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.
Pdeformer: Towards a foundation model for one- dimensional partial differential equations.arXiv preprint arXiv:2402.12652
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GeoPT pre-trains on over one million geometry samples augmented with synthetic dynamics to improve neural physics simulators on fluid and solid mechanics benchmarks while reducing labeled data needs by 20-60% and accelerating convergence by 2x.
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.
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.
citing papers explorer
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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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GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training
GeoPT pre-trains on over one million geometry samples augmented with synthetic dynamics to improve neural physics simulators on fluid and solid mechanics benchmarks while reducing labeled data needs by 20-60% and accelerating convergence by 2x.
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Flow marching for a generative PDE foundation model
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.
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A Mathematical Explanation of Transformers
The Transformer is interpreted as discretization of a structured integro-differential equation in continuous domains for tokens and features, unifying attention, feedforward, and normalization via operator and variational views.