Related papers: ECO: Energy-Constrained Operator Learning for Chao…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…
We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…
Machine learning detects patterns, block chain guarantees trust and immutability, and modern causal inference identifies directional linkages, yet none alone exposes the full energetic anatomy of complex systems; the Hamiltonian Higher…
Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on…
Among the most relevant processes in the Earth system for human habitability are quasi-periodic, ocean-driven multi-year events whose dynamics are currently incompletely characterized by physical models, and hence poorly predictable. This…
Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…
We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…
Foundation models often generate unreliable answers, while heuristic uncertainty estimators fail to fully distinguish correct from incorrect outputs, causing users to accept erroneous answers without any statistical guarantee. We address…
Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these…
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…
This paper demonstrates the benefits of imposing stability on data-driven Koopman operators. The data-driven identification of stable Koopman operators (DISKO) is implemented using an algorithm \cite{mamakoukas_stableLDS2020} that computes…
This paper addresses the eco-driving problem for connected vehicles on urban roads, considering localization uncertainty. Eco-driving is defined as longitudinal speed planning and control on roads with the presence of a sequence of traffic…
We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic…
In this article, we investigate the implications of the unsupervised learning rule known as Input-Correlations (ICO) learning in the nonlinear dynamics of two linearly coupled PT-symmetric Li\'enard oscillators. The fixed points of the…
We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a…