensional clinical and multi‑omics data by learning temporal dependencies through self‑attention【https://www.emergentmind.com/topics/transformer-based-survival-analysis】. However, they remain challenged by non‑proportional hazards, left truncation, and interval censoring—features ubiquitous in aging datasets【https://www.emergentmind.com/topics/transformer-based-survival-analysis】. Parallel work in materials science shows that physics‑informed neural networks (PINNs) embed governing PDEs into loss functions, yielding 15‑fold data reduction and accurate remaining‑useful‑life predictions for nuclear reactor steels and supercapacitors【https://arxiv.org/abs/2504.13797】【https://arxiv.org/abs/2508.17303】. The MKDPINN framework further demonstrates meta‑learning for degradation dynamics under data scarcity【https://arxiv.org/abs/2504.13797】.

It's well known that transformer models struggle with non‑proportional hazards in longitudinal aging data.

Hypothesis A hybrid architecture that couples a transformer encoder with a physics‑informed decoder—where the decoder enforces a biologically grounded hazard PDE (e.g., a Gompertz‑Makeham‑type equation modulated by oxidative stress and inflammasome activity)—will outperform standalone transformers in predicting individual lifespan and healthspan when trained on longitudinal multi‑omics cohorts, specifically by correctly modeling time‑varying hazard ratios that violate proportionality assumptions.

Mechanistic reasoning Biological aging can be conceptualized as a progressive accumulation of molecular damage that follows deterministic biophysical laws (e.g., reaction‑kinetics of protein cross‑linking, mitochondrial ROS production) superimposed on stochastic cellular insults. Transformer layers excel at extracting latent temporal patterns from heterogeneous omics streams, capturing interactions such as epigenomic drift influencing inflammasome signaling. By feeding the transformer’s latent representation into a PINN loss that penalizes deviation from the chosen hazard PDE, the model is compelled to learn parameters that reflect underlying damage‑accumulation rates rather than merely statistical correlations. This constraints the hazard function to obey known biophysical dynamics, alleviating the non‑proportional hazard problem that plagues pure data‑driven approaches.

Testable predictions

1. On a benchmark aging dataset (e.g., UK Biobank longitudinal omics + electronic health records), the hybrid model will achieve a statistically significant increase in Antolini’s C‑index (≥0.03 absolute gain) compared to the best transformer‑only baseline【https://arxiv.org/html/2504.17568v1】.
2. The learned hazard‑PDE parameters will correlate with independent biomarkers of oxidative stress (e.g., plasma 8‑iso‑PGF2α) and inflammasome activity (e.g., serum IL‑1β), providing a mechanistic link absent in black‑box predictions.
3. When the physics‑informed term is disabled (i.e., loss reduces to standard partial likelihood), performance on interval‑censored and left‑truncated subsets will drop to transformer‑only levels, confirming the contribution of the PDE constraint.

Experimental design

• Assemble a longitudinal cohort with at least three omics layers (transcriptome, methylome, proteome) collected biennially over 15 years, linked to mortality and morbidity outcomes.
• Preprocess data into subject‑specific time series; mask missing visits to simulate real‑world censoring.
• Implement the hybrid model: transformer encoder (4‑layer, 8 heads) → latent vector → PINN decoder that outputs hazard rate λ(t) = λ₀·exp(θ·X(t))·exp(γ·D(t)), where D(t) is a damage state governed by dD/dt = k₁·ROS(t) − k₂·Repair(t) (the PDE).
• Train using a joint loss: L = L_partial‑likelihood + α·‖∂D/∂t − (k₁·ROS − k₂·Repair)‖² + β·‖λ(t) − λ_PDE(t)‖².
• Compare against baselines: DeepSurv, TTSurv, SurLonFormer, and a pure PINN (no transformer).
• Evaluate using Harrell’s C‑index for overall discrimination and Antolini’s C‑index for time‑varying hazards; perform calibration plots for predicted vs. observed survival.
• Conduct ablation studies: varying α, β, and substituting alternative hazard PDEs (Weibull, logistic).

Falsifiability If the hybrid model fails to improve Antolini’s C‑index by at least 0.02 over transformer baselines, or if the inferred PDE parameters show no significant association with oxidative/inflammasome markers, the hypothesis is refuted. Conversely, successful validation would support the notion that embedding biophysical degradation laws into deep survival learners enhances predictive fidelity for aging trajectories.