Hypothesis: Physics-Informed Transformer Survival Models (PITS) for Aging

Core Idea Integrate physics-informed neural networks (PINNs) that encode aging hallmark pathways (e.g., mitochondrial dysfunction, senescence-associated secretory phenotype) as partial differential equation (PDE) constraints into transformer-based survival architectures (SurLonFormer, SurvTRACE) to capture non-proportional hazards and longitudinal multi-omics trajectories.

Mechanistic Rationale Transformer self-attention excels at modeling sequential omics but ignores known biophysical laws governing macromolecular damage accumulation. PINNs embed governing equations (e.g., reaction-diffusion for ROS spread, fractional-order kinetics for tau aggregation) directly into the loss, forcing the network to respect conservation principles and long-memory effects observed in neurodegeneration [4]. By coupling these PDE constraints with the transformer’s temporal encoding, we hypothesize that the model will better disentangle causal aging processes from correlative biomarkers, yielding improved calibration under non-proportional hazards where Antolini’s C-index is required [7].

Testable Predictions

1. On a longitudinal aging cohort (e.g., UK Biobank with multi-omics baseline and follow-up mortality), a PITS model will achieve a statistically significant increase in Antolini’s C-index (>0.03 absolute) over SurLonFormer alone and over a standard PINN that omits transformer attention.
2. Feature importance derived from the transformer’s attention heads will align with known hallmark pathways enforced by the PDE terms (e.g., higher weight on mitochondrial-gene expression when the ROS diffusion PDE is active).
3. Perturbing the PDE constraint weight (λ) will produce a monotonic trade-off between physical plausibility (measured by PDE residual norm) and predictive performance, allowing identification of an optimal λ that maximizes both.

Experimental Design

• Data: Multi-omics (transcriptomics, proteomics, methylation) at baseline and two follow-ups, plus time-to-event (death or major morbidity) for ≥5,000 participants.
• Models: (a) SurLonFormer baseline [1]; (b) Pure PINN with CAPUTO fractional derivative for amyloid/tau dynamics [4]; (c) PITS combining (a) and (b) via joint loss L = L_survival + λ·L_PDE.
• Evaluation: Antolini’s C-index, calibration plots, PDE residual analysis, attention-pathway enrichment (GSEA).
• Falsification: If PITS does not outperform both baselines across multiple λ values, or if attention weights show no enrichment for PDE-guided pathways, the hypothesis is falsified.

Novel Insight Unlike prior works that treat PINNs and transformers as separate modules [3,5,6], we propose a hard coupling where the transformer’s latent dynamics are directly regularized by biophysical PDEs, enabling the model to extrapolate beyond observed ages by simulating underlying damage accumulation—a step toward mechanistic, generalizable aging clocks.

References [1] SurLonFormer: https://www.emergentmind.com/topics/transformer-based-survival-analysis [2] DeepOmicsSurv: https://pmc.ncbi.nlm.nih.gov/articles/PMC12031713/ [3] PINNs for wind-farm degradation: https://www.scribd.com/document/734430386/Use-of-physics-informed-neural-networks-for-ageing-prediction-and-lifetime-extension-of-wind-farm-components [4] Fractional-order PINNs for Alzheimer’s: https://www.frontiersin.org/journals/neuroinformatics/articles/10.3389/fninf.2026.1748481/full [5] CoPINN strategy: https://icml.cc/virtual/2025/poster/46458 [6] Evolutionary-gradient hybrid: https://arxiv.org/html/2501.06572v5 [7] Antolini’s C-index: https://arxiv.org/html/2504.17568v1 [8] DeepSurv code: https://github.com/jaredleekatzman/DeepSurv