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Researcher profile

Matthijs van Leeuwen

Matthijs van Leeuwen contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
ApplicationsArtificial IntelligenceComputational Engineering, Finance, and ScienceInformation TheoryMachine Learningmath.IT

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Published work

4 published item(s)

preprint2026arXiv

MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling

Optimization modeling translates real decision-making problems into mathematical optimization models and solver-executable implementations. Although language models are increasingly used to generate optimization formulations and solver code, existing benchmarks are almost entirely text-only. This omits many optimization-modeling tasks that arise in operational practice, where requirements are described in text but instance information is conveyed through visual artifacts such as tables, graphs, maps, schedules, and dashboards. We introduce multimodal optimization modeling, a benchmark setting in which models must construct both a mathematical formulation and executable solver code from a text-and-visual problem specification. To evaluate this setting, we develop a solver-grounded framework that generates structured optimization instances, verifies each with an exact solver, and builds both the model-facing inputs and hidden reference files from the same verified source. We instantiate the framework as MM-OptBench, a benchmark of 780 solver-verified instances spanning 6 optimization families, 26 subcategories, and 3 structural difficulty levels. We evaluate 9 multimodal large language models (MLLMs), including 6 frontier general-purpose models and 3 math-specialized models, with aggregate, family-level, difficulty-level, and failure-mode analyses. The results show that the task remains far from solved: the best two models reach 52.1% and 51.3% pass@1, while on average across the six general-purpose MLLMs, pass@1 is 43.4% on easy instances and 15.9% on hard instances. All three math-specialized MLLMs solve 0/780 instances. Failure attribution shows that errors arise both when extracting instance data from text and visuals and when turning extracted data into solver-correct formulations and code. MM-OptBench provides a testbed for solver-grounded, decision-oriented multimodal intelligence.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Finding Efficient Trade-offs in Multi-Fidelity Response Surface Modeling

In the context of optimization approaches to engineering applications, time-consuming simulations are often utilized which can be configured to deliver solutions for various levels of accuracy, commonly referred to as different fidelity levels. It is common practice to train hierarchical surrogate models on the objective functions in order to speed-up the optimization process. These operate under the assumption that there is a correlation between the high- and low-fidelity versions of the problem that can be exploited to cheaply gain information. In the practical scenario where the computational budget has to be allocated between multiple fidelities, limited guidelines are available to help make that division. In this paper we evaluate a range of different choices for a two-fidelity setup that provide helpful intuitions about the trade-off between evaluating in high- or low-fidelity. We present a heuristic method based on subsampling from an initial Design of Experiments (DoE) to find a suitable division of the computational budget between the fidelity levels. This enables the setup of multi-fidelity optimizations which utilize the available computational budget efficiently, independent of the multi-fidelity model used.

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preprint2022arXiv

Truly Unordered Probabilistic Rule Sets for Multi-class Classification

Rule set learning has long been studied and has recently been frequently revisited due to the need for interpretable models. Still, existing methods have several shortcomings: 1) most recent methods require a binary feature matrix as input, while learning rules directly from numeric variables is understudied; 2) existing methods impose orders among rules, either explicitly or implicitly, which harms interpretability; and 3) currently no method exists for learning probabilistic rule sets for multi-class target variables (there is only one for probabilistic rule lists). We propose TURS, for Truly Unordered Rule Sets, which addresses these shortcomings. We first formalize the problem of learning truly unordered rule sets. To resolve conflicts caused by overlapping rules, i.e., instances covered by multiple rules, we propose a novel approach that exploits the probabilistic properties of our rule sets. We next develop a two-phase heuristic algorithm that learns rule sets by carefully growing rules. An important innovation is that we use a surrogate score to take the global potential of the rule set into account when learning a local rule. Finally, we empirically demonstrate that, compared to non-probabilistic and (explicitly or implicitly) ordered state-of-the-art methods, our method learns rule sets that not only have better interpretability but also better predictive performance.

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preprint2021arXiv

Estimating Conditional Mutual Information for Discrete-Continuous Mixtures using Multi-Dimensional Adaptive Histograms

Estimating conditional mutual information (CMI) is an essential yet challenging step in many machine learning and data mining tasks. Estimating CMI from data that contains both discrete and continuous variables, or even discrete-continuous mixture variables, is a particularly hard problem. In this paper, we show that CMI for such mixture variables, defined based on the Radon-Nikodym derivate, can be written as a sum of entropies, just like CMI for purely discrete or continuous data. Further, we show that CMI can be consistently estimated for discrete-continuous mixture variables by learning an adaptive histogram model. In practice, we estimate such a model by iteratively discretizing the continuous data points in the mixture variables. To evaluate the performance of our estimator, we benchmark it against state-of-the-art CMI estimators as well as evaluate it in a causal discovery setting.

0 citations0 reviewsNo code linkedOpen access