Research map / Probabilistic and scientific modeling / Differential equations and PDEs
FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FP64 instead of FP32 for vanilla PINN training (ablation) | PINN · Convection | rRMSE: 0.7640 -> 0.0072 | Helped |
| Use FP64 instead of FP32 for vanilla PINN training (ablation) | PINN · Reaction | rRMSE: 0.9778 -> 0.0502 | Helped |
| Use FP64 instead of FP32 for vanilla PINN training (ablation) | PINN · Wave | rRMSE: 0.2837 -> 0.0081 | Helped |
| Use FP64 instead of FP32 for vanilla PINN training (ablation) | PINN · Allen-Cahn | rRMSE: 0.9662 -> 0.0545 | Helped |
| Reduce precision from FP32 to TF32 (ablation) | PINNsFormer and PINNMamba · Convection (β=50) | rMAE | Hurt |
| Increase training precision to FP64 (ablation) | PINN models · Convection (β=50) | solution error | Helped |
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- Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · similarity 0.88)
- PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.88)
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