<ul><li>Evolution equations, including ODEs and PDEs, are challenging to integrate accurately over long times.</li><li>Physics-informed neural networks (PINNs) offer a mesh-free framework for solving PDEs but suffer from temporal error accumulation.</li><li>To address this, integral regularization PINNs (IR-PINNs) introduce an integral-based residual term to improve temporal accuracy.</li><li>IR-PINNs outperform original PINNs and other methods in capturing long-time behaviors, providing a robust and accurate solution for evolution equations.</li></ul>

Integral regularization PINNs for evolution equations

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