TNOs lift neural operators to topological cell complexes via Discrete Exterior Calculus for cross-dimensional coupling, subsuming prior NOs and showing accuracy gains on PDE benchmarks with irregular geometries.
Briggs, Van Emden Henson, and Steve F
7 Pith papers cite this work, alongside 1,884 external citations. Polarity classification is still indexing.
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A spectral-multigrid Poisson solver for spherical and cylindrical coordinates achieves second-order accuracy on uniform and logarithmic radial grids with vacuum boundary handling via screening mass and scales to 4096 cores.
NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
A fused gather-GEMM-scatter CUDA kernel achieves 4.6-7.3x end-to-end speedup and 3.2-4.9x lower energy for matrix-free 3D SIMP topology optimization on RTX 4090 compared to three-stage baselines.
Cascading smoothers are sequences of single-step block-diagonal operators whose levels are chosen by Frobenius-norm minimization of successive error propagators and perform at or above classical smoothers on Poisson, interface, and Stokes problems.
The paper provides an exposition of multigrid basics in a variational setting, presenting the V-cycle as an iterative solver and full multigrid as a direct solver for discretization-level accuracy at low cost.
citing papers explorer
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Topological Neural Operators
TNOs lift neural operators to topological cell complexes via Discrete Exterior Calculus for cross-dimensional coupling, subsuming prior NOs and showing accuracy gains on PDE benchmarks with irregular geometries.
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A fast spectral-multigrid Poisson solver in non-Cartesian geometries
A spectral-multigrid Poisson solver for spherical and cylindrical coordinates achieves second-order accuracy on uniform and logarithmic radial grids with vacuum boundary handling via screening mass and scales to 4096 cores.
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NPSolver: Neural Poisson Solver with Iterative Physics Supervision
NPSolver trains neural Poisson solvers label-free by supervising with a small number of preconditioned conjugate gradient steps and adds Boundary-Aware Transolver for mixed boundaries, outperforming baselines on 2D/3D irregular geometries.
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NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
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Matrix-Free 3D SIMP Topology Optimization with Fused Gather-GEMM-Scatter Kernels
A fused gather-GEMM-scatter CUDA kernel achieves 4.6-7.3x end-to-end speedup and 3.2-4.9x lower energy for matrix-free 3D SIMP topology optimization on RTX 4090 compared to three-stage baselines.
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Cascading Smoothers for Multigrid
Cascading smoothers are sequences of single-step block-diagonal operators whose levels are chosen by Frobenius-norm minimization of successive error propagators and perform at or above classical smoothers on Poisson, interface, and Stokes problems.
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Multigrid Primer: Basic Principles
The paper provides an exposition of multigrid basics in a variational setting, presenting the V-cycle as an iterative solver and full multigrid as a direct solver for discretization-level accuracy at low cost.