CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
Unisolver: Pde-conditional transformers are universal pde solvers.arXiv preprint arXiv:2405.17527
6 Pith papers cite this work. Polarity classification is still indexing.
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MVNN learns measure-dependent drift terms in McKean-Vlasov equations from particle data using an embedding network, with proofs of well-posedness, propagation of chaos, and universal approximation under low-dimensional assumptions.
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
SuperWing supplies 4,239 diverse wing shapes and 28,856 flow-field solutions that let Transformer models predict surface aerodynamics to 2.5 drag-count error and generalize zero-shot to DLR-F6 and NASA CRM wings.
SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.
A replay-based continual learning strategy for physics-informed neural operators mitigates catastrophic forgetting on prior physical problems while enabling efficient adaptation to new data using only physical constraints.
citing papers explorer
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CATO: Charted Attention for Neural PDE Operators
CATO learns a continuous latent chart for efficient axial attention on PDE meshes and adds derivative-aware supervision to improve accuracy and reduce oversmoothing on general geometries.
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MVNN: A Measure-Valued Neural Network for Learning McKean-Vlasov Dynamics from Particle Data
MVNN learns measure-dependent drift terms in McKean-Vlasov equations from particle data using an embedding network, with proofs of well-posedness, propagation of chaos, and universal approximation under low-dimensional assumptions.
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Latent Generative Solvers for Generalizable Long-Term Physics Simulation
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
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SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design
SuperWing supplies 4,239 diverse wing shapes and 28,856 flow-field solutions that let Transformer models predict surface aerodynamics to 2.5 drag-count error and generalize zero-shot to DLR-F6 and NASA CRM wings.
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Spectral-inspired Operator Learning with Limited Data and Unknown Physics
SINO learns PDE operators from limited data using spectral features from frequency indices, a Pi-block for nonlinearities, and a low-pass filter, achieving 1-2 orders of magnitude better accuracy than prior methods on 2D/3D benchmarks.
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Replay-Based Continual Learning for Physics-Informed Neural Operators
A replay-based continual learning strategy for physics-informed neural operators mitigates catastrophic forgetting on prior physical problems while enabling efficient adaptation to new data using only physical constraints.