Topic
Nonlinear modelling
About: Nonlinear modelling is a research topic. Over the lifetime, 572 publications have been published within this topic receiving 11618 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a variety of nonlinear models that are appropriate for modelling plant growth and, for each, calculate function-derived growth rates, which allow unbiased comparisons among species at a common time or size.
Abstract: Summary
1 Plant growth is a fundamental ecological process, integrating across scales from physiology to community dynamics and ecosystem properties Recent improvements in plant growth modelling have allowed deeper understanding and more accurate predictions for a wide range of ecological issues, including competition among plants, plant–herbivore interactions and ecosystem functioning
2 One challenge in modelling plant growth is that, for a variety of reasons, relative growth rate (RGR) almost universally decreases with increasing size, although traditional calculations assume that RGR is constant Nonlinear growth models are flexible enough to account for varying growth rates
3 We demonstrate a variety of nonlinear models that are appropriate for modelling plant growth and, for each, show how to calculate function-derived growth rates, which allow unbiased comparisons among species at a common time or size We show how to propagate uncertainty in estimated parameters to express uncertainty in growth rates Fitting nonlinear models can be challenging, so we present extensive worked examples and practical recommendations, all implemented in R
4 The use of nonlinear models coupled with function-derived growth rates can facilitate the testing of novel hypotheses in population and community ecology For example, the use of such techniques has allowed better understanding of the components of RGR, the costs of rapid growth and the linkage between host and parasite growth rates We hope this contribution will demystify nonlinear modelling and persuade more ecologists to use these techniques
595 citations
TL;DR: In this paper, the geometrically nonlinear behavior of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme.
Abstract: The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs.
Different objective functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear response. The problem is circumvented by optimizing the structures for multiple loading conditions or by minimizing the complementary elastic work. Examples show that differences in stiffnesses of structures optimized using linear and nonlinear modelling are generally small but they can be large in certain cases involving buckling or snap-through effects.
496 citations
TL;DR: The authors examined the forecast accuracy of linear autoregressive, smooth transition auto-regression (STAR), and neural network (NN) time series models for 47 macroeconomic variables of the G7 economies.
315 citations
TL;DR: A method to model nonlinear systems using polynomial nonlinear state space equations by identifying first the best linear approximation of the system under test is proposed.
304 citations
21 May 2001
TL;DR: This paper gives a short introduction to some new developments related to support vector machines (SVM), a new class of kernel based techniques introduced within statistical learning theory and structural risk minimization which lends to solving convex optimization problems and also the model complexity follows from this solution.
Abstract: Neural networks such as multilayer perceptrons and radial basis function networks have been very successful in a wide range of problems. In this paper we give a short introduction to some new developments related to support vector machines (SVM), a new class of kernel based techniques introduced within statistical learning theory and structural risk minimization. This new approach lends to solving convex optimization problems and also the model complexity follows from this solution. We especially focus on a least squares support vector machine formulation (LS-SVM) which enables to solve highly nonlinear and noisy black-box modelling problems, even in very high dimensional input spaces. While standard SVMs have been basically only applied to static problems like classification and function estimation, LS-SVM models have been extended to recurrent models and use in optimal control problems. Moreover, using weighted least squares and special pruning techniques, LS-SVMs can be employed for robust nonlinear estimation and sparse approximation. Applications of (LS)-SVMs to a large variety of artificial and real-life data sets indicate the huge potential of these methods.
290 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 1 |
| 2021 | 22 |
| 2020 | 19 |
| 2019 | 27 |
| 2018 | 22 |
| 2017 | 25 |