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.

Generative AI is rapidly transforming the landscape of mathematical research by solving many open mathematical problems.
I will talk about these advances from the perspective of formalized mathematics.
Many of these AI solutions come with an AI-generated formalization in Lean.
These might not help to understand the mathematical argument, but do provide some guarantees about the correctness of the proof.
I will discuss to what extent we can trust Lean formalizations and what there is left to check and my perspectives on autoformalization.

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.

Managing research data is inseparably linked to managing research software. The community has several tools and services available for this purpose. This ecosystem is currently extended in two dimensions within NFDIxCS. First, infrastructure is provided to support reuse of software in different environments. Second, interoperability of services is addressed by a technical architecture that balances aspects of comfort and security. At the same time, this enables links to be established between developments that have so far been carried out within the individual consortia.

In her talk, Sonja Schimmler will examine how generative AI is reshaping the way researchers create, share, and reuse articles, data, models, and code. As this shift introduces new challenges for transparency and reproducibility, research data infrastructures must adapt. She will explore how these systems are evolving to manage diverse scholarly artifacts and leverage AI themselves.

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.

Nobody can have failed to have notice that the mathematical world has become engulfed in an AI-generated storm. For those of us who create and maintain mathematical research data, the possibilities are huge. And yet considerations of what this revolution might mean for the principals of FAIR mathematics, and the creation and sharing of mathematical datasets, has been conspicuously absent from the conversations at both the national and international level. Equally important is what this means for computer algebra, where many of the discussions we've had within the community over the past decade are eerily relevant now in the context of generative AI. I want to use this talk to present some concerns and opportunities that I see. In particular, I want to suggest a series of concrete proposals for projects and collaborations that, I believe, will help shape a FAIR future for mathematics.

The MaRDI portal already provides FAIR-aligned access to publications, datasets, software, algorithms and workflows. What it does not yet offer is a machine-actionable operations layer: a protocol-level way to discover, retrieve and process portal entities without knowing the Wikibase data model. We present our work on exposing portal entities as FAIR Digital Objects via a DOIP gateway placed in front of the knowledge graph. We walk through the entity-to-FDO mapping, the choice of a gateway over changes to the Wikibase installation, and the open questions in defining FDO profiles for mathematical objects. We close with an outlook on the added value of this approach for the MaRDI ecosystem and invite discussion on which types and operations the community needs most.

Modern scientific workflows increasingly depend on research software, yet numerical experiments still often face challenges in reliability, robustness, and reproducibility. Although novel algorithms continue to emerge in computational mathematics, their adoption across disciplines is frequently limited by the difficulty of integrating them into established workflows. Additionally, research data in the domain is insufficiently annotated, inconsistently structured, or difficult to access, while the lack of standardized benchmarks hinders transparent and reproducible performance evaluation. In multi-step research processes, data, tools, and domain-specific knowledge are also rarely captured in forms that can be translated into automated workflows.

To address these challenges, we provide an ontology‑based, standardized specification for data and metadata management, benchmarking, and workflow representation across mathematical domains, implemented in MaRDI services. Because these benchmarks and workflows are semantically described and machine‑actionable, results produced by researchers or by automated AI systems can be checked against community‑accepted reference results. Designed for extensibility, customizability, and reproducibility, these services support a flexible, domain‑independent approach to scientific benchmarks and workflows within and across mathematical communities, and provide a verifiable foundation for AI‑assisted research in which domain experts curate the knowledge these systems rely on.

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.

After a lot of work behind the scenes, MaRDIans as well as NFDI friends and partners now have access to a versatile and customizable Conference Kit. The first half of this session celebrates its official release. In a live demo, its customization options, along the lines of typical use cases, will be explored, interactively gathering feedback. In the second half of the session, the ConfKit will serve as a guiding example and foundation of the envisioned OER self-learning material for outreach and novel (hopefully improved) MaRDI services. This opens up the stage to a brief overview of the outreach strategy for the second funding period as suggested by the newly formed TA-E.