Related papers: Why more physics can help achieving better mathema…
Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…
A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a…
It is becoming common to hear teaching advice about spending more time on the "physics of the problem" so that students will get more physical insight and develop a stronger intuition that can be very helpful when thinking about physics…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Physical modeling closes the gap between perception in terms of measurements and abstraction in terms of theoretical models. Physical modeling is a major objective in physics and is generally regarded as a creative process. How good are…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
Learning to use math in science is a non-trivial task. It involves many different skills (not usually taught in a math class) that help blend physical knowledge with mathematical symbology. One of these is the idea of quantification: that…
Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
Physical laws are strikingly simple, yet there is no a priori reason for them to be so. I propose that nomic realists -- Humeans and non-Humeans -- should recognize simplicity as a fundamental epistemic guide for discovering and evaluating…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…
The modeling theory of instruction is widely applied and highly successful in high-school instruction, and seldom in university physics. One reason is lack of familiarity with models in the physics classroom. Ongoing curriculum development…