A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
8 Pith papers cite this work. Polarity classification is still indexing.
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MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.
FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
AOT-POT adaptively reshapes complex PDE solution operators via input-dependent transformations and parallel stream mixing to enable effective large-scale pre-training, yielding SOTA results on 12 benchmarks with minimal added parameters.
U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
citing papers explorer
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Any-Dimensional Invariant Universality
A systematic approach maps any-dimensional invariant functions to a unique function on an infinite-dimensional limit space admitting a topology with compact sets where universality holds, with examples of non-universal architectures and fixes.
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A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds
MEEC equips point clouds with a discrete exterior calculus that satisfies exact conservation and is differentiable in point positions, allowing a single trained kernel to produce compatible physics on unseen geometries and parameters.
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Discovering Physical Directions in Weight Space: Composing Neural PDE Experts
Fine-tuning neural PDE operators to regime endpoints reveals a physical direction in weight space that CCM uses to compose accurate merged models for new or extrapolated regimes from metadata or short prefixes.
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FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation
FD-Bench supplies the first modular, reproducible benchmark and leaderboard for comparing neural PDE solvers on fluid dynamics tasks with direct numerical solver baselines.
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AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training
AOT-POT adaptively reshapes complex PDE solution operators via input-dependent transformations and parallel stream mixing to enable effective large-scale pre-training, yielding SOTA results on 12 benchmarks with minimal added parameters.
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U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics
U-HNO uses adaptive per-point routing in a U-shaped hybrid architecture to achieve state-of-the-art accuracy on PDE benchmarks with sharp localized features.
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Solving and learning advective multiscale Darcian dynamics with the Neural Basis Method
The Neural Basis Method uses a predefined neural basis space and operator residual metric to deliver accurate single solves and fast parametric learning for multiscale Darcian dynamics.
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A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.