A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
Data-driven discovery of partial differential equations.Science advances, 3(4):e1602614
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EqOD combines symmetry-based library reduction with stability selection to reach F1=1.000 on several noisy PDE identification tasks where prior methods fail.
Higher-order LaSDI uses a high-order finite-difference scheme and rollout loss to improve long-term prediction accuracy in reduced-order models for parameterized PDEs, shown on the 2D Burgers equation.
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Physics-Informed Neural Networks for Joint Source and Parameter Estimation in Advection-Diffusion Equations
A multi-network PINN with NTK-based adaptive weighting jointly estimates source functions, velocity, diffusion parameters, and the solution field in advection-diffusion PDEs from noisy sparse data.
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EqOD: Symmetry-Informed Stability Selection for PDE Identification
EqOD combines symmetry-based library reduction with stability selection to reach F1=1.000 on several noisy PDE identification tasks where prior methods fail.
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Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
Higher-order LaSDI uses a high-order finite-difference scheme and rollout loss to improve long-term prediction accuracy in reduced-order models for parameterized PDEs, shown on the 2D Burgers equation.