Related papers: Formalising the Continuous/Discrete Modeling Step

The term Model-Driven Engineering (MDE) is typically used to describe software development approaches in which abstract models of software systems are created and systematically transformed to concrete implementations. In this paper we give…

An adaptive discretization refinement strategy for steady state discrete mesoscale models of coupled mechanics and mass transport in concrete is presented. Coupling is provided by two phenomena: the Biot's theory of poromechanics and an…

Consistency models have recently been introduced to accelerate sampling from diffusion models by directly predicting the solution (i.e., data) of the probability flow ODE (PF ODE) from initial noise. However, the training of consistency…

The Transformer architecture has revolutionized artificial intelligence, yet a principled theoretical understanding of its internal mechanisms remains elusive. This paper introduces a novel analytical framework that reconceptualizes the…

This paper introduces a general approach for synthesizing procedural models of the state-transitions of a given discrete system. The approach is general in that it accepts different target languages for modeling the state-transitions of a…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

In this paper we provide theoretical results that relate steady states of continuous and discrete models arising from biology.

We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…

In this note, we explore a middle ground between data-driven model reduction and data-driven control. In particular, we use snapshots collected from the system to build reduced models that can be expressed in terms of data. We illustrate…

Model-based experimental design is attracting increasing attention in chemical process engineering. Typically, an iterative procedure is pursued: an approximate model is devised, prescribed experiments are then performed and the resulting…

A neural ordinary differential equation (neural ODE) is a machine learning model that is commonly described as a continuous-depth generalization of a residual network (ResNet) with a single residual block, or conversely, the ResNet can be…

Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order…

A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time…

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Model steering, which involves intervening on hidden representations at inference time, has emerged as a lightweight alternative to finetuning for precisely controlling large language models. While steering efficacy has been widely studied,…

Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate…

A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…

Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…

Opinion Dynamics models can be, for most of them, divided between discrete and continuous. They are used in different circumstances and the relationship between them is not clear. Here we will explore the relationship between a model where…