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

by   Milad Ramezankhani, et al.

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.


page 1

page 2

page 3

page 4


Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) are emerging as popular mesh-fr...

Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains

Physics-informed neural networks (PINNs) are increasingly employed to re...

Long-time integration of parametric evolution equations with physics-informed DeepONets

Ordinary and partial differential equations (ODEs/PDEs) play a paramount...

PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising dee...

Physics-Informed Neural Nets-based Control

Physics-informed neural networks (PINNs) impose known physical laws into...

On Theory-training Neural Networks to Infer the Solution of Highly Coupled Differential Equations

Deep neural networks are transforming fields ranging from computer visio...

Please sign up or login with your details

Forgot password? Click here to reset