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.
Proof.Since ˙r(t) =K G rrγ(t),(175) left-multiplying byU ⊤ and usingK G rr =UΛU ⊤ gives ˙er(t) =U ⊤ ˙r(t) =U ⊤K G rrγ(t) =U ⊤UΛU ⊤γ(t) = Λeγ(t),(176) which proves (167)
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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.