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Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically…
We identify the task of measuring data to quantitatively characterize the composition of machine learning data and datasets. Similar to an object's height, width, and volume, data measurements quantify different attributes of data along…
Extracting valuable insights from vast amounts of information is a critical process that involves acquiring, storing, managing, analyzing, and visualizing data. Providing an abstract overview of data analytics applications is crucial to…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
During the last decade, the information technology industry has adopted a data-driven culture, relying on online metrics to measure and monitor business performance. Under the setting of big data, the majority of such metrics approximately…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
Contact tracing is an effective method to control emerging diseases. Since the 1980's, mathematical modelers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations of contact…
The dramatic increase of observational data across industries provides unparalleled opportunities for data-driven decision making and management, including the manufacturing industry. In the context of production, data-driven approaches can…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…
Simulation is an integral part in the process of developing autonomous vehicles and advantageous for training, validation, and verification of driving functions. Even though simulations come with a series of benefits compared to real-world…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that…
In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more. Consequently, statistical and machine learning models tailored to different data encodings are important. We focus on data…
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…
Modeling has become a widespread, useful tool in mathematics applied to diverse fields, from physics to economics to biomedicine. Practitioners of modeling may use algebraic or differential equations, to the elements of which they attribute…
Artificial intelligence (AI) provides many opportunities to improve private and public life. Discovering patterns and structures in large troves of data in an automated manner is a core component of data science, and currently drives…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…