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…
Forecasting Without Full Identification: Reliability and Computational Cost in Clot-Growth Simulation
Lennon J. Shikhman, Ying Qian, Lily DiPaulo +1
We forecast clot growth from sparse early measurements with incomplete biochemical information. Using 1,000 simulated trajectories, we compare inverse search, which weights candida…
Discretization and Statistical Consistency of Functional Flow Matching
Lennon J. Shikhman
Functional flow matching learns to generate random functions, such as velocity fields or solutions of partial differential equations, by continuously transforming a simple probabil…
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…
PDECheck: A Diagnostic Software Suite for Auditing Learned PDE Simulators
Lennon J. Shikhman
PDECheck audits learned PDE simulators through callable propagators or saved predictions. It evaluates relative error, temporal composition, finite-difference generators, and…
Post-Launch Capability Expansion of Vision-Language Models via Prompting for On-Orbit Spacecraft Inspection
Nicholas A. Welsh, Lennon J. Shikhman, Monty Nehru Attazs +3
Spaceborne inspection systems often deploy perception models prior to launch, after which updating model weights or expanding fixed label sets becomes operationally impractical. Wh…
Kernel-Robust Dynamics for Reaction-Diffusion Equations with Measure-Valued Delay
Lennon Shikhman
We study reaction-diffusion equations with finite signed measure delays and nonlinear, possibly nonlocal feedback. We treat abstract reactions that are Lipschitz on bounded -b…
Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
Lennon J. Shikhman, Shane Gilbertie
Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data. Physical states a…
Semigroup Consistency as a Diagnostic for Learned Physics Simulators
Lennon J. Shikhman
Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout.…
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
Lennon J. Shikhman
Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field…
One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers
Lennon J. Shikhman
Neural PDE solvers are often described as learning solution operators that map problem data to PDE solutions. In this work, we argue that this interpretation is generally incorrect…
Entropy Production in Machine Learning Under Fokker-Planck Probability Flow
Lennon Shikhman
Machine learning models deployed in nonstationary environments inevitably experience performance degradation due to data drift. While numerous drift detection heuristics exist, mos…
Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families
Lennon Shikhman
Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on…