SGNO achieves stable long-horizon PDE rollouts by organizing autoregressive steps as spectral evolution updates with a constrained diagonal generator and learned correction, delivering a median 74.8% reduction in GMean100 error across ten APEBench tasks.
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IRNO augments neural operators with learned fixed-point iterative refinement modules and a progressive spectral loss, achieving up to 56% error reduction on turbulent flow and large drops in high-frequency normalized errors on active matter.
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SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rollouts
SGNO achieves stable long-horizon PDE rollouts by organizing autoregressive steps as spectral evolution updates with a constrained diagonal generator and learned correction, delivering a median 74.8% reduction in GMean100 error across ten APEBench tasks.
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Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation
IRNO augments neural operators with learned fixed-point iterative refinement modules and a progressive spectral loss, achieving up to 56% error reduction on turbulent flow and large drops in high-frequency normalized errors on active matter.