Related papers: A hybrid model for large neural network descriptio…

We present a new method for parameter identification of ODE system descriptions based on data measurements. Our method works by splitting the system into a number of subsystems and working on each of them separately, thereby being easily…

Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

Most recent advances in machine learning and analytics for process control pose the question of how to naturally integrate new data-driven methods with classical process models and control. We propose a process modeling framework enabling…

The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

Panel data involving longitudinal measurements of the same set of participants taken over multiple time points is common in studies to understand childhood development and disease modeling. Deep hybrid models that marry the predictive power…

Recent theoretical and experimental work in neuroscience has focused on the representational and dynamical character of neural manifolds --subspaces in neural activity space wherein many neurons coactivate. Importantly, neural populations…

In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open…

Individual-based hybrid modelling of spatially distributed systems is usually expensive. Here, we consider a hybrid system in which mobile agents spread over the space and interact with each other when in close proximity. An…

A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…

Modeling spreading processes in complex random networks plays an essential role in understanding and prediction of many real phenomena like epidemics or rumor spreading. The dynamics of such systems may be represented algorithmically by…

We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…

This is a living document that will be updated when appropriate. MIIND [1, 2] is a population-level neural simulator. It is based on population density techniques, just like DIPDE [3]. Contrary to DIPDE, MIIND is agnostic to the underlying…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate gradient (NCG) descent optimization scheme for training,…

Deep Neural Networks (DNN) have been successful in en- hancing noisy speech signals. Enhancement is achieved by learning a nonlinear mapping function from the features of the corrupted speech signal to that of the reference clean speech…

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…