Related papers: Machine Learning for Mathematical Software
Vibe coding, the much-touted use of AI techniques for programming, faces two overwhelming obstacles: the difficulty of specifying goals ("prompt engineering" is a form of requirements engineering, one of the toughest disciplines of software…
This study emphasizes how crucial it is to visualize machine learning models, especially for the banking industry, in order to improve interpretability and support predictions in high stakes financial settings. Visual tools enable…
Machine Learning (ML) is applicable to scientific problems, i.e. to those which have a well defined answer, only if this answer can be brought to a peculiar form ${\cal G}: X\longrightarrow Z$ with ${\cal G}(\vec x)$ expressed as a…
Scientific machine learning (SciML) models are transforming many scientific disciplines. However, the development of good modeling practices to increase the trustworthiness of SciML has lagged behind its application, limiting its potential…
Programs to solve so-called constraint problems are complex pieces of software which require many design decisions to be made more or less arbitrarily by the implementer. These decisions affect the performance of the finished solver…
Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…
Artificial intelligence is gaining strength and materials science can both contribute to and profit from it. In a simultaneous progress race, new materials, systems and processes can be devised and optimized thanks to machine learning…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
Machine Learning is a powerful tool to reveal and exploit correlations in a multi-dimensional parameter space. Making predictions from such correlations is a highly non-trivial task, in particular when the details of the underlying dynamics…
In [1, 2], we have explored the theoretical aspects of feature extraction optimization processes for solving largescale problems and overcoming machine learning limitations. Majority of optimization algorithms that have been introduced in…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
In this work, we show a methodology aimed to improve the quality of the assessment process for subjects related to basic programming. The method takes into account the relevance of the items and the students answers to follow different…
Currently, many verification algorithms are available to improve the reliability of software systems. Selecting the appropriate verification algorithm typically demands domain expertise and non-trivial manpower. An automated algorithm…
Computational models in chemistry rely on a number of approximations. The effect of such approximations on observables derived from them is often unpredictable. Therefore, it is challenging to quantify the uncertainty of a computational…
We are interested in the application of Machine Learning (ML) technology to improve mathematical software. It may seem that the probabilistic nature of ML tools would invalidate the exact results prized by such software, however, the…
There has been considerable growth and interest in industrial applications of machine learning (ML) in recent years. ML engineers, as a consequence, are in high demand across the industry, yet improving the efficiency of ML engineers…
We review state-of-the-art formal methods applied to the emerging field of the verification of machine learning systems. Formal methods can provide rigorous correctness guarantees on hardware and software systems. Thanks to the availability…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
AI and machine learning based approaches are becoming ubiquitous in almost all engineering fields. Control engineering cannot escape this trend. In this paper, we explore how AI tools can be useful in control applications. The core tool we…