Related papers: Neural Integro-Differential Equations
The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
In future power systems, the detailed structure and dynamics may not always be fully known. This is due to an increasing number of distributed energy resources, such as photovoltaic generators, battery storage systems, heat pumps and…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
Modeling sequential patterns from data is at the core of various time series forecasting tasks. Deep learning models have greatly outperformed many traditional models, but these black-box models generally lack explainability in prediction…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…
The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century. Recent developments in artificial intelligence (AI) have accelerated this progress.…
In several practical applications, particularly healthcare, clinical data of each patient is individually recorded in a database at irregular intervals as required. This causes a sparse and irregularly sampled time series, which makes it…
Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural…
Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…