Exploring the Unknowable Using Simulation: Structural Uncertainty in Multiscale Models

Multiscale systems, characterized by a range of spatial-temporal scales, arise widely in many scientific domains; from studies of protein conformational dynamics to multiphase processes and from nuclear physics to galaxy collisions. However, although multiscale modelling and simulation has enjoyed significant success within the past decade, many important questions remain open and have barely been explored. Multiscale models involve approximations in the representation of the real/multiscale system, to reduce its complexity to something insightful and tractable. However, one must choose what to 'approximate' as there is a trade-off between computational tractability and inevitable information loss. This also affects the process of 'bridging the gaps' in-between scales. As a result, there are numerous uncertainties present in multiscale models.
In this project, it is proposed to explore the structural uncertainty of multiscale models through a combination of computational techniques and nested optimisation algorithms, leading to a final "compromise" (solution) model. This will be applied to a multiscale biological problem, i.e. the formation of atherosclerotic plaque.
A multiscale model of atherosclerosis in mice will be proposed, based on previous research. Hypotheses will be integrated, spanning different biological/time scales. A scale separation map will be created, following. For each scale, processes/sub-processes will appear, and an optimisation function will be created, to satisfy the question "what is a good model for this scale?".
Relying on experimental data for validation, simulation or evolutionary optimisation techniques will be used to find the best fit, searching Pareto efficiency. Pareto is a state of allocation of resources in which it is impossible to make any one individual better-off without making at least one individual worse-off. There is a trade-off in biological systems consistent with the basis of life. It is expected that a set of choices will be presented to the modeller; by finding a Pareto-frontier and restricting attention to the set of choices that are Pareto-efficient, trade-offs can be made within this set, rather than considering the full range of every parameter. If an optimum cannot be found, this might reveal "structural" problems with the model at that scale, leading to an improvement cycle, until Pareto-optimality is reached.
After all scale-specific optima are found, a global optimisation cycle will be executed to find trade-offs between optimal solutions at different scales with an additional set of constraints: equations bridging the gap in-between scales, in order to find a solution that satisfies the "whole". Emergent behaviour will also appear, so, this will not be a case of confirming that scale-specific solutions "add up". It implies a new Pareto search, hopefully narrowed by the single-scale optimisation processes undergone previously.
Part of the process is to propose new ideas of how atherosclerosis works, with alternative ''model structures'' in principle nesting all alternatives within a larger global model. This requires enough knowledge and ingenuity to think of "all" important alternatives. The proviso being that what is modelled must first be imagined. This will depend on what science can tell. "What has not yet been imagined cannot be modelled, no matter how many experts are consulted. For immediate decisions, strong [and probably wrong] assumptions are required".