# A generic physics-informed neural network-based framework for reliability assessment of multi-state systems

arXiv: https://arxiv.org/abs/2112.00220 · HTML: https://mlsanity.com/paper/2112.00220/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 87 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Physics-Informed Deep Learning: A Promising Technique for System Reliability Assessment](https://mlsanity.com/paper/2108.10828/) (2021)
- [Adaptive network reliability analysis: Methodology and applications to power grid](https://mlsanity.com/paper/2109.05360/) (2021)

## Built on by (most cited first, 4 of 4)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2408.11104/) (2024)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients](https://mlsanity.com/paper/2609.14841/) (2026)

## Abstract (arXiv)

In this paper, we leverage the recent advances in physics-informed neural network (PINN) and develop a generic PINN-based framework to assess the reliability of multi-state systems (MSSs). The proposed methodology consists of two major steps. In the first step, we recast the reliability assessment of MSS as a machine learning problem using the framework of PINN. A feedforward neural network with two individual loss groups are constructed to encode the initial condition and state transitions governed by ordinary differential equations (ODEs) in MSS. Next, we tackle the problem of high imbalance in the magnitude of the back-propagated gradients in PINN from a multi-task learning perspective. Particularly, we treat each element in the loss function as an individual task, and adopt a gradient surgery approach named projecting conflicting gradients (PCGrad), where a task's gradient is projected onto the norm plane of any other task that has a conflicting gradient. The gradient projection operation significantly mitigates the detrimental effects caused by the gradient interference when training PINN, thus accelerating the convergence speed of PINN to high-precision solutions to MSS reliability assessment. With the proposed PINN-based framework, we investigate its applications for MSS reliability assessment in several different contexts in terms of time-independent or dependent state transitions and system scales varying from small to medium. The results demonstrate that the proposed PINN-based framework shows generic and remarkable performance in MSS reliability assessment, and the incorporation of PCGrad in PINN leads to substantial improvement in solution quality and convergence speed.