A unified training framework for mesh-based ML surrogates in CFD improves accuracy and long-horizon stability by enforcing spatial derivative consistency via multi-node prediction, using temporal cross-attention correction, and adding 3D rotary positional embeddings.
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Modulation-based meta-learning in a Hamiltonian framework enables accurate few-shot adaptation and generalization across parameter space for structure-preserving dynamics without explicit system parameterization.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
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Mesh Based Simulations with Spatial and Temporal awareness
A unified training framework for mesh-based ML surrogates in CFD improves accuracy and long-horizon stability by enforcing spatial derivative consistency via multi-node prediction, using temporal cross-attention correction, and adding 3D rotary positional embeddings.
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Meta-learning Structure-Preserving Dynamics
Modulation-based meta-learning in a Hamiltonian framework enables accurate few-shot adaptation and generalization across parameter space for structure-preserving dynamics without explicit system parameterization.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.