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High level domain specific languages for the finite element method underpin high productivity programming environments for simulations based on partial differential equations (PDE) while employing automatic code generation to achieve high…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Scientific software-defined as computer programs, scripts, or code used in scientific research, data analysis, modeling, or simulation-has become central to modern research. However, there is limited research on the readability and…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Contribution: We demonstrate that it is feasible to include field specific problems in introductory mathematics courses to motivate engineering students. This is done in a way that still allows large parts of the course to be common to all…
One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts.…
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…
Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so…
Novice programmers often struggle to understand how code executes and to form the abstract mental models necessary for effective problem-solving, challenges that are amplified in large, diverse introductory courses where students'…
Code search is vital in the maintenance and extension of software systems. Past works have used separate language models for the natural language and programming language artifacts on models with multiple encoders and different loss…
This second paper in a multi-part series builds on the first, which introduced the Ways of Thinking for Engineering Design-based Physics (WoT4EDP) framework for STEM education in an introductory undergraduate physics course. Here, we apply…
The functional programming paradigm has a long and storied history, with its beginnings in the Lambda Calculus. In recent decades, pure functional languages such as Haskell have been shown to be highly effective in producing robust software…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
This study examines how AI code assistants shape novice programmers experiences during a two-part exam in an introductory programming course. In the first part, students completed a programming task with access to AI support; in the second,…
This work presents a brief discussion and a plan towards the analytical solving of Partial Differential Equations (PDEs) using symbolic computing, as well as an implementation of part of this plan as the PDEtools software-package of…
Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…
We introduce a newly designed undergraduate-level interdisciplinary course in scientific computing that aims to prepare students as the next generation of research-oriented computational scientists and engineers. The course offers students…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including…