相关论文: A hybrid model for large neural network descriptio…

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…

We investigate multicellular sender receiver systems embedded in hydrogel beads, where diffusible signals mediate interactions among heterogeneous cells. Such systems are modeled by PDE ODE couplings that combine three dimensional diffusion…

We study the global existence of solutions of a discrete (ODE based) model on a graph describing the formation of biological transportation networks, introduced by Hu and Cai. We propose an adaptation of this model so that a macroscopic…

Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…

Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…

Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…

Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…

Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…

Diffusion-based and neural communication are two interesting domains in molecular communication. Both of them have distinct advantages and are exploited separately in many works. However, in some cases, neural and diffusion-based ways have…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

Epidemiological forecasting from surveillance data is a hard problem and hybridizing mechanistic compartmental models with neural models is a natural direction. The mechanistic structure helps keep trajectories epidemiologically plausible,…

Hybrid neural ordinary differential equations (neural ODEs) integrate mechanistic models with neural ODEs, offering strong inductive bias and flexibility, and are particularly advantageous in data-scarce healthcare settings. However,…

We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…

The human brain is a complex system defined by multi-way, higher-order interactions invisible to traditional pairwise network models. Although a diverse array of analytical methods has been developed to address this shortcoming, the field…

Population protocols are a fundamental model in distributed computing, where many nodes with bounded memory and computational power have random pairwise interactions over time. This model has been studied in a rich body of literature aiming…

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…