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.
Therefore, ∇θL(X2) G = 1 Nr NrX i=1 R′ f(s i;ϕ) ∂sf(s i;ϕ)∇ θsi = 2 Nr NrX i=1 ri R′ f(X2) i ∂sf(X2) i ∇θri,(204) which proves the first statement
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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.