Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
Generative latent neural PDE solver using flow matching
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Enforcing semi-group consistency on a time-conditioned secant velocity field via Symmetry Rupture improves rollout accuracy and efficiency when learning physical dynamics from discrete observations.
PerFlow decouples observation conditioning from physics enforcement in rectified flows using constraint-preserving projections and invariance guarantees for fast, physics-consistent reconstruction of spatiotemporal dynamics.
Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.
Di-BiLPS combines a variational autoencoder, latent diffusion, and contrastive learning to achieve state-of-the-art accuracy on PDE problems with as little as 3% observations while supporting zero-shot super-resolution and lower computational cost.
Stronger physics priors in neural networks for spatio-temporal shear flow forecasting yield substantially lower training carbon footprints than weak or no priors, though inference savings are less consistent.
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Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
Enforcing semi-group consistency on a time-conditioned secant velocity field via Symmetry Rupture improves rollout accuracy and efficiency when learning physical dynamics from discrete observations.
- Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing