Low-L2-error neural operators for PDE warm-starts can yield indefinite Jacobians; energy-penalized fine-tuning restores positive definiteness and achieves up to 5.4x speedup on 6.4M DOF hyperelasticity problems.
Unified form language: A domain-specific language for weak formulations of partial differential equations
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A constrained LLM front-end for FEniCS multi-physics simulations dispatches to human-written templates and achieves 100% valid parses plus 90-100% geometry success on benchmarks while avoiding LLM-generated solver code.
A structure-preserving upwind DG scheme with convex splitting for the Cahn-Hilliard-Darcy tumor growth model that maintains mass conservation, pointwise bounds, and a discrete energy law.
A Bloch domain wall in a ferromagnetic racetrack between superconductors allows position-based control of the Josephson critical current with tunable 0-pi transitions and current loop formation.
Stochastic material heterogeneity modeled with Gaussian random fields in a nonlocal framework fundamentally changes phase nucleation, localization, and macroscopic mechanical response in architected metamaterials.
Numerical construction of Hayward boson stars shows that frozen states produce Schwarzschild-like shadows with no extra photon rings while non-frozen states show multiple photon rings inside the shadow.
Metriplectic systems converge to entropy extrema at fixed Hamiltonian under stated conditions; a Landau-inspired class reduces the check to two simpler conditions for use in equilibrium relaxation schemes.
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
A conformal finite element and implicit Euler discretization is proposed and analyzed for the Biot-contact variational problem, proving existence, uniqueness, stability, and a priori error estimates, with numerical verification of the rates.
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Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Low-L2-error neural operators for PDE warm-starts can yield indefinite Jacobians; energy-penalized fine-tuning restores positive definiteness and achieves up to 5.4x speedup on 6.4M DOF hyperelasticity problems.
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A Constrained Natural-Language Interface for Variational Multi-Physics Finite Element Simulations in FEniCS
A constrained LLM front-end for FEniCS multi-physics simulations dispatches to human-written templates and achieves 100% valid parses plus 90-100% geometry success on benchmarks while avoiding LLM-generated solver code.
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Structure-preserving upwind DG scheme for a Cahn-Hilliard-Darcy model of tumor growth
A structure-preserving upwind DG scheme with convex splitting for the Cahn-Hilliard-Darcy tumor growth model that maintains mass conservation, pointwise bounds, and a discrete energy law.
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Josephson coupling through a magnetic racetrack
A Bloch domain wall in a ferromagnetic racetrack between superconductors allows position-based control of the Josephson critical current with tunable 0-pi transitions and current loop formation.
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Influence of Heterogeneity on the Response of Architected Metamaterials
Stochastic material heterogeneity modeled with Gaussian random fields in a nonlocal framework fundamentally changes phase nucleation, localization, and macroscopic mechanical response in architected metamaterials.
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Light Rings, Accretion Disks and Shadows of Hayward Boson Stars
Numerical construction of Hayward boson stars shows that frozen states produce Schwarzschild-like shadows with no extra photon rings while non-frozen states show multiple photon rings inside the shadow.
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Metriplectic relaxation to equilibria
Metriplectic systems converge to entropy extrema at fixed Hamiltonian under stated conditions; a Landau-inspired class reduces the check to two simpler conditions for use in equilibrium relaxation schemes.
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On a linear DG approximation of chemotaxis models with damping gradient nonlinearities
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
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Numerical analysis of the Biot equations coupled to frictional contact mechanics
A conformal finite element and implicit Euler discretization is proposed and analyzed for the Biot-contact variational problem, proving existence, uniqueness, stability, and a priori error estimates, with numerical verification of the rates.