Related papers: The Lie Detector
A Lie system is a non-autonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, a so-called (nonlinear) superposition rule of a finite number of particular solutions…
Bayesian likelihood-free methods implement Bayesian inference using simulation of data from the model to substitute for intractable likelihood evaluations. Most likelihood-free inference methods replace the full data set with a summary…
The ability to generate physically plausible ensembles of variable sources is critical to the optimization of time-domain survey cadences and the training of classification models on datasets with few to no labels. Traditional data…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We develop the equations of motion for full body models that describe the dynamics of rigid bodies, acting under their mutual gravity. The equations are derived using a variational approach where variations are defined on the Lie group of…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…
In paper by I.T. Habibullin and our joint paper the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on the requirement of the existence of an infinite set of Darboux…
In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic coefficients. For $m$ simultaneous inequalities we require at least $m+2$ variables,…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…
For over fifty years, the dynamical systems perspective has had a prominent role in evolutionary biology and economics, through the lens of game theory. In particular, the study of replicator differential equations on the standard…
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
Two simple ways to identify and explain fake Lax pairs are provided. The two methods are complementary, one involves finding a gauge transformation which can be used to remove the associated nonlinear system's dependent variable(s) from a…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
Symmetries are key properties of physical models and of experimental designs, but any proposed symmetry may or may not be realized in nature. In this paper, we introduce a practical and general method to test such suspected symmetries in…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
A key ingredient to achieving intelligent behavior is physical understanding that equips robots with the ability to reason about the effects of their actions in a dynamic environment. Several methods have been proposed to learn dynamics…