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The multilevel Monte Carlo (MLMC) method is highly efficient for estimating expectations of a functional of a solution to a stochastic differential equation (SDE). However, MLMC estimators may be unstable and have a poor (noncanonical)…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
Given the importance of urban sustainability and resilience to the future of our planet, there is a need to better understand the interconnectedness between the social, economic, environmental, and governance outcomes that underline these…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the…
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and R\"ossler models with their iconic attractors, and demonstrate…
Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs…
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC…
Model Predictive Control (MPC) is a successful control methodology, which is applied to increasingly complex systems. However, real-time feasibility of MPC can be challenging for complex systems, certainly when an (extremely) large number…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to…
Recent studies highlight economic complexity's role in mitigating fiscal crises, often measured via an economy's trade structure. Trade, however, is just one facet of an economy's structure and omits critical innovative activities like…
Large language models exhibit a puzzling inconsistency: they solve complex problems yet frequently fail on seemingly simpler ones. We investigate whether LLMs internally encode problem difficulty in a way that aligns with human judgment,…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
Standpoint linear temporal logic SLTL is a recent formalism able to model possibly conflicting commitments made by distinct agents, taking into account aspects of temporal reasoning. In this paper, we analyse the computational properties of…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
In the stochastic gradient descent (SGD) for sequential simulations such as the neural stochastic differential equations, the Multilevel Monte Carlo (MLMC) method is known to offer better theoretical computational complexity compared to the…
Over the last two decades, the Latent Position Model (LPM) has become a prominent tool to obtain model-based visualizations of networks. However, the geometric structure of the LPM is inherently symmetric, in the sense that outgoing and…
As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because…
This study contributes to the body of work on instabilities in the homogeneous cooling system focusing on clustering in the multiphase gas-particle system. The critical system size for the onset of instability, $L^*_c$, is studied via three…