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Computational models provide crucial insights into complex biological processes such as cancer evolution, but their mechanistic nature often makes them nonlinear and parameter-rich, complicating calibration. We systematically evaluate…
Mathematical models are routinely applied to interpret biological data, with common goals that include both prediction and parameter estimation. A challenge in mathematical biology, in particular, is that models are often complex and…
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…
Machine learning holds tremendous promise for transforming the fundamental practice of scientific discovery by virtue of its data-driven nature. With the ever-increasing stream of research data collection, it would be appealing to…
Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
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 estimation of unknown values of parameters (or hidden variables, control variables) that characterise a physical system often relies on the comparison of measured data with synthetic data produced by some numerical simulator of the…
Choosing a suitable model and determining its associated parameters from fitting to experimental data is fundamental for many problems in biomechanics. Models of shear-thinning complex fluids, dating from the work of Bird, Carreau, Cross…
Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive…
Cancer pathology is unique to a given individual, and developing personalized diagnostic and treatment protocols are a primary concern. Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
Modeling of brain tumor dynamics has the potential to advance therapeutic planning. Current modeling approaches resort to numerical solvers that simulate the tumor progression according to a given differential equation. Using…
Rapid technological advances have allowed for molecular profiling across multiple omics domains from a single sample for clinical decision making in many diseases, especially cancer. As tumor development and progression are dynamic…
Background: The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
Identifiability concerns finding which unknown parameters of a model can be quantified from given input-output data. Many linear ODE models, used in systems biology and pharmacokinetics, are unidentifiable, which means that parameters can…
The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case,…