Mathematical models of biology commonly use differential equation formulations. Certain application areas, such as signal transduction modeling or scientific machine learning, involve models that contain many parameters. Efficient training of these models requires sensitivity analysis that scales well as the number of parameters grows. Hence, adjoint sensitivity analysis (ASA) is typically...
The field of scientific machine learning (SciML) seeks to fuse traditional mathematical modeling with advances in machine learning to balance mechanist equations with data-driven inference, resulting in computational models that preserve scientific knowledge while readily adapting to the unknown through data-driven discovery. These advancements are setting the foundation for which SciML...
Identifying tipping points in spatially distributed ecosystems is critical for conservation but remains challenging due to the complexity of nonlinear dynamics, spatial connectivity, and limited observational data. We present a framework combining Universal Differential Equations (UDEs) with a novel dynamic gradient matching algorithm to learn ecosystem dynamics from large-scale remotely...
Biological data often exhibit substantial heterogeneity between individuals. While part of this variability reflects random biological variation, systematic differences may arise from physiological diversity or disease. To reflect this diversity in mechanistic models, we often use the same mathematical equations, while individuals differ in parameter values that govern system dynamics....
Drug-induced damage to the blood-forming system, also called
hematotoxicity, is a frequent side effect of cytotoxic chemotherapy. Due
to high patient heterogeneity, it remains difficult to predict
individual treatment responses. Mechanistic models describing
thrombopoiesis provide some physiological interpretability but often
fail to capture individual irregular patient trajectories....
Mechanistic ordinary differential equation (ODE) models are a powerful tool for studying biological systems. However, their predictive power is constrained by gaps, biases, and inconsistencies in the literature. They typically also require quantitative time-lapse data for training, which is time-consuming to collect. While training could benefit from integrating other modalities such as omics...
Cells respond to their environment through protein networks often dysregulated in cancer, making predictive modelling crucial. Because experiments capture only limited observables, coarse-graining is needed to uncover low-dimensional descriptions. Yet classical approaches rely on idealised assumptions, leaving it unclear when partial experimental observations support reduced system dynamics....
Parameter fitting workflows, in which model parameter values are recovered from data, are well established in mathematical biology. The introduction of universal differential equations (UDEs) extends this framework by enabling the estimation of not only scalar parameters but also unknown functions. Examples include learning a proteinโs production rate as a function of its transcription factor...
Mechanistic differential equation models are widely used in biology and medicine, but have limited ability to handle incomplete system knowledge. Hybrid modelling approaches (also termed โScientific Machine Learning") aim to address this by combining mechanistic differential equations with data-driven machine learning components. This minisymposium focuses on a conceptually simple, yet...
