Research map / Optimization / Implicit bias and generalization
Gradient Descent Finds the Global Optima of Two-Layer Physics-Informed Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Over-parameterization (larger network width m) | two-layer PINN trained by gradient descent on 1-D heat equation · 1-D heat equation | training loss | Helped |
| Over-parameterization (larger network size) | two-layer PINN on 1-D heat equation · 1-D heat equation | relative error | Helped |
| Gram matrix positive definiteness via non-parallel training samples (no near-parallel assumption needed) | two-layer PINN theory · theoretical analysis | minimal eigenvalue of Gram matrix | No clear effect |
| Use of learning rate scaled to smallest Gram eigenvalue (eta = O(lambda0+eigen)) | gradient descent for PINNs · theory | loss convergence rate | Helped |
Closest papers by meaning
- Dual Cone Gradient Descent for Training Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.90)
- Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective (NeurIPS 2025 · similarity 0.90)
- Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks (NeurIPS 2026 · similarity 0.90)
- Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · similarity 0.89)
- ConFIG: Towards Conflict-free Training of Physics Informed Neural Networks (ICLR 2025 · similarity 0.89)
- The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.88)
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