Related papers: Formalising the Continuous/Discrete Modeling Step
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…
A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…
Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them,…
Most of the works on planning and learning, e.g., planning by (model based) reinforcement learning, are based on two main assumptions: (i) the set of states of the planning domain is fixed; (ii) the mapping between the observations from the…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
Drifting Models have emerged as a new paradigm for one-step generative modeling, achieving strong image quality without iterative inference. The premise is to replace the iterative denoising process in diffusion models with a single…
In this paper we introduce 1-$D$ and 2-$D$ discrete models for the dynamic granular matter formation process in the form of a system of difference equations. This approach allows us to differentiate between the influx of the rolling layer…
The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
This report describes de design of an experiment that intends to compare two variants of a modeldriven system development method, so as to assess the impact of requirements engineering practice in the quality of the conceptual models. The…
Deep neural networks are behind many of the recent successes in machine learning applications. However, these models can produce overconfident decisions while encountering out-of-distribution (OOD) examples or making a wrong prediction.…
We propose a discrete traffic flow model with discrete time. Continuum limit of this model is equivalent to the optimal velocity model. It has also an ultradiscrete limit and a piecewise-linear type of traffic flow model is obtained. Both…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
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…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
This paper considers how a formal mathematically-based model can be used in support of evolutionary software development, and in particular how such a model can be kept consistent with the implementation as it changes to meet new…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…