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.
Scientific machine learning for closure models in multiscale problems: A review
7 Pith papers cite this work, alongside 4 external citations. Polarity classification is still indexing.
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Generalized Forcing Method generates diverse data for training linear transport PDE closure models via compatible body forces in zero-initial-condition simulations, with explicit and implicit variants applied to shear and inhomogeneous flows.
Conditional normalizing flows learn a probabilistic mapping from low-fidelity to high-fidelity ROM coefficients for closure correction in 2D Navier-Stokes vortex merging, with direct and residual strategies providing uncertainty quantification.
Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
Case study applies SAE probing with enstrophy triage to a continuum-dynamics foundation model and reports intermittent feature consistency that does not align with standard physics while linking some output discrepancies to specific feature changes.
Hybrid NODE retains mechanistic kinetics for free-radical polymerization and learns only the radical concentration closure, achieving RMSE 0.013 on noisy unseen conditions versus 0.31 and 0.68 for data-driven baselines with as few as ten measurements.
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.
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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Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models
Generalized Forcing Method generates diverse data for training linear transport PDE closure models via compatible body forces in zero-initial-condition simulations, with explicit and implicit variants applied to shear and inhomogeneous flows.
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Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows
Conditional normalizing flows learn a probabilistic mapping from low-fidelity to high-fidelity ROM coefficients for closure correction in 2D Navier-Stokes vortex merging, with direct and residual strategies providing uncertainty quantification.
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Wavelet Flow Matching for Multi-Scale Physics Emulation
Wavelet Flow Matching emulates multi-scale PDE-governed systems by transporting velocities directly in a hierarchical wavelet representation via U-Net, yielding improved long-horizon stability and spectral accuracy on fluid benchmarks.
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Sparse probes and murky physics: a case study of interpretability challenges in a foundation model for continuum dynamics
Case study applies SAE probing with enstrophy triage to a continuum-dynamics foundation model and reports intermittent feature consistency that does not align with standard physics while linking some output discrepancies to specific feature changes.
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Hybrid Neural Ordinary Differential Equations for Data-Efficient Polymerization Modeling with Incomplete Kinetics
Hybrid NODE retains mechanistic kinetics for free-radical polymerization and learns only the radical concentration closure, achieving RMSE 0.013 on noisy unseen conditions versus 0.31 and 0.68 for data-driven baselines with as few as ten measurements.
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Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.