MaRDI Annual Meeting 2026

Often, several statistical methods can address a given research question for a given dataset. In many practical cases, particularly with complex data and sophisticated methods, mathematical theory alone cannot definitively determine which method is most appropriate. In this challenging context, empirical evaluations of method performance are crucial for developing guidance for data analysts. Researchers conducting these evaluations apply candidate methods to simulated or real datasets with varying characteristics relevant to the considered field of application and assess the results produced by these methods, which can be viewed as (statistical) research data.

In my talk, I will present work conducted by my group over the past few years on the appropriate design of such empirical evaluations, the identification of potential bias sources threatening replicability, and the use of these evaluations to provide reliable methodological guidance to data analysts. Specifically, I will share insights from the international 'STRengthening Analytical Thinking for Observational Studies' (STRATOS) initiative, which aims to deliver accessible and accurate guidance for the design and analysis of observational studies.

Turning powerful language models into reliable scientific collaborators takes more than model quality: it demands rigorous verification, mathematical guardrails, and an architecture that lets coding agents run long-horizon experiments autonomously. In this talk, I will present a practical framework for AI-assisted research that aims to compress the research cycle. The framework turns general-purpose coding agents into autonomous research assistants through a five-level taxonomy of human-AI collaboration, a set of methodological commandments encoding scientific rigor, and a sandboxed environment supporting sessions from quick explorations to multi-day, multi-node experiments. I will discuss the possibilities and limitations of agentic AI in research, and briefly illustrate the framework.

Der Beitrag stellt pHS-Bench vor, ein Benchmark-Projekt des SFB 1701 in Wuppertal für Methoden und Software im Bereich port-Hamiltonscher Systeme. Mit Leaderboard- und Blind-Testing-Funktionalitäten ergeben sich neue Fragestellungen, etwa zur Entwicklung geeigneter Metriken, zur fairen Evaluation und zur Akzeptanz in der Community. Eine Integration in MaRDIMark verspricht zugleich eine höhere Nachhaltigkeit, Reproduzierbarkeit und Sichtbarkeit der Benchmarks und eröffnet damit besondere Synergien zwischen pHS-Bench und MaRDI.

MathAlgoDB and MathModDB organize knowledge about numerical algorithms and mathematical models in MaRDI. We report on the current state of both databases and outline our plans for the second funding phase: merging them in content and technology on the MaRDI Portal so that they become part of the MaRDI knowledge graph, and extending the approach to further MaRDI databases and other classes of mathematical objects, such as statistical models. A key challenge is to populate these resources at scale: knowledge may come from experts directly or be extracted from existing scientific literature. We present an LLM-assisted workflow that transforms natural-language input into structured database proposals, using extraction contracts, JSON and SHACL validation, provenance, and human review. It can also analyze current articles to identify algorithms, models, numerical experiments, and their relationships. We discuss how this approach can support the scalable and reliable growth of mathematical knowledge graphs.

We sketch our plans for a community-led platform for publishing computational notebooks, in which each notebook is intended to receive a persistent identifier via Zenodo and be linked to the MaRDI Knowledge Graph. We outline the envisioned technical setup and first ideas for FAIR-compliant submission templates.