Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.
In the strictly negative definite case eΓ≺0, E(t)≤κ(K)E(0)e 2λmax(H)t ≤κ(K)E(0)e −2λmin(K)|λmax(eΓ)|t,(224) whereλ max(H)<0and κ(K) := λmax(K) λmin(K) .(225) 38
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When and Why Adversarial Training Improves PINNs: A Neural Tangent Kernel Perspective
Adversarial training improves PINNs by using the discriminator to mitigate spectral bias and stiffness, with a new NTK-based framework providing theoretical grounding and a practical algorithm.