DLDMF disentangles latent dynamics for parameterized PDEs by feeding parameters into a latent embedding that initializes a parameter-conditioned Neural ODE, then uses dynamic manifold fusion with a shared decoder to reconstruct spatiotemporal fields for better generalization and extrapolation.
On the construction and comparison of difference schemes.SIAM journal on numerical analysis, 5(3):506–517
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NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
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Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs
DLDMF disentangles latent dynamics for parameterized PDEs by feeding parameters into a latent embedding that initializes a parameter-conditioned Neural ODE, then uses dynamic manifold fusion with a shared decoder to reconstruct spatiotemporal fields for better generalization and extrapolation.
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Neural equilibria for long-term prediction of nonlinear conservation laws
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.