相关论文: Kinetics Parameter Optimization via Neural Ordinar…
In this paper, we implement Neural Ordinary Differential Equations in a Variational Autoencoder setting for generative time series modeling. An object-oriented approach to the code was taken to allow for easier development and research and…
We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
Neural Ordinary Differential Equations (ODEs) have been successful in various applications due to their continuous nature and parameter-sharing efficiency. However, these unique characteristics also introduce challenges in training,…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
This paper presents a method for identifying mechanical parameters of robots or objects, such as their mass and friction coefficients. Key features are the use of off-the-shelf physics engines and the adaptation of a Bayesian optimization…
Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring…
Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
We present a new approach for estimating parameters in rational ODE models from given (measured) time series data. In typical existing approaches, an initial guess for the parameter values is made from a given search interval. Then, in a…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
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…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…