Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Competitive Physics Informed Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the squared-residual PINN objective with the CPINN adversarial saddle-point formulation and train with ACGD | PINN · 2D Poisson | relative L2 error: 1.2 \times 10^{-4} -> 1.7 \times 10^{-8} | Helped |
| Replace PINN + Adam with CPINN + ACGD | PINN · Nonlinear Schrödinger | relative L2 error: 5\times 10^{-3} -> 6\times 10^{-4} | Helped |
| Use CPINN rather than PINN | PINN · Viscous Burgers | relative error | Helped |
| Use CPINN rather than curriculum-learning PINN | PINN with curriculum learning · Allen–Cahn | relative error | Hurt |
| Use CGD without adaptive step sizes instead of ACGD | CPINN · 2D Poisson | relative L2 error: 1.7 \times 10^{-8} -> 3.5 \times 10^{-4} | Hurt |
| Use ExtraAdam instead of ACGD | CPINN · 2D Poisson | relative L2 error: 1.7 \times 10^{-8} -> 1.6 | Hurt |
| Use ExtraSGD instead of ACGD | CPINN · 2D Poisson | relative L2 error: 1.7 \times 10^{-8} -> 1.2 \times 10^{-4} | Hurt |
| Use ACGD rather than Adam for the CPINN optimization | CPINN · 2D Poisson | relative L2 error: 1.6 -> 1.7 \times 10^{-8} | Helped |
Closest papers by meaning
- Efficient Error Certification for Physics-Informed Neural Networks (ICML 2024 · similarity 0.92)
- RoPINN: Region Optimized Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.92)
- PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs (NeurIPS 2024 · similarity 0.91)
- Sub-Sequential Physics-Informed Learning with State Space Model (ICML 2025 · similarity 0.91)
- PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.91)
- Dual Cone Gradient Descent for Training Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.90)
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