Related papers: Unveiling Scaling Laws of Parameter Identifiabilit…
Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models…
Multiscale modeling of complex systems is crucial for understanding their intricacies. Data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. On the other hand,…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…
Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based…
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…
The use of machine learning models in system identification has increased due to their ability to approximate complex nonlinear dynamics with high accuracy. However, often it is not clear how the performance of trained models scales with…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…
Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…
Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model…
This paper presents a hierarchical Bayesian modeling framework for the uncertainty quantification in modal identification of linear dynamical systems using multiple vibration data sets. This novel framework integrates the state-of-the-art…
An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot…
How much data is enough to make a scientific discovery? As biomedical datasets scale to millions of samples and AI models grow in capacity, progress increasingly depends on predicting when additional data will substantially improve…
Disease models are used to examine the likely impact of therapies, interventions and public policy changes. Ensuring that these are well calibrated on the basis of available data and that the uncertainty in their projections is properly…
Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…
In Structural Health Monitoring (SHM), the recovery of distributed mechanical parameters from sparse data is often ill-posed, raising critical questions about identifiability and the reliability of inferred states. While deterministic…
Computational molecular modeling and visualization has seen significant progress in recent years with sev- eral molecular modeling and visualization software systems in use today. Nevertheless the molecular biology community lacks…
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with…
In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for…