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Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…

Mathematical Physics · Physics 2022-06-20 Evan Patterson , Andrew Baas , Timothy Hosgood , James Fairbanks

Empirical research plays a fundamental role in the machine learning domain. At the heart of impactful empirical research lies the development of clear research hypotheses, which then shape the design of experiments. The execution of…

Machine Learning · Computer Science 2024-05-29 Daniel Vranješ , Oliver Niggemann

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the…

Data Analysis, Statistics and Probability · Physics 2024-10-07 Sihao Cheng , Rudy Morel , Erwan Allys , Brice Ménard , Stéphane Mallat

Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading…

History and Philosophy of Physics · Physics 2019-04-09 Michał Eckstein , Paweł Horodecki

Adaptive exploration methods propose ways to learn complex policies via alternating between exploration and exploitation. An important question for such methods is to determine the appropriate moment to switch between exploration and…

Artificial Intelligence · Computer Science 2026-02-11 Leonidas Bakopoulos , Georgios Chalkiadakis

Physics-guided machine learning (PGML) has become a prevalent approach in studying scientific systems due to its ability to integrate scientific theories for enhancing machine learning (ML) models. However, most PGML approaches are tailored…

Machine Learning · Computer Science 2025-02-11 Runlong Yu , Chonghao Qiu , Robert Ladwig , Paul Hanson , Yiqun Xie , Xiaowei Jia

We present a systematic evaluation of representation learning objectives for particle physics within a unified framework. Our study employs a shared transformer-based particle-cloud encoder with standardized preprocessing, matched sampling,…

Machine Learning · Computer Science 2025-11-18 Michael Chen , Raghav Kansal , Abhijith Gandrakota , Zichun Hao , Jennifer Ngadiuba , Maria Spiropulu

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine…

Machine Learning · Computer Science 2026-05-29 Mengdi Chu , Yang Liu , Ayan Biswas , Han-Wei Shen

The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify that kind of models is to discard some of the…

Soft Condensed Matter · Physics 2025-11-11 Simone Rusconi , Christina Schenk , Razvan Ceuca , Arghir Zarnescu , Elena Akhmatskaya

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…

History and Overview · Mathematics 2022-05-25 Inge S. Helland

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…

Machine Learning · Statistics 2023-01-02 Hongkang Yang

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,…

adap-org · Physics 2008-02-03 Steen Rasmussen , Christopher Barrett

Questions of participant understanding of the nature of an activity have been addressed in anthropology and sociolinguistics with the concepts of frames and framing. For example, a student may frame a learning activity as an opportunity for…

Physics Education · Physics 2007-12-04 Rachel E. Scherr , David Hammer

Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…

Requirements Engineering Methods (REMs) support Requirements Engineering (RE) tasks, from elicitation, through modeling and analysis, to validation and evolution of requirements. Despite the growing interest to design, validate and teach…

Software Engineering · Computer Science 2012-03-09 Ivan Jureta

Many scientific fields, from medicine to seismology, rely on analyzing sequences of events over time to understand complex systems. Traditionally, machine learning models must be built and trained from scratch for each new dataset, which is…

Machine Learning · Computer Science 2026-01-21 David Berghaus , Patrick Seifner , Kostadin Cvejoski , Ramses J. Sanchez

The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and while it…

Physics Education · Physics 2015-08-21 N. G. Holmes , Carl E. Wieman , D. A. Bonn

Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast time scales. Several empirical statistical properties of these networks have been shown to be robust across a…

Physics and Society · Physics 2023-02-03 Didier Le Bail , Mathieu Génois , Alain Barrat

We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…

Machine Learning · Computer Science 2020-01-16 Lior Wolf , Tomer Galanti , Tamir Hazan

In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…

Numerical Analysis · Mathematics 2016-09-21 Jing Li , Panos Stinis
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