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SS-ESOAP: Self-Scaled Adaptive Preconditioning for Physics-Informed Learning

arXiv · AI, language, vision and robotics · article · Aug 29, 2026 · UTC

Physics-informed neural networks (PINNs) often face ill-conditioned objectives that limit high-accuracy training. Dense quasi-Newton methods improve local conditioning but require expensive optimizer state, while Kronecker-factored methods such as SOAP scale to larger networks but rely on periodic basis updates. We introduce \method, which augments SOAP-style preconditioning with a scalar secant-energy correction adapted to Kronecker geometry and an adaptive basis update followed by variance-state downscaling. We characterize the directional secant matching induced by the scalar correction and

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