Residual-based attention in physics-informed neural networks

Understand

Driven by the need for more efficient and seamless integration of physical models and data, physics-informed neural networks (PINNs) have seen a surge of interest in recent years.

• However, ensuring the reliability of their convergence and accuracy remains a challenge.
• In this work, we propose an efficient, gradient-less weighting scheme for PINNs that accelerates the convergence of dynamic or static systems.
• This simple yet effective attention mechanism is a bounded function of the evolving cumulative residuals and aims to make the optimizer aware of problematic regions at no extra computational cost or adversarial learning.