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Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
This paper presents the current version of our (Elementary) Mathematical Data Model ((E)MDM), which is based on the na\"ive theory of sets, relations, and functions, as well as on the first-order predicate calculus with equality. Many…
Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…
Large language models (LLMs) based on transformer architectures are typically described through collections of architectural components and training procedures, obscuring their underlying computational structure. This review article…
Definition Modeling, the task of generating definitions, was first proposed as a means to evaluate the semantic quality of word embeddings-a coherent lexical semantic representations of a word in context should contain all the information…
While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…
Semantic associations such as the link between "bird" and "flew" are foundational for language modeling as they enable models to go beyond memorization and instead generalize and generate coherent text. Understanding how these associations…
Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical…
Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of…
There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations…
We introduce a framework for computer-aided derivation of multi-scale models. It relies on a combination of an asymptotic method used in the field of partial differential equations with term rewriting techniques coming from computer…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
Current machine learning models are evaluated through behavioral snapshots, with benchmark accuracies, win rates and outcome-based metrics. Model explanations and evaluations, however, are fundamentally intertwined: understanding why a…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
Metamodeling is used as a general technique for integrating and defining models from different domains. This technique can be used in diverse application domains, especially for purposes of standardization. Also, this process mainly has a…
In this paper we demonstrate an approach to model structure and behavior of distributed systems, to map those models to a lightweight execution engine by using a functional programming language and to systematically define and execute tests…
Large language models (LLMs) are transforming cellular biology by enabling the development of "virtual cells"--computational systems that represent, predict, and reason about cellular states and behaviors. This work provides a comprehensive…
In this paper we present the modeling support infrastructure for domain-specific application definition. This consists of a set of meta-models and the associated generators to allow the definition of reusable and domain-specific behavior…
The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting…
In this paper we show by using the example of UML, how a software engineering method can benefit from an integrative mathematical foundation. The mathematical foundation is given by a mathematical system model. This model provides the basis…