14 papers
Sharp spectral-scale stability for parabolic equations with measure-valued delay
Lennon J. Shikhman
We study the dependence of parabolic solution operators on a finite signed measure describing the delay law. For a positive self-adjoint generator with compact inverse, a weighted…
Predicting blood clot growth from sparse post-onset measurements with latent neural differential equations
Lennon J. Shikhman, Ying Qian, He Li
Computational models of blood clotting improve understanding of thrombus formation, but their clinical application remains limited because many model inputs are difficult to measur…
Discretization and Statistical Consistency of Functional Flow Matching
Lennon J. Shikhman
Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values. Under scattered or adaptive refinement, the resulti…
Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes
Lennon J. Shikhman, Michael Galarnyk, Aadi Dash +1
Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark expose…
Operator Boosting Produces Pareto-Efficient PDE Surrogates
Lennon J. Shikhman
Neural operators are widely used as surrogate solution maps for partial differential equations (PDEs), but full-size models can be costly to store, deploy, and evaluate in many-que…
A Diagnostic Software Suite for Auditing Learned PDE Simulators
Lennon J. Shikhman
Learned PDE simulators are increasingly used as low-cost replacements for expensive numerical solvers, but standard relative error does not determine whether a learned model…