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The rise of foundation models -- large, pretrained machine learning models that can be finetuned to a variety of tasks -- has revolutionized the fields of natural language processing and computer vision. In high-energy physics, the question…

With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…

Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…

This extensive review was written for the ``Encyclopedia of Complexity and System Science'' (Springer, 2008) and addresses a broad audience ranging from engineers to applied mathematicians, computer scientists and physicists. It provides an…

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…

Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…

This position paper takes a broad look at Physics-Enhanced Machine Learning (PEML) -- also known as Scientific Machine Learning -- with particular focus to those PEML strategies developed to tackle dynamical systems' challenges. The need to…

Accurate physical modeling with 3D-printing techniques could lead to new approaches to study structure and dynamics of biological systems complementing computational methods. Computational biology has become an important part of research…

Since the turn of the millennium, computational modelling of biological systems has evolved remarkably and sees matured use spanning basic and clinical research. While the topic of the peri-millennial debate about the virtues and…

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include…

Predictive models are one of the most important techniques that are widely applied in many areas of software engineering. There have been a large number of primary studies that apply predictive models and that present well-preformed studies…

We present a pedagogical work-in-progress. This textbook aims to introduce Hilbert space representations for quantum and classical dynamics, outlining the mathematical foundations, practical guidance, and Python implementation of dynamical…

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…

The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis.…

Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of…

The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematicians and physicists.

Basic issues of the general model-building framework of the mechanics of complex bodies are discussed. Attention is focused on the representation of the material elements, the conditions for the existence of ground states in conservative…

Learning dynamics is at the heart of many important applications of machine learning (ML), such as robotics and autonomous driving. In these settings, ML algorithms typically need to reason about a physical system using high dimensional…

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily…

This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…