Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
Journal of Computational physics , volume=
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Geometric Pareto Control embeds Pareto solutions in a Lie group submanifold and navigates via Riemannian gradient flow to achieve 100% feasibility and low suboptimality in control tasks without retraining.
A framework that structurally enforces divergence-free velocity and long-range transport coherence in 3D fluid reconstruction from 2D videos via divergence-free kernels advecting Lagrangian Gaussian splats.
Physics-informed constraints on implicit neural representations yield more accurate and stable predictions of stirred-tank flows than purely data-driven models when training data is scarce, with diminishing returns at larger dataset sizes.
A reinforcement learning policy learns to adaptively harvest data samples, improving empirical constraint satisfaction and training efficiency for Lyapunov NNs and PINNs.
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Physics-Informed Neural PDE Solvers via Spatio-Temporal MeanFlow
Spatio-Temporal MeanFlow adapts MeanFlow to PDEs by replacing the generative velocity field with the physical operator and extending the integral constraint to the spatio-temporal domain, yielding a unified solver for time-dependent and stationary equations with improved accuracy and generalization.
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Geometric Pareto Control: Riemannian Gradient Flow of Energy Function via Lie Group Homotopy
Geometric Pareto Control embeds Pareto solutions in a Lie group submanifold and navigates via Riemannian gradient flow to achieve 100% feasibility and low suboptimality in control tasks without retraining.
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LagrangianSplats: Divergence-Free Transport of Gaussian Primitives for Fluid Reconstruction
A framework that structurally enforces divergence-free velocity and long-range transport coherence in 3D fluid reconstruction from 2D videos via divergence-free kernels advecting Lagrangian Gaussian splats.
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Adaptive Data Harvesting for Efficient Neural Network Learning with Universal Constraints
A reinforcement learning policy learns to adaptively harvest data samples, improving empirical constraint satisfaction and training efficiency for Lyapunov NNs and PINNs.