Related papers: Machine Learning Algebraic Geometry for Physics
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest…
Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which…
This paper presents a transformative framework for artificial neural networks over graded vector spaces, tailored to model hierarchical and structured data in fields like algebraic geometry and physics. By exploiting the algebraic…
Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds,…
Most problems in Earth sciences aim to do inferences about the system, where accurate predictions are just a tiny part of the whole problem. Inferences mean understanding variables relations, deriving models that are physically…
Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…
Machine learning is poised as a very powerful tool that can drastically improve our ability to carry out scientific research. However, many issues need to be addressed before this becomes a reality. This article focuses on one particular…
Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals…
Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra.…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
Machine learning methods have found novel application areas in various disciplines as they offer low-computational cost solutions to complex problems. Recently, metasurface design has joined among these applications, and neural networks…
In this review, we highlight recent developments in the application of machine learning for molecular modeling and simulation. After giving a brief overview of the foundations, components, and workflow of a typical supervised learning…
Over the past five years, modern machine learning has been quietly revolutionizing particle physics. Old methodology is being outdated and entirely new ways of thinking about data are becoming commonplace. This article will review some…
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…
Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
With the volume and availability of astronomical data growing rapidly, astronomers will soon rely on the use of machine learning algorithms in their daily work. This proceeding aims to give an overview of what machine learning is and delve…
Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…