SSH-Net: A Deep Neural Network for Predicting Failure Time Distribution Functions under Competing Risks with Application to GPU Data
Proposes SSH-Net, a deep neural network integrated with cause-specific competing risks model, for failure time distribution prediction on GPU data, leveraging hierarchical data structures.
Key Findings
Methodology
The SSH-Net architecture combines cause-specific competing risks modeling with a hierarchical deep neural network framework. It employs multiple sub-networks to separately process different covariate groups, such as global and hierarchical features, and integrates their outputs through a shared layer. The model predicts cause-specific hazard functions using a piecewise constant hazard assumption, with each hazard rate estimated within predefined time intervals. The loss function is based on the penalized cause-specific log-likelihood, incorporating a smoothness penalty to ensure hazard function continuity. Training involves hyperparameter tuning via grid search, optimizing the number of time bins, regularization parameters, and network depth. The model outputs cause-specific hazard functions, which are integrated to obtain cumulative incidence functions (CIFs). Validation on simulated and real GPU failure data demonstrates superior predictive accuracy measured by RMSE, Brier score, and AUC, outperforming existing models like DeepHit and NFG.
Key Results
- In simulation studies, SSH-Net reduced RMSE by approximately 20% and increased AUC to over 0.88 compared to DeepHit and NFG, indicating higher prediction accuracy and robustness across various scenarios.
- Applied to Titan GPU failure data, SSH-Net accurately captured the hazard function trends for different failure types, with CIF predictions closely matching observed failure probabilities, and mean RMSE below 0.05. The model identified key risk factors such as spatial location, temperature, and usage hours, providing valuable insights for maintenance planning.
- The hierarchical covariate processing allowed the model to handle complex spatial-temporal features effectively, demonstrating its potential for real-world reliability analysis in large-scale systems.
Significance
This work advances survival analysis by integrating deep learning with cause-specific competing risks models, especially suited for complex hierarchical data structures. It addresses the limitations of classical parametric models and existing neural network approaches by providing interpretable hazard functions and robust predictions. The model's ability to incorporate physical system hierarchies and spatial information makes it highly relevant for engineering reliability, predictive maintenance, and risk management. Its application to GPU failure data exemplifies its practical utility, potentially transforming how industries approach failure prediction and system health monitoring. Furthermore, the methodology opens avenues for extending deep survival analysis to other domains like healthcare, finance, and environmental risk assessment, where multi-faceted risk factors influence event timings.
Technical Contribution
The core technical innovation lies in designing a hierarchical neural network architecture that aligns with the data's physical and hierarchical structure. The model employs cause-specific hazard functions estimated via piecewise constant assumptions, with each hazard rate modeled by a dedicated sub-network. The shared layer facilitates information fusion, while separate sub-networks handle different covariate groups, enhancing interpretability and prediction accuracy. The loss function combines cause-specific likelihood with a smoothness penalty, inspired by P-spline techniques, to produce stable hazard estimates. This approach effectively balances model flexibility with regularization, reducing overfitting. Compared to existing models like DeepHit, which discretize time and treat hazards as independent, SSH-Net explicitly models hazard continuity and leverages data structure for hyperparameter tuning, leading to improved performance and interpretability.
Novelty
This study is the first to embed the hierarchical and physical structure of data directly into the neural network architecture for competing risks survival analysis. Unlike prior models such as DeepHit and NFG, which treat failure times as discrete or continuous but lack structural alignment, SSH-Net explicitly models cause-specific hazards with a layered, interpretable design. The integration of a smoothness penalty for hazard functions, combined with data-driven hyperparameter tuning, distinguishes it from existing approaches. Its ability to handle complex spatial-temporal covariates and hierarchical features in a unified framework represents a significant step forward in the field, enabling more accurate and interpretable failure predictions in engineering systems.
Limitations
- The assumption of piecewise constant hazards may oversimplify scenarios with smoothly varying hazard functions, potentially reducing accuracy in such cases. Future work could incorporate continuous hazard models or spline-based approaches.
- Hyperparameter tuning relies on grid search and cross-validation, which can be computationally intensive, especially with large datasets or high-dimensional covariates. More efficient optimization strategies are needed.
- The current model primarily handles static covariates; extending it to dynamic, time-varying features remains a challenge. Additionally, model interpretability could be further enhanced with post-hoc explanation methods.
Future Work
Future research will focus on developing continuous hazard function estimation techniques, such as spline-based or neural ODE approaches, to better capture smooth hazard variations. Efforts will also be made to improve hyperparameter optimization efficiency, possibly through Bayesian optimization or meta-learning. Extending the model to incorporate time-varying covariates and dynamic risk factors will broaden its applicability. Additionally, integrating causal inference frameworks could enhance interpretability and causal understanding of risk factors. Finally, applying SSH-Net to other domains like healthcare (e.g., disease progression) and finance (e.g., default risk) will test its generalizability and impact.
AI Executive Summary
Predicting failure times in complex engineering systems remains a critical challenge, especially when multiple failure modes and hierarchical data structures are involved. Traditional survival analysis models, such as Cox proportional hazards, often rely on parametric assumptions and struggle to accommodate the intricacies of real-world data. Recent advances in deep learning have introduced models like DeepHit and NFG, which relax parametric constraints and improve predictive performance. However, these models often treat all covariates uniformly, neglecting the hierarchical and physical structure inherent in many systems.
This paper introduces SSH-Net, a novel deep neural network architecture designed specifically for cause-specific competing risks scenarios with hierarchical data. By associating sub-networks with different covariate groups—such as spatial location, system hierarchy, and operational parameters—SSH-Net captures complex interactions and physical relationships. The model employs a cause-specific hazard framework, assuming hazards are piecewise constant over time intervals, and outputs hazard functions that are both interpretable and smooth thanks to a penalty-based regularization.
The core innovation lies in the hierarchical network design, which aligns with the physical structure of systems like GPUs in supercomputers. This approach enables more accurate hazard estimation, better uncertainty quantification, and improved predictive accuracy. Validation on simulated data and real GPU failure datasets demonstrates that SSH-Net outperforms existing models in key metrics such as RMSE, Brier score, and AUC. In particular, the model effectively captures the influence of spatial and operational covariates, providing actionable insights for maintenance and reliability management.
The significance of this work extends beyond GPU reliability. Its flexible, interpretable architecture can be adapted to various domains involving multi-risk, hierarchical data—such as medical prognosis, financial risk modeling, and environmental hazard prediction. By bridging the gap between data structure and neural network design, SSH-Net sets a new standard for deep survival analysis in complex systems.
Looking ahead, future research will explore continuous hazard modeling, dynamic covariates, and causal inference integration. The goal is to develop more versatile, efficient, and interpretable models that can support proactive decision-making across industries, ultimately enhancing system safety, efficiency, and longevity.
Deep Dive
Abstract
Competing risks are commonly observed in engineering fields and can bring challenges to time-to-event data modeling when the application scenarios are complicated. Recently, deep neural networks have received great attention for prediction with competing risks, due to their flexibility and high learning capability. However, the complexity of neural network structure brings extra difficulty in hyperparameter tuning based on different data inputs. Additionally, when an engineered system has complex physical structures with multiple hierarchical levels, treating all structural levels as a single group of inputs may fail to capture critical information. To address the issues, we propose a Structured Segmented Hazard Deep Neural Network (SSH-Net) for failure time prediction under cause-specific competing risks framework. Our approach associates neural network structure with data structures, and allows different covariate groups to impact the failure prediction through separate sub-networks. The neural network is constructed based on a cause-specific competing risks model. The SSH-Net outputs cause-specific hazard functions, and utilizes the penalized log-likelihood as the loss function. The prediction accuracy of SSH-Net is validated through simulation studies by evaluating the Brier score, the area under receiver operating characteristic curves (AUC), and the root mean square error (RMSE) of the predicted cause-specific cumulative incident function. We further demonstrate the model's ability to predict failure time distribution functions using the Titan GPU failure time data.