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Ordinary Differential Equations
Many modeling problems with engineering applications can be formulated using ordinary differential equations (ODEs). There are a few different...
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Ordinary Differential Equations
An ordinary differential equation (ODE) is an equation that involves the derivatives of one independent variable. An ODE is different from partial...
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Ordinary Differential Equations
Haksun Li, PhDa*
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Ordinary Differential Equations
A differential equation is an equation that contains a function and one or more of its derivatives. They have been studied ever since the invention...
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A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations
This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations....
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On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems
AbstractThis paper presents an original package for investigating numerical solutions of ordinary differential equations, which is built in the Sage...
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Learning Interacting Dynamic Systems with Neural Ordinary Differential Equations
Interacting Dynamic Systems refer to a group of agents which interact with others in a complex and dynamic way. Modeling Interacting Dynamic Systems...
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An Analysis of Universal Differential Equations for Data-Driven Discovery of Ordinary Differential Equations
In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide...
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A feedforward neural network framework for approximating the solutions to nonlinear ordinary differential equations
In this paper, we propose a method to approximate the solutions to nonlinear ordinary differential equations (ODE) using a deep learning feedforward...
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A Joint estimation approach to sparse additive ordinary differential equations
Ordinary differential equations (ODEs) are widely used to characterize the dynamics of complex systems in real applications. In this article, we...
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Time-aware neural ordinary differential equations for incomplete time series modeling
Internet of Things realizes the ubiquitous connection of all things, generating countless time-tagged data called time series. However, real-world...
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Data driven discovery of systems of ordinary differential equations using nonconvex multitask learning
In physical sciences, dynamic systems are modeled using their parameters within governing equations that often form a system of ordinary differential...
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Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach
In this paper, we introduce a new method based on a library of chemical reactions for constructing a system of ordinary differential equations from...
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Ordinary Differential Equations
There is a lot of definitions, terminology and theory around ordinary differential equations (ODEs). We introduce the terminology and properties that...
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Solving Differential Equations
I have already mentioned that books on calculus tend to be thick, and they do not always include a section on solving differential equations—this...
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Semantic Segmentation Using Neural Ordinary Differential Equations
The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself....
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nmODE: neural memory ordinary differential equation
Brain neural networks are regarded as dynamical systems in neural science, in which memories are interpreted as attractors of the systems....
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Partial Differential Equations
A partial differential equation (PDE) relates the quantities of a multivariate function and its various partial derivatives in an equation. An...
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Verified Numerical Methods for Ordinary Differential Equations
Ordinary differential equations (ODEs) are used to model the evolution of the state of a system over time. They are ubiquitous in the physical...
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Continuous Depth Recurrent Neural Differential Equations
Recurrent neural networks (RNNs) have brought a lot of advancements in sequence labeling tasks and sequence data. However, their effectiveness is...