Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Characterizing possible failure modes in physics-informed neural networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train progressively from lower to higher convection coefficients (ablation) | PINN · 1D convection β=20 | relative error: $7.50\times 10^{-1}$ -> $9.84 \times 10^{-3}$ | Helped |
| Train progressively from lower to higher convection coefficients (ablation) | PINN · 1D convection β=30 | relative error: $8.97 \times 10^{-1}$ -> $2.02 \times 10^{-2}$ | Helped |
| Train progressively from lower to higher convection coefficients (ablation) | PINN · 1D convection β=40 | relative error: $9.61 \times 10^{-1}$ -> $5.33 \times 10^{-2}$ | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D convection β=30 | relative error: $7.38 \times 10^{-1}$ -> $2.13 \times 10^{-1}$ (Δt=0.05), $1.05 \times 10^{-1}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D convection β=40 | relative error: $8.25 \times 10^{-1}$ -> $4.58 \times 10^{-1}$ (Δt=0.05), $2.41 \times 10^{-1}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction-diffusion ν=2, ρ=5 | relative error: $5.07 \times 10^{-1}$ -> $2.04 \times 10^{-2}$ (Δt=0.05), $1.18 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction-diffusion ν=3, ρ=5 | relative error: $7.98 \times 10^{-1}$ -> $1.92 \times 10^{-2}$ (Δt=0.05), $1.56 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction-diffusion ν=4, ρ=5 | relative error: $8.84 \times 10^{-1}$ -> $2.37 \times 10^{-2}$ (Δt=0.05), $1.59 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction-diffusion ν=5, ρ=5 | relative error: $9.35 \times 10^{-1}$ -> $2.36 \times 10^{-2}$ (Δt=0.05), $2.39 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction-diffusion ν=6, ρ=5 | relative error: $9.60 \times 10^{-1}$ -> $2.81 \times 10^{-2}$ (Δt=0.05), $2.69 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction ρ=5 | relative error: $9.79 \times 10^{-1}$ -> $7.06 \times 10^{-2}$ (Δt=0.05), $7.09 \times 10^{-2}$ (Δt=0.1) | Helped |
| Predict time segments instead of the entire space-time state (ablation) | PINN · 1D reaction ρ=6–8 | relative error: ρ=6: $9.88 \times 10^{-1}$ -> $8.25 \times 10^{-2}$ / $7.78 \times 10^{-2}$; ρ=7: $9.92 \times 10^{-1}$ -> $8.16 \times | Helped |
Closest papers by meaning
- Efficient Error Certification for Physics-Informed Neural Networks (ICML 2024 · similarity 0.92)
- Sub-Sequential Physics-Informed Learning with State Space Model (ICML 2025 · similarity 0.92)
- Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · similarity 0.91)
- PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.90)
- Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks (NeurIPS 2026 · similarity 0.90)
- ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks (ICLR 2025 · similarity 0.90)
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