Shell-horizon certificates bound rollout steps on decoded physical invariants from measurable model defects in latent world models, showing some geometric priors survive representation learning while others do not.
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Boundary-conformal quadrature with closed-form azimuthal coefficients, tangency-based panel splitting, and square-root substitution restores spectral and fourth-order convergence in IITM for convex polyhedra.
Z²-Sampling implicitly realizes zero-cost zigzag trajectories for curvature-aware semantic alignment in diffusion models by reducing multi-step paths via operator dualities and temporal caching while synthesizing a directional derivative penalty.
An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.
Spectral Deferred Correction methods achieve at least order p after p iterations when viewed as Runge-Kutta methods, with order jumps of two possible for collocation methods using specific implicit error discretizations.
Introduces semilinear order conditions for Runge-Kutta methods on stiff semilinear ODEs via orthogonality relations and rooted trees, proving uniform global error bounds independent of stiffness.
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
Enforcing semi-group consistency on a time-conditioned secant velocity field via Symmetry Rupture improves rollout accuracy and efficiency when learning physical dynamics from discrete observations.
A mixed formulation for Cosserat rod dynamics is cast as an infinite-dimensional nonlinear port-Hamiltonian system and discretized with structure-preserving finite elements to yield energy-momentum consistent time integration.
High-order essentially explicit discretizations using Fourier Galerkin plus projection-relaxation conserve mass, momentum, and energy for BBM, KdV, and NLS equations.
A fully discrete strain-based model for continuum robot dynamics via Lie group variational integrators, combined with an EKF-based observer for states and disturbances, validated on hardware.
ELGIN is a graph-based physics-informed surrogate model that predicts carrier flow and polydisperse particle motion in dental aerosol scenarios, achieving lower tracking errors and 37x speedup versus full OpenFOAM CFD in a preliminary single-case test.
An open-source Jax-based SPH simulator generates training data for LPV state-space surrogates that approximate fuel sloshing dynamics and enable 100x faster closed-loop spacecraft simulations under zero gravity.
citing papers explorer
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When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models
Shell-horizon certificates bound rollout steps on decoded physical invariants from measurable model defects in latent world models, showing some geometric priors survive representation learning while others do not.
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Boundary-conformal integration for the invariant-imbedding T-matrix method: high-order convergence for faceted particles
Boundary-conformal quadrature with closed-form azimuthal coefficients, tangency-based panel splitting, and square-root substitution restores spectral and fourth-order convergence in IITM for convex polyhedra.
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$Z^2$-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models
Z²-Sampling implicitly realizes zero-cost zigzag trajectories for curvature-aware semantic alignment in diffusion models by reducing multi-step paths via operator dualities and temporal caching while synthesizing a directional derivative penalty.
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Adaptive Riemannian Manifold Hamiltonian Monte Carlo with Hierarchical Metric
An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.
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Spectral Deferred Corrections in the framework of Runge-Kutta methods
Spectral Deferred Correction methods achieve at least order p after p iterations when viewed as Runge-Kutta methods, with order jumps of two possible for collocation methods using specific implicit error discretizations.
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A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
Introduces semilinear order conditions for Runge-Kutta methods on stiff semilinear ODEs via orthogonality relations and rooted trees, proving uniform global error bounds independent of stiffness.
-
A Diagnostic Software Suite for Auditing Learned PDE Simulators
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
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Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency
Enforcing semi-group consistency on a time-conditioned secant velocity field via Symmetry Rupture improves rollout accuracy and efficiency when learning physical dynamics from discrete observations.
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Mixed formulation and structure-preserving discretization of Cosserat rod dynamics in a port-Hamiltonian framework
A mixed formulation for Cosserat rod dynamics is cast as an infinite-dimensional nonlinear port-Hamiltonian system and discretized with structure-preserving finite elements to yield energy-momentum consistent time integration.
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Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schr\"odinger equations
High-order essentially explicit discretizations using Fourier Galerkin plus projection-relaxation conserve mass, momentum, and energy for BBM, KdV, and NLS equations.
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Discrete Geometric Modeling and Extended State Estimation of Continuum Robots
A fully discrete strain-based model for continuum robot dynamics via Lie group variational integrators, combined with an EKF-based observer for states and disturbances, validated on hardware.
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Physics-Informed Graph Neural Network Surrogates for Turbulent Nanoparticle Dispersion in Dental Clinical Environments
ELGIN is a graph-based physics-informed surrogate model that predicts carrier flow and polydisperse particle motion in dental aerosol scenarios, achieving lower tracking errors and 37x speedup versus full OpenFOAM CFD in a preliminary single-case test.
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Data-driven Learning of LPV Surrogate Models of Fuel Sloshing
An open-source Jax-based SPH simulator generates training data for LPV state-space surrogates that approximate fuel sloshing dynamics and enable 100x faster closed-loop spacecraft simulations under zero gravity.
- A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold