Related papers: PETSc/TS: A Modern Scalable ODE/DAE Solver Library

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…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Neural Ordinary Differential Equations (ODEs) was recently introduced as a new family of neural network models, which relies on black-box ODE solvers for inference and training. Some ODE solvers called adaptive can adapt their evaluation…

Exascale I/O initiatives will require new and fully integrated I/O models which are capable of providing straightforward functionality, fault tolerance and efficiency. One solution is the Distributed Asynchronous Object Storage (DAOS)…

We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie…

Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

In this paper, we present a new SDC scheme for solving semi-explicit DAEs with the ability to be parallelized in which only the differential equations are numerically integrated is presented. In Shu et al. (2007) it was shown that SDC for…

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…

Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Neural ordinary differential equations (Neural ODEs) propose the idea that a sequence of layers in a neural network is just a discretisation of an ODE, and thus can instead be directly modelled by a parameterised ODE. This idea has had…

We study SMT problems over the reals containing ordinary differential equations. They are important for formal verification of realistic hybrid systems and embedded software. We develop delta-complete algorithms for SMT formulas that are…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…