Related papers: Symmetry-Informed Term Filtering for Continuum Equ…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
Discovering compact governing equations from experimental observations is one of the defining objectives of quantitative science, yet practical discovery pipelines routinely fail when measurements are noisy, relevant state variables are…
Symmetry-informed machine learning can exhibit advantages over machine learning which fails to account for symmetry. In the context of continuous symmetry detection, current state of the art experiments are largely limited to detecting…
Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework…
In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry,…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry…
In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…
Constrained combinatorial optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search…
The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition…
Exploiting symmetry inherent in data can significantly improve the sample efficiency of a learning procedure and the generalization of learned models. When data clearly reveals underlying symmetry, leveraging this symmetry can naturally…
We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates.…
In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
The Gardner method, traditionally used to generate conservation laws of integrable equations, is generalized to generate symmetries. The method is demonstrated for the KdV, Camassa-Holm and Sine-Gordon equations. The method involves…
Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear…