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
7 Pith papers cite this work. Polarity classification is still indexing.
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CHOP reduces relative inference error on OOD operator tasks for scalar conservation laws and mean-field control by composing frozen ICON with explicit closed-form elementary operators that remain interpretable.
IV-Net is a multigrid-inspired convolutional neural operator that approximates solutions to linear elliptic PDEs with high-contrast coefficients and shows better accuracy than POD and other neural operators on heterogeneous coercive problems.
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.
PI-DOSnet is a physics-informed operator learning framework using operator splitting that enables data-free long-time inference of evolution PDE solutions, with energy stability shown for the Allen-Cahn equation at large time steps.
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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Harness In-Context Operator Learning with Chain of Operators
CHOP reduces relative inference error on OOD operator tasks for scalar conservation laws and mean-field control by composing frozen ICON with explicit closed-form elementary operators that remain interpretable.
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IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients
IV-Net is a multigrid-inspired convolutional neural operator that approximates solutions to linear elliptic PDEs with high-contrast coefficients and shows better accuracy than POD and other neural operators on heterogeneous coercive problems.
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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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PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations
PI-DOSnet is a physics-informed operator learning framework using operator splitting that enables data-free long-time inference of evolution PDE solutions, with energy stability shown for the Allen-Cahn equation at large time steps.
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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.