Related papers: Exploring the tropical Pacific manifold in models …
Economic assessment in environmental science concerns the measurement or valuation of environmental impacts, adaptation, and vulnerability. Integrated assessment modeling is a unifying framework of environmental economics, which attempts to…
A possible deepening of the ocean mixed layer was investigated at a selected point of the Patagonian continental shelf where a significant positive wind speed trend was estimated. Using a 1-dimensional vertical numerical model (S2P3) forced…
Anthropogenic influences have been linked to tropical cyclone (TC) poleward migration, TC extreme precipitation, and an increased proportion of major hurricanes [1, 2, 3, 4]. Understanding past TC trends and variability is critical for…
A central challenge in climate science and applied mathematics is developing data-driven models of multiscale systems that capture both stationary statistics and responses to external perturbations. Current neural climate emulators aim to…
This work introduces a formulation of model predictive control (MPC) which adaptively reasons about the complexity of the model based on the task while maintaining feasibility and stability guarantees. Existing MPC implementations often…
We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order…
Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often…
In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
A central objective of topological data analysis is to identify topologically significant features in data represented as a finite point cloud. We consider the setting where the ambient space of the point sample is a compact Riemannian…
Sub-seasonal climate forecasting (SSF) focuses on predicting key climate variables such as temperature and precipitation in the 2-week to 2-month time scales. Skillful SSF would have immense societal value, in areas such as agricultural…
A new procedure is proposed for the dimensional reduction of time series. Similarly to principal components, the procedure seeks a low-dimensional manifold that minimizes information loss. Unlike principal components, however, the new…
Marine invasive species spread through global shipping and generate substantial ecological and economic impacts. Traditional risk assessments require detailed records of ballast water and traffic patterns, which are often incomplete,…
Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original…
Continuous attractor networks (CANs) are a well-established class of models for representing low-dimensional continuous variables such as head direction, spatial position, and phase. In canonical spatial domains, transitions along the…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as…