Related papers: The Lie Detector
Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We…
In in this paper we show how using D.A. it is found a simple change of variables (c.v.) that brings us to obtain differential equations simpler than the original one. In a pedagogical way (at least we try to do that) and in order to make…
Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries)…
Great labels make great models. However, traditional labeling approaches for tasks like object detection have substantial costs at scale. Furthermore, alternatives to fully-supervised object detection either lose functionality or require…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
We discuss a method that employs a multilayer perceptron to detect deviations from a reference model in large multivariate datasets. Our data analysis strategy does not rely on any prior assumption on the nature of the deviation. It is…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
Estimating the impact of systematic uncertainties in particle physics experiments is challenging, especially since the detector response is unknown analytically in most situations and needs to be estimated through Monte Carlo (MC)…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
As latent diffusion models (LDMs) democratize image generation capabilities, there is a growing need to detect fake images. A good detector should focus on the generative models fingerprints while ignoring image properties such as semantic…
In deepfake detection, it is essential to maintain high performance by adjusting the parameters of the detector as new deepfake methods emerge. In this paper, we propose a method to automatically and actively select the small amount of…
Lie theory of continuous transformations provides a unified and powerful approach for handling differential equations. Unfortunately, any small perturbation of an equation usually destroys some important symmetries, and this reduces the…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
We introduce a method for efficiently solving initial-boundary value problems (IBVPs) that uses Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations,…
We introduce and demonstrate two linear inverse modelling methods for systems of stochastic ODE's with accuracy that is independent of the dimensionality (number of elements) of the state vector representing the system in question.…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
The Lie-point symmetry method is used to find some closed-form solutions for a constitutive equation modeling stress in elastic materials. The partial differential equation (PDE), which involves a power law with arbitrary exponent n, was…
Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system…