相关论文: Cause and Cure of Sloppiness in Ordinary Different…

Dynamic models of biochemical networks typically consist of sets of non-linear ordinary differential equations involving states (concentrations or amounts of the components of the network) and parameters describing the reaction kinetics.…

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy; the system behavior depends only on a few `stiff'…

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter…

The functioning of many biochemical networks is often robust -- remarkably stable under changes in external conditions and internal reaction parameters. Much recent work on robustness and evolvability has focused on the structure of neutral…

We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Sloppy models are complex nonlinear models with outcomes that are significantly affected by only a small subset of parameter combinations. Despite forming an important universality class and arising frequently in practice, formal and…

Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations…

Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised…

This work introduces a stochastic hierarchical optimization framework inspired by Sloppy Model theory for the efficient calibration of physical models. Central to this method is the use of a reduced Hessian approximation, which identifies…

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…

Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…

In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…

Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…

Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…