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We present a metamodel for modeling control and data flows on subclass scales in object-oriented systems. UML Profiles were used as a representation mean and a complete metamodel definition was provided with an example of a diagram…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…
The study of high dimensional data sets often rely on their low dimensional projections that preserve the local geometry of the original space. While numerous methods have been developed to summarize this space as variations of tree-like…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
Outcomes with a natural order commonly occur in prediction tasks and often the available input data are a mixture of complex data like images and tabular predictors. Deep Learning (DL) models are state-of-the-art for image classification…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
More often than not, there is a need to understand the structure of complex computer code: what functions and in what order they are called, how information travels around static, input, and output variables, what depends on what. As a…
The representation of workflows and processes is essential in materials science engineering, where experimental and computational reproducibility depend on structured and semantically coherent process models. Although numerous ontologies…
Neural processes (NPs) are a class of models that learn stochastic processes directly from data and can be used for inference, sampling and conditional sampling. We introduce a new NP model based on flow matching, a generative modeling…
The Unified Modeling Language (UML) is rapidly emerging as a de-facto standard for modelling OO systems. Given this role, it is imperative that the UML needs a well-defined, fully explored semantics. Such semantics is required in order to…
In software engineering processes, systems are first specified using a modeling language such as UML. These initial designs are often collaboratively created, many times in meetings where different domain experts use whiteboards, paper or…
Many systems can be described in terms of networks of discrete elements and their various relationships to one another. A semantic network, or multi-relational network, is a directed labeled graph consisting of a heterogeneous set of…
We describe here our perception of complex systems, of how we feel the different layers of description are important part of a correct complex system simulation. We describe a rough models categorization between rules based and law based,…
The object-oriented class is, in general, the most utilized element in programming and modeling. It is employed throughout the software development process, from early domain analysis phases to later maintenance phases. A class diagram…
The design of complex engineering systems is an often long and articulated process that highly relies on engineers' expertise and professional judgment. As such, the typical pitfalls of activities involving the human factor often manifest…
The Extract, Transform, Load (ETL) workflow is fundamental for populating and maintaining data warehouses and other data stores accessed by analysts for downstream tasks. A major shortcoming of modern ETL solutions is the extensive need for…