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.
hub
Message passing neural pde solvers
11 Pith papers cite this work. Polarity classification is still indexing.
11
Pith papers citing it
hub tools
citation-role summary
background 1
baseline 1
citation-polarity summary
verdicts
UNVERDICTED 11representative citing papers
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.
A latent Structured Spectral Propagator enables stable autoregressive PDE forecasting by decoupling spatial details from recurrent modal dynamics.
SP-ADMM learns energy-stable derivative stencils for Maxwell equations from noisy data by enforcing skew-adjointness through reduced parameterization of periodic convolution stencils.
IKNO replaces first-order kernel integrals in neural operators with infinite-order versions that have efficient closed-form approximations and reports SOTA accuracy on time-dependent and time-independent benchmarks.
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.
A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.
Late Fusion Neural Operators disentangle state and parameter learning to outperform FNO and CAPE-FNO on advection, Burgers, and reaction-diffusion PDEs with 72% average RMSE reduction in and out of domain.
A structure-preserving GNN solver for parametric hyperbolic conservation laws achieves superior long-horizon stability and orders-of-magnitude speedups over high-resolution simulations on supersonic flow benchmarks.
DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.
citing papers explorer
-
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.
-
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.
-
Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators
A latent Structured Spectral Propagator enables stable autoregressive PDE forecasting by decoupling spatial details from recurrent modal dynamics.
-
An Energy Stable Approach for Learning Derivative Operators from Noisy Data for Maxwells Equations
SP-ADMM learns energy-stable derivative stencils for Maxwell equations from noisy data by enforcing skew-adjointness through reduced parameterization of periodic convolution stencils.
-
IKNO: Infinite-order Kernel Neural Operators
IKNO replaces first-order kernel integrals in neural operators with infinite-order versions that have efficient closed-form approximations and reports SOTA accuracy on time-dependent and time-independent benchmarks.
-
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.
-
A Hybridizable Neural Time Integrator for Stable Autoregressive Forecasting
A hybrid transformer-FEM integrator provides provable discrete energy preservation and gradient bounds for stable autoregressive forecasting of chaotic systems, with 65x fewer parameters and 9000x speedup in a fusion surrogate trained on 12 simulations.
-
Late Fusion Neural Operators for Extrapolation Across Parameter Space in Partial Differential Equations
Late Fusion Neural Operators disentangle state and parameter learning to outperform FNO and CAPE-FNO on advection, Burgers, and reaction-diffusion PDEs with 72% average RMSE reduction in and out of domain.
-
A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws
A structure-preserving GNN solver for parametric hyperbolic conservation laws achieves superior long-horizon stability and orders-of-magnitude speedups over high-resolution simulations on supersonic flow benchmarks.
-
Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling
DIANO builds coarse-grid latent spaces for fluid dynamics data via neural operator encoding and decoding while integrating a differentiable PDE solver directly in the latent space for end-to-end physics-constrained training.
-
Neural equilibria for long-term prediction of nonlinear conservation laws
NeurDE learns the equilibrium closure within a kinetic solver to outperform larger neural models on long-term predictions of nonlinear conservation laws including shocks.