KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
Fourier continuation for exact derivative computation in physics- informed neural operators
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FNO extended to complex frequencies via Ehrenpreis-Palamodov principle improves state and optimal control learning for PDE systems, with order-of-magnitude lower training errors and better non-periodic boundary predictions on nonlinear Burgers' equation.
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
citing papers explorer
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KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
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FNO$^{\angle \theta}$: Extended Fourier neural operator for learning state and optimal control of distributed parameter systems
FNO extended to complex frequencies via Ehrenpreis-Palamodov principle improves state and optimal control learning for PDE systems, with order-of-magnitude lower training errors and better non-periodic boundary predictions on nonlinear Burgers' equation.
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Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.