Related papers: Self-Supervised Evolution Operator Learning for Hi…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
Transformers have become the dominant architecture for sequence modeling tasks such as natural language processing or audio processing, and they are now even considered for tasks that are not naturally sequential such as image…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…
The number of studies that combine Evolutionary Machine Learning and self-supervised learning has been growing steadily in recent years. Evolutionary Machine Learning has been shown to help automate the design of machine learning algorithms…
Supervised learning has become a cornerstone of modern machine learning, yet a comprehensive theory explaining its effectiveness remains elusive. Empirical phenomena, such as neural analogy-making and the linear representation hypothesis,…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Datasets from single-molecule experiments often reflect a large variety of molecular behaviour. The exploration of such datasets can be challenging, especially if knowledge about the data is limited and a priori assumptions about expected…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…
Evolutionary Computation is a branch of computer science with which, traditionally, High Energy Physics has fewer connections. Its methods were investigated in this field, mainly for data analysis tasks. These methods and studies are,…
Self-supervision is one of the hallmarks of representation learning in the increasingly popular suite of foundation models including large language models such as BERT and GPT-3, but it has not been pursued in the context of multivariate…
A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for…
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…
We present a framework for the unsupervised learning of neurosymbolic encoders, which are encoders obtained by composing neural networks with symbolic programs from a domain-specific language. Our framework naturally incorporates symbolic…
Koopman analysis of a general dynamics system provides a linear Koopman operator and an embedded eigenfunction space, enabling the application of standard techniques from linear analysis. However, in practice, deriving exact operators and…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
We address the problem of learning self-supervised representations from unlabeled image collections. Unlike existing approaches that attempt to learn useful features by maximizing similarity between augmented versions of each input image or…
Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence.…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…