相关论文: A note on the adjoint method for neural ordinary d…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this…

The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…

A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…

Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…

In this paper, we investigate the influence of noise giving an estimate of the gradient having a acute angle with the original. Noise amplitude has a relative model. The work offers both theoretical calculations and theorems, as well as…

We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…

This paper is a step-by-step, self-contained guide to the complete training cycle of a Physics-Informed Neural Network (PINN) -- a topic that existing tutorials and guides typically delegate to automatic differentiation libraries without…

Neural ordinary differential equations (NODEs) is an invertible neural network architecture promising for its free-form Jacobian and the availability of a tractable Jacobian determinant estimator. Recently, the representation power of NODEs…

Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compared to fully connected neural networks, PINNs based on…

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 article considers the discrete analogue of the method of quickest descent for an inverse Acoustics problem in case of a smooth source. The authors derived the gradient of functional in differential and discrete cases, described the…

Many popular feature-attribution methods for interpreting deep neural networks rely on computing the gradients of a model's output with respect to its inputs. While these methods can indicate which input features may be important for the…

Forward Gradients - the idea of using directional derivatives in forward differentiation mode - have recently been shown to be utilizable for neural network training while avoiding problems generally associated with backpropagation gradient…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…