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We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…
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…
We study the chaotic properties of a turbulent conducting fluid using direct numerical simulation in the Eulerian frame. The maximal Lyapunov exponent is measured for simulations with varying Reynolds number and magnetic Prandtl number. We…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…
In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the…
Time series forecasting is essential across domains from finance to supply chain management. This paper introduces ForecastGAN, a novel decomposition based adversarial framework addressing limitations in existing approaches for…
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
Planning long-horizon manipulation motions using a set of predefined skills is a central challenge in robotics; solving it efficiently could enable general-purpose robots to tackle novel tasks by flexibly composing generic skills. Solutions…
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
The Rising Multi-Armed Bandit (RMAB) framework models environments where expected rewards of arms increase with plays, which models practical scenarios where performance of each option improves with the repeated usage, such as in robotics…
Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…
Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…
This position paper argues that the next generation of artificial intelligence in meteorological and climate sciences must transition from fragmented hybrid heuristics toward a unified paradigm of physics-guided multimodal transformers.…
This work addresses the classic machine learning problem of online prediction with expert advice. A new potential-based framework for the fixed horizon version of this problem has been recently developed using verification arguments from…
We confirm a long-standing conjecture concerning shear-induced chaos in stochastically perturbed systems exhibiting a Hopf bifurcation. The method of showing the main chaotic property, a positive Lyapunov exponent, is a computer-assisted…