# A Sequential Meta-Transfer (SMT) Learning to Combat Complexities of Physics-Informed Neural Networks: Application to Composites Autoclave Processing

arXiv: https://arxiv.org/abs/2308.06447 · HTML: https://mlsanity.com/paper/2308.06447/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 48 references that are in the map.
- First posted on arXiv 12 Aug 2023.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Meta-Transfer Learning for Few-Shot Learning](https://mlsanity.com/paper/1812.02391/) (2018)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks](https://mlsanity.com/paper/2007.04542/) (2020)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Long-time integration of parametric evolution equations with physics-informed DeepONets](https://mlsanity.com/paper/2106.05384/) (2021)
- [When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?](https://mlsanity.com/paper/2109.09444/) (2021)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions](https://mlsanity.com/paper/2302.14227/) (2023)
- [Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs](https://mlsanity.com/paper/2101.08366/) (2021)
- [Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains](https://mlsanity.com/paper/2104.10873/) (2021)
- [A novel meta-learning initialization method for physics-informed neural networks](https://mlsanity.com/paper/2107.10991/) (2021)
- [L-HYDRA: Multi-Head Physics-Informed Neural Networks](https://mlsanity.com/paper/2301.02152/) (2023)
- [Reproducing Activation Function for Deep Learning](https://mlsanity.com/paper/2101.04844/) (2021)

## Built on by (most cited first, 3 of 3)

- [An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study](https://mlsanity.com/paper/2406.14715/) (2024)
- [GITO: Graph-Informed Transformer Operator for Learning Complex Partial Differential Equations](https://mlsanity.com/paper/2506.13906/) (2025)
- [Accelerated Gradient-based Design Optimization Via Differentiable Physics-Informed Neural Operator: A Composites Autoclave Processing Case Study](https://mlsanity.com/paper/2502.11504/) (2025)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) have gained popularity in solving nonlinear partial differential equations (PDEs) via integrating physical laws into the training of neural networks, making them superior in many scientific and engineering applications. However, conventional PINNs still fall short in accurately approximating the solution of complex systems with strong nonlinearity, especially in long temporal domains. Besides, since PINNs are designed to approximate a specific realization of a given PDE system, they lack the necessary generalizability to efficiently adapt to new system configurations. This entails computationally expensive re-training from scratch for any new change in the system. To address these shortfalls, in this work a novel sequential meta-transfer (SMT) learning framework is proposed, offering a unified solution for both fast training and efficient adaptation of PINNs in highly nonlinear systems with long temporal domains. Specifically, the framework decomposes PDE's time domain into smaller time segments to create "easier" PDE problems for PINNs training. Then for each time interval, a meta-learner is assigned and trained to achieve an optimal initial state for rapid adaptation to a range of related tasks. Transfer learning principles are then leveraged across time intervals to further reduce the computational cost.Through a composites autoclave processing case study, it is shown that SMT is clearly able to enhance the adaptability of PINNs while significantly reducing computational cost, by a factor of 100.