Physics-Informed Neural Networks Hit Stiff ODE Wall for k > 50
When spring constant exceeds 50, PINNs collapse to trivial zero solution.
Deep Dive
A researcher learning physics-informed neural networks (PINNs) on a damped harmonic oscillator (m*y'' + mu*y' + k*y = 0) found that the network predicts a trivial zero solution when the stiffness parameter k exceeds 50. Attempts including reducing the learning rate, increasing data points, reusing weights trained at lower k values, and incrementally increasing k in steps of 20 all failed to resolve the issue.
Key Points
- PINN fails to learn damped harmonic oscillator when stiffness parameter k exceeds 50, predicting zero solution.
- Remedies like lower learning rate, more data points, weight transfer, and incremental k stepping were ineffective.
- Stiff ODEs create sharp loss landscapes that standard neural network training cannot navigate without advanced techniques.
Why It Matters
This limitation hinders PINN adoption in real-world engineering, where stiff ODEs are ubiquitous in mechanics and circuits.