Research

Journal and Conference Papers

[4] L. J. Shikhman. Semigroup Consistency as a Diagnostic for Learned Physics Simulators. AI4Physics Workshop at the 43rd International Conference on Machine Learning. [paper][arXiv]

[3] L. J. Shikhman. Diagnosing Failure Modes of Neural Operators Across Classes of PDEs, Transactions on Machine Learning Research. [paper][arXiv][code]

[2] N. Welsh*, L. J. Shikhman*, M. N. Attzs, S. K. Putane, V. M. Nguyen, R. T. White. Post-Launch Capability Expansion of Vision-Language Models via Prompting for On-Orbit Spacecraft Inspection. CVPR 2026 Workshop on AI4Space. [paper] [arXiv]

[1] L. J. Shikhman. One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers. AI & PDEs Workshop at the 14th International Conference on Learning Representations. [paper][arxiv][code]

Invited Talks

[1] L. J. Shikhman, L. Lawler. Deploying Physics Models at the Edge: Quantized AI for Weather and Fluid Simulation on Dell Pro Max with GB10. Optimized AI Conference, 2026, Atlanta, GA.

Manuscripts in Review

[6] L.J. Shikhman, S. Gilbertie. Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs. Submitted to Journal of Computational Physics. [arXiv]

[5] L. J. Shikhman. Kernel-Robust Dynamics for Reaction-Diffusion Equations with Measure-Valued Delay. Under review at Nonlinear Differential Equations and Applications. [arXiv]

[4] L. J. Shikhman, L. DiPaulo. HS-FNO: History-Space Fourier Neural Operators for Delayed Distributed-Parameter Control Systems. Submitted to AIAA SciTech Forum 2027.

[3] L. J. Shikhman, N. Welsh, R. T. White. Frozen Vision–Language Models for Low-SWaP Spacecraft Inspection. Submitted to AIAA SciTech Forum 2027.

[2] S. Koenig, L. J. Shikhman. Operator Learning for PDE-Constrained Design Optimization of Aerospace Propulsion Flow Fields. Submitted to AIAA SciTech Forum 2027.

[1] L. J. Shikhman, M. Galarnyk, A. Dash, N. Welsh. Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes. Under review at the 40th Annual Conference on Neural Information Processing Systems.