Research map / Image generation / GANs

When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective

NeurIPS 2026 · Image generation › GANs · approach: GAN latent optimization and evaluation · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Analyzes adversarially trained PINNs (GAN-style discriminator shaping residual training) via a constant-NTK dynamical framework, derives a residual-energy descent law, and proposes an adaptive alternating scheme with rollback that improves PINN accuracy across several PDEs.

Problem

Adversarial (GAN-based) training improves PINNs empirically, but static optimal-discriminator divergence theory cannot explain why it works or fails; the training dynamics are not understood.

Approach

Model the discriminator-induced residual weighting in the NTK regime to derive a residual-energy decay law (dE/dt = r^T K γ); use this to define a rollback algorithm that keeps discriminator and generator updates only when they decrease residual energy.

Key results

• GAN-RB reaches 2.57e-06 validation error on viscous Burgers and 2.39e-11 on Laplace, versus 8.12e-06 for GAN without rollback.
• LSGAN-RB attains 5.86e-13 validation error on Poisson, versus 1.02e-08 for LSGAN and 9.78e-13 for DEQGAN.
• Under G:D=10:1 the positive part of r^T K γ has the lowest positive ratio (0.0075) and weakest violations among tested successful ratios.

Surprising findings

• Vanilla GAN and LSGAN perform well in practical alternating optimization despite the classical divergence theory suggesting degenerate training signal.
• Rollback is weaker for WGAN-GP and can hurt performance on some problems.

Limitations

• Constant-NTK assumption ignores kernel evolution and finite width.
• Training can still oscillate under some PDEs and settings even with rollback.
• Analysis is restricted to first-order, constant-kernel regime.

Experimental setup

Datasets: Poisson Laplace viscous Burgers Reaction-Diffusion Klein-Gordon

Benchmarks: Poisson Laplace viscous Burgers Reaction-Diffusion Klein-Gordon

Metrics: validation error training error residual energy positive ratio of r^T K γ

Baselines: DEQGAN GAN LSGAN WGAN-GP

Builds on: GAN LSGAN WGAN-GP DEQGAN neural tangent kernel

Closest papers by meaning

• Challenges in Training PINNs: A Loss Landscape Perspective (ICML 2024 · similarity 0.91)
• PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling (NeurIPS 2025 · similarity 0.89)
• Dual Cone Gradient Descent for Training Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.87)
• RoPINN: Region Optimized Physics-Informed Neural Networks (NeurIPS 2024 · similarity 0.87)
• Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective (NeurIPS 2025 · similarity 0.87)
• PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks (ICLR 2024 · similarity 0.87)