Langevin Sampling and Diffusion Estimation for Molecular Systems
May 2026 – present · Research Collaborator, Department of Mathematics, Iowa State University. Advisor: Prof. David Herzog. Funded by NSF award DMS-2246491.
- Built an end-to-end Python simulation pipeline implementing MALA and projected Euler–Maruyama samplers for overdamped Langevin dynamics, staged from a one-dimensional periodic potential to a solvated ion in a three-dimensional Lennard-Jones bath; estimated self-diffusion and mobility coefficients from long-run trajectory data.
- Derived the closed-form Lifson–Jackson diffusivity D = 1/I₀(1)² ≈ 0.62386 as an exact benchmark and validated the estimators against it before scaling to three dimensions, where the pipeline reproduces published solvated-ion results.
- Author weekly technical reports, including a companion note supporting the group's CLT-based error analysis.
Large Deviation Theory for Rare-Event Analysis in Queueing Systems
Nov. 2024 – present · Undergraduate Research Fellow, Department of Mathematics, Iowa State University. Advisor: Prof. Ruoyu Wu. Dean's High Impact Undergraduate Research Award.
- Developed the first importance-sampling methodology for rare-event estimation in the mean-field join-the-shortest-queue model, deriving state-dependent exponential tilting from the Budhiraja–Friedlander–Wu (2021) large-deviation rate function; stated a logarithmic-efficiency conjecture with a proof sketch via the Dupuis–Wang subsolution framework.
- Built a reproducible, performance-tuned Python simulation framework (Xoshiro256** with deterministic seeding) and validated it across 27 configurations (n ≤ 100, ρ ∈ {0.7, 0.9, 0.95}): estimates agree with crude Monte Carlo within 95% confidence intervals wherever crude Monte Carlo succeeds, and extend to probabilities as small as 10⁻³¹, where it fails entirely.
- Designed and benchmarked two heuristic tilting families (rate-reversal, level-weighted) with pilot-run selection; diagnosed over-tilting at extreme rarity through likelihood-ratio calibration statistics, motivating the ongoing computation of the optimal state-dependent tilt.
Stability Analysis of Cell-Average Neural Networks for PDEs
May 2026 – present · Undergraduate Researcher, Department of Mathematics, Iowa State University. Advisor: Prof. Jue Yan. Funded by the NSF D4 NRT. Joint with Mengyuan Yang.
- Adapting von Neumann stability analysis to neural-network PDE solvers: deriving the linearized amplification factor of the learned time-stepping scheme and characterizing how perturbations propagate through it, toward stability conditions on the trained weights analogous to those of classical finite-difference methods.
- Reimplementing the group's solver in Python to enable systematic stability experiments across schemes and step sizes.
Metastable Failures in Prefix-Cached LLM Agent Serving
Aug. 2026 – present · Research project, Advanced Topics in High-Performance Computing (COM S 6250), Department of Computer Science, Iowa State University. Advisor: Prof. Ali Jannesari, SwaPP Lab.
- Asking whether a short burst of agent traffic can push a healthy LLM serving engine into a self-sustaining all-miss, low-throughput state, and which scheduling and admission mechanisms prevent it. Built a discrete-event simulator of a continuous-batching engine with prefix caching (scheduling policies, eviction rules, memory-allocation modes, and re-implementations of recently proposed mechanisms) and a queueing-theoretic "thrashing curve" model of when caching helps, when it collapses, and when admission control restores stability.
- Run real-engine experiments (SGLang serving a 7B-parameter model on NVIDIA A100 GPUs) on Iowa State's Nova HPC cluster through SLURM, with predictions registered before each run, paired control arms, and every reported number traced to a results directory, a commit and a cluster job ID. Toward an arXiv preprint.
Calibrating Volatility Forecasts with Early, One-Sided Feedback
Aug. 2026 – present · Research project, Advanced Topics in Machine Learning (COM S 6730), Department of Computer Science, Iowa State University. Advisor: Prof. Hongyang Gao.
- A forecast of a cumulative quantity is scored only when its horizon ends, but its increments are non-negative, so a miss becomes certain the moment the running sum crosses the issued bound. Designed a model-agnostic calibration layer over any quantile forecaster that credits those certain early misses and keeps explicit accounts of forecasts still pending; proved its long-run coverage guarantee under early crediting, bounded correction and missing data, and checked it numerically over tens of thousands of adversarial runs.
- Built a leakage-audited data pipeline (5-minute spot bars, 2020–2025, with a sealed and hashed test set), a regime-shift simulation study with exact oracle quantiles and pre-registered hypotheses, and delayed-feedback conformal and classical volatility baselines, including a temporal convolutional network trained on HPC GPUs. Paper in preparation.
Reliability of Tool-Using LLM Agents
Aug. 2026 – present · Research project, Advanced Topics in Artificial Intelligence (COM S 6720), Department of Computer Science, Iowa State University. Advisor: Prof. Yang Li.
- When an agent stalls, when is restarting it worth more than waiting, and how can the probability of a failure too rare for direct simulation be estimated? Two pre-registered pilots on real agents, one on restart policies and one on rare failures, with the direction still being chosen.