arXiv subjects

Andy Zhu

Publications and source records attributed to Andy Zhu.

8 recordsLinked to original sources

arXiv2026

AI CFD Scientist: Toward Open-Ended Computational Fluid Dynamics Discovery with Physics-Aware AI Agents

Recent LLM-based agents have closed substantial portions of the scientific discovery loop in software-only machine-learning research, in chemistry, and in biology. Extending the same loop to high-fidelity physical simulators is harder, because solver completion does not imply physical validity and many failure modes appear only in field-level imagery rather than in solver logs. We present AI CFD Scientist, an open-source AI scientist for computational fluid dynamics (CFD) that, to our knowledge, is the first to span literature-grounded ideation, validated execution, vision-based physics verification, source-code modification, and figure-grounded writing within a single inspectable workflow. Three coupled pathways cover parameter sweeps within a fixed solver, case-local C++ library compilation for new physical models, and open-ended hypothesis search against a reference comparator, all running on OpenFOAM through Foam-Agent. At the center of the framework is a vision-language physics-verification gate that inspects rendered flow fields before any result is accepted, rerun, or written into a manuscript. On five tasks under a shared GPT-5.5 backbone, AI CFD Scientist autonomously discovers a Spalart-Allmaras runtime correction that reduces lower-wall Cf RMSE against DNS by 7.89% on the periodic hill at Reh=5600; under matched LLM cost, two strong general AI-scientist baselines (ARIS, DeepScientist) execute partial CFD workflows but lack the domain-specific validity gates needed to convert runs into defensible scientific claims; and a controlled planted-failure ablation shows that the vision-language gate detects 14 of 16 silent failures missed by solver-level checks. Code, prompts, and run artifacts are released at https://github.com/csml-rpi/cfd-scientist.

physics.flu-dyn↗

arXiv2026

MoEEdit: Efficient and Routing-Stable Knowledge Editing for Mixture-of-Experts LLMs

Knowledge editing (KE) enables precise modifications to factual content in large language models (LLMs). Existing KE methods are largely designed for dense architectures, limiting their applicability to the increasingly prevalent sparse Mixture-of-Experts (MoE) models that underpin modern scalable LLMs. Although MoEs offer strong efficiency and capacity scaling, naively adapting dense-model editors is both computationally costly and prone to routing distribution shifts that undermine stability and consistency. To address these challenges, we introduce MoEEdit, the first routing-stable framework for parameter-modifying knowledge editing in MoE LLMs. Our method reparameterizes expert updates via per-expert null-space projections that keep router inputs invariant and thereby suppress routing shifts. The resulting block-structured optimization is solved efficiently with a block coordinate descent (BCD) solver. Experiments show that MoEEdit attains state-of-the-art efficacy and generalization while preserving high specificity and routing stability, with superior compute and memory efficiency. These results establish a robust foundation for scalable, precise knowledge editing in sparse LLMs and underscore the importance of routing-stable interventions.

cs.LG↗

arXiv2026

GRIP: Algorithm-Agnostic Machine Unlearning for Mixture-of-Experts via Geometric Router Constraints

Machine unlearning in Mixture-of-Experts (MoE) large language models presents a critical yet under-explored challenge. Current unlearning methods applied to MoE architectures often exploit dynamic routing as an optimization shortcut: rather than genuinely erasing knowledge from expert parameters, they manipulate routers to redirect queries away from the originally assigned experts. This not only causes severe utility degradation but also leaves hazardous knowledge intact. Consequently, adversaries can bypass the router to recover sensitive information directly from dormant experts. In this study, we propose Geometric Routing Invariance Preservation (GRIP), an algorithm-agnostic framework that resolves these failure modes by enforcing hard geometric constraints on router updates. By projecting router gradient updates into the null space of the retain set's routing matrix, GRIP suppresses routing manipulation without freezing the router entirely, thereby directing the unlearning pressure into the expert parameters themselves across all relevant experts. GRIP offers two complementary variants: training-time stochastic projection and a post-training closed-form analytical correction. Extensive experiments on two MoE models across hazardous knowledge removal and copyright unlearning benchmarks demonstrate that GRIP restores routing stability from 0.21 to >0.94, improves retain accuracy by up to 89%, and reduces white-box adversarial knowledge recovery from 11% to just 3% while in line with dense-architecture unlearning under black-box prompt attack, establishing geometric constraints as a principled solution for genuine unlearning in sparse MoE architectures.

cs.LG↗

arXiv2025

Mod-5 Galois images from abelian surfaces

For $J$ an abelian surface, the Galois representation $\varrho_{J, \ell} : {\rm Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \rightarrow {\rm Aut}(J[\ell]) \simeq {\rm GSp}_4(\mathbb{F}_\ell)$ is typically surjective, with smaller images indicating extra arithmetic structure. It is already known how to probabilistically compute whether $\rho_{J, \ell}$ is surjective, and recent work by Chidambaram computes $\operatorname{im} \rho_{J, \ell}$ for $\ell = 2, 3$. We probabilistically compute $\rho_{J, 5}$ for the Jacobians of 95% of genus 2 curves in the L-functions and Modular Forms Database (LMFDB) for which $\rho_{J, 5}$ is not yet known. For the remaining Jacobians, we determine the order of the image and give a short list of candidate images.

math.NT↗

arXiv2025

A Role-Aware Multi-Agent Framework for Financial Education Question Answering with LLMs

Question answering (QA) plays a central role in financial education, yet existing large language model (LLM) approaches often fail to capture the nuanced and specialized reasoning required for financial problem-solving. The financial domain demands multistep quantitative reasoning, familiarity with domain-specific terminology, and comprehension of real-world scenarios. We present a multi-agent framework that leverages role-based prompting to enhance performance on domain-specific QA. Our framework comprises a Base Generator, an Evidence Retriever, and an Expert Reviewer agent that work in a single-pass iteration to produce a refined answer. We evaluated our framework on a set of 3,532 expert-designed finance education questions from Study.com, an online learning platform. We leverage retrieval-augmented generation (RAG) for contextual evidence from 6 finance textbooks and prompting strategies for a domain-expert reviewer. Our experiments indicate that critique-based refinement improves answer accuracy by 6.6-8.3% over zero-shot Chain-of-Thought baselines, with the highest performance from Gemini-2.0-Flash. Furthermore, our method enables GPT-4o-mini to achieve performance comparable to the finance-tuned FinGPT-mt_Llama3-8B_LoRA. Our results show a cost-effective approach to enhancing financial QA and offer insights for further research in multi-agent financial LLM systems.

cs.CL↗

arXiv2024

A Report on Financial Regulations Challenge at COLING 2025

Financial large language models (FinLLMs) have been applied to various tasks in business, finance, accounting, and auditing. Complex financial regulations and standards are critical to financial services, which LLMs must comply with. However, FinLLMs' performance in understanding and interpreting financial regulations has rarely been studied. Therefore, we organize the Regulations Challenge, a shared task at COLING 2025. It encourages the academic community to explore the strengths and limitations of popular LLMs. We create 9 novel tasks and corresponding question sets. In this paper, we provide an overview of these tasks and summarize participants' approaches and results. We aim to raise awareness of FinLLMs' professional capability in financial regulations.

cs.CE↗

arXiv2023

Personalized Predictions of Glioblastoma Infiltration: Mathematical Models, Physics-Informed Neural Networks and Multimodal Scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans.Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion PDE model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse domain method is employed to handle the complex brain geometry within the PINN framework. Our method is validated both on synthetic and patient datasets, and shows promise for real-time parametric inference in the clinical setting for personalized GBM treatment.

cs.LG↗

arXiv2013

Multireference Alignment using Semidefinite Programming

The multireference alignment problem consists of estimating a signal from multiple noisy shifted observations. Inspired by existing Unique-Games approximation algorithms, we provide a semidefinite program (SDP) based relaxation which approximates the maximum likelihood estimator (MLE) for the multireference alignment problem. Although we show that the MLE problem is Unique-Games hard to approximate within any constant, we observe that our poly-time approximation algorithm for the MLE appears to perform quite well in typical instances, outperforming existing methods. In an attempt to explain this behavior we provide stability guarantees for our SDP under a random noise model on the observations. This case is more challenging to analyze than traditional semi-random instances of Unique-Games: the noise model is on vertices of a graph and translates into dependent noise on the edges. Interestingly, we show that if certain positivity constraints in the SDP are dropped, its solution becomes equivalent to performing phase correlation, a popular method used for pairwise alignment in imaging applications. Finally, we show how symmetry reduction techniques from matrix representation theory can simplify the analysis and computation of the SDP, greatly decreasing its computational cost.

cs.DS↗