Related papers: Kinetics-Informed Neural Networks
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…
To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…
We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional layers to solve an…
Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…
Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
We investigate the potential of numerical algorithms to decipher the kinetic parameters involved in multi-step chemical reactions. To this end we study a dimerization kinetics of protein as a model system. We follow the dimerization…
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Since the advent of the ``Neural Ordinary Differential Equation (Neural ODE)'' paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic…
Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…
Differential equations (DE) constrained optimization plays a critical role in numerous scientific and engineering fields, including energy systems, aerospace engineering, ecology, and finance, where optimal configurations or control…
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
Predicting the degradation processes of molecules over long timescales is a key aspect of industrial materials design. However, it is made computationally challenging by the need to construct large networks of chemical reactions that are…
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…
The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…
Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…