Instantons for the Destabilization of the Inner Solar System

Extreme events in transitional turbulence

Transitional localized turbulence in shear flows is known to either decay to an absorbing laminar state or to proliferate via splitting. The average passage times from one state to the other depend super-exponentially on the Reynolds number and lead to a crossing Reynolds number above which proliferation is more likely than decay. In this paper, we apply a rare-event algorithm, Adaptative Multilevel Splitting, to the deterministic Navier-Stokes equations to study transition paths and estimate large passage times in channel flow more efficiently than direct simulations. We establish a connection with extreme value distributions and show that transition between states is mediated by a regime that is self-similar with the Reynolds number. The super-exponential variation of the passage times is linked to the Reynolds number dependence of the parameters of the extreme value distribution. Finally, motivated by instantons from Large Deviation theory, we show that decay or splitting events approach a most-probable pathway. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.

Enhancing human-machine teaming for medical prognosis through neural ordinary differential equations (NODEs)

Machine learning (ML) has recently been demonstrated to rival expert-level human accuracy in prediction and detection tasks in a variety of domains, including medicine. Despite these impressive findings, however, a key barrier to the full realization of ML’s potential in medical prognoses is technology acceptance. Recent efforts to produce explainable AI (XAI) have made progress in improving the interpretability of some ML models, but these efforts suffer from limitations intrinsic to their design: they work best at identifying why a system fails, but do poorly at explaining when and why a model’s prediction is correct. We posit that the acceptability of ML predictions in expert domains is limited by two key factors: the machine’s horizon of prediction that extends beyond human capability, and the inability for machine predictions to incorporate human intuition into their models. We propose the use of a novel ML architecture, Neural Ordinary Differential Equations (NODEs) to enhance human understanding and encourage acceptability. Our approach prioritizes human cognitive intuition at the center of the algorithm design, and offers a distribution of predictions rather than single outputs. We explain how this approach may significantly improve human-machine collaboration in prediction tasks in expert domains such as medical prognoses. We propose a model and demonstrate, by expanding a concrete example from the literature, how our model advances the vision of future hybrid human-AI systems.