arXiv subjects

Jianda Du

Publications and source records attributed to Jianda Du.

4 recordsLinked to original sources

arXiv2026

Agon: An Autonomous Large-Scale Omnidisciplinary Research System Built on Prompt Economy

Large language models are making research production scalable, shifting the bottleneck from producing artifacts to judging claims. We present \textsc{Agon}, a research orchestrator that validates what can be checked inside the workflow and leaves the remaining judgments to human scientists. \textsc{Agon} is built on six design principles: Prompt Economy, Future-Facing, Minimal Prompts, OmniDisciplinary, Massive Parallelism, and Zero-Code. We ran \textsc{Agon} across domains for 444 iterations of Prompt Economy loops, using only small starting topics and no human-written experimental code. These deployments demonstrate scalability while exposing new classes of failure. We organize these failures into a taxonomy along severity, fixability, visibility, and capability locus. The taxonomy separates failures the loops can see and fix from those that require human judgment. Together, these results show that \textsc{Agon} is pushing research toward a new paradigm: machine scales, human steers.

cs.SE↗

arXiv2026

AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing

PDEs are central to scientific and engineering modeling, yet designing accurate numerical solvers typically requires substantial mathematical expertise and manual tuning. Recent neural network-based approaches improve flexibility but often demand high computational cost and suffer from limited interpretability. We introduce \texttt{AutoNumerics}, a multi-agent framework that autonomously designs, implements, debugs, and verifies numerical solvers for general PDEs directly from natural language descriptions. Unlike black-box neural solvers, our framework generates transparent solvers grounded in classical numerical analysis. We introduce a coarse-to-fine execution strategy and a residual-based self-verification mechanism. Experiments on 24 canonical and real-world PDE problems demonstrate that \texttt{AutoNumerics} achieves competitive or superior accuracy compared to existing neural and LLM-based baselines, and correctly selects numerical schemes based on PDE structural properties, suggesting its viability as an accessible paradigm for automated PDE solving.

cs.AI↗

arXiv2024

Learning Epidemiological Dynamics via the Finite Expression Method

Modeling and forecasting the spread of infectious diseases is essential for effective public health decision-making. Traditional epidemiological models rely on expert-defined frameworks to describe complex dynamics, while neural networks, despite their predictive power, often lack interpretability due to their ``black-box" nature. This paper introduces the Finite Expression Method, a symbolic learning framework that leverages reinforcement learning to derive explicit mathematical expressions for epidemiological dynamics. Through numerical experiments on both synthetic and real-world datasets, FEX demonstrates high accuracy in modeling and predicting disease spread, while uncovering explicit relationships among epidemiological variables. These results highlight FEX as a powerful tool for infectious disease modeling, combining interpretability with strong predictive performance to support practical applications in public health.

cs.LG↗

arXiv2024

Gromov-Hausdorff distances between quotient metric spaces

The Hausdorff distance measures how far apart two sets are in a common metric space. By contrast, the Gromov-Hausdorff distance provides a notion of distance between two abstract metric spaces. How do these distances behave for quotients of spaces under group actions? Suppose a group $G$ acts by isometries on two metric spaces $X$ and $Y$. In this article, we study how the Hausdorff and Gromov-Hausdorff distances between $X$ and $Y$ and their quotient spaces $X/G$ and $Y/G$ are related. For the Hausdorff distance, we show that if $X$ and $Y$ are $G$-invariant subsets of a common metric space, then we have $d_{\mathrm{H}}(X,Y)=d_{\mathrm{H}}(X/G,Y/G)$. However, the Gromov-Hausdorff distance does not preserve this relationship: we show how to make the ratio $\frac{d_{\mathrm{GH}}(X/G,Y/G)}{d_{\mathrm{GH}}(X,Y)}$ both arbitrarily large and arbitrarily small, even if $X$ is an arbitrarily dense $G$-invariant subset of $Y$.

math.MG↗