Related papers: Reconstructing a dynamical system and forecasting …

Seasonal forecasting remains challenging due to the inherent chaotic nature of atmospheric dynamics. This paper introduces DeepSeasons, a novel deep learning approach designed to enhance the accuracy and reliability of seasonal forecasts.…

Integral equations are widely used in fields such as applied modeling, medical imaging, and system identification, providing a powerful framework for solving deterministic problems. While parameter identification for differential equations…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

Data-driven models based on deep learning algorithms intend to overcome the limitations of traditional constitutive modelling by directly learning from data. However, the need for extensive data that collate the full state of the material…

Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification…

We present a novel Deep Neural Network (DNN) architecture for non-linear system identification. We foster generalization by constraining DNN representational power. To do so, inspired by fading memory systems, we introduce inductive bias…

Ensembling a neural network is a widely recognized approach to enhance model performance, estimate uncertainty, and improve robustness in deep supervised learning. However, deep ensembles often come with high computational costs and memory…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However,…

The complex physics involved in atmospheric turbulence makes it very difficult for ground-based astronomy to build accurate scintillation models and develop efficient methodologies to remove this highly structured noise from valuable…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple…

The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

This paper presents a novel framework for demystification of convolutional deep learning models for time-series analysis. This is a step towards making informed/explainable decisions in the domain of time-series, powered by deep learning.…