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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Message passing neural pde solvers
15 Pith papers cite this work. Polarity classification is still indexing.
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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.
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
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.
Multi-token prediction accounts for nearly all rollout stability gains on synthetic three-component seismograms, with sharp dependence on context covering the full P-S interval and magnitude-based losses unable to prevent polarity flips.
LEIA is a world model for autoregressive 3D simulation of architected materials under interactive loading, benchmarked on MicroPlate and applied to surrogate-guided de novo design search with finite-element validation.
AFNO learns continuous-time dynamics in latent space via flow matching for time-dependent PDEs to reduce error accumulation in long-horizon forecasts.
A constrained least-squares (ADMM) learns a skew-symmetric derivative stencil for 1D Maxwell equations that conserves discrete energy exactly while matching centered-difference accuracy.
citing papers explorer
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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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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.
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Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
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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.
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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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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.
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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.
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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.
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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.
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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.
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When Do Autoregressive Sequence Models Forecast Physical Wavefields? A Controlled Study on Synthetic Seismograms
Multi-token prediction accounts for nearly all rollout stability gains on synthetic three-component seismograms, with sharp dependence on context covering the full P-S interval and magnitude-based losses unable to prevent polarity flips.
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LEIA: Learned Environment for Interactive Architected Materials
LEIA is a world model for autoregressive 3D simulation of architected materials under interactive loading, benchmarked on MicroPlate and applied to surrogate-guided de novo design search with finite-element validation.
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Autoregression-Free Neural Operators for Time-Dependent PDEs
AFNO learns continuous-time dynamics in latent space via flow matching for time-dependent PDEs to reduce error accumulation in long-horizon forecasts.
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An Energy Stable Approach for Learning Derivative Operators from Noisy Data for Maxwells Equations
A constrained least-squares (ADMM) learns a skew-symmetric derivative stencil for 1D Maxwell equations that conserves discrete energy exactly while matching centered-difference accuracy.