Construction of C^{β0} (β0<1/3) divergence-free vector fields and κ_q → 0 such that advection-diffusion scalars exhibit anomalous dissipation while remaining bounded in C^α0 with β0 + 2α0 < 1, confirming the Armstrong-Vicol conjecture.
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Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.
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Scalar anomalous dissipation and optimal regularity via iterated homogenization
Construction of C^{β0} (β0<1/3) divergence-free vector fields and κ_q → 0 such that advection-diffusion scalars exhibit anomalous dissipation while remaining bounded in C^α0 with β0 + 2α0 < 1, confirming the Armstrong-Vicol conjecture.
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Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.