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Stochasticity plays a key role in many biological systems, necessitating the calibration of stochastic mathematical models to interpret associated data. For model parameters to be estimated reliably, it is typically the case that they must…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
Probabilistic models inform an increasingly broad range of business and policy decisions ultimately made by people. Recent algorithmic, computational, and software framework development progress facilitate the proliferation of Bayesian…
We present how a probabilistic model can describe the asymptotic behaviour of the iterations, especially for ODE with an approach of the Poincar\'e-Bendixon's problem in $\mathbb{R}^d$. On pr\'esente un mod\`ele probabiliste pour d\'ecrire…
Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical…
Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem,…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
Partially observable Markov Decision Processes (POMDPs) are a standard model for agents making decisions in uncertain environments. Most work on POMDPs focuses on synthesizing strategies based on the available capabilities. However, system…
This paper introduces a new modeling framework for optimization under uncertainty, called Probable Event Constrained Optimization (PECO). Unlike conventional chance-constrained formulations, which only limit the probability of constraint…
Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique…
Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to…
Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to…
We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…
Probabilistic model checking is an approach to the formal modelling and analysis of stochastic systems. Over the past twenty five years, the number of different formalisms and techniques developed in this field has grown considerably, as…
We address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is…
Ensuring structural reliability remains a core concern in civil engineering, yet the quantitative effects of quality control measures on material variability and safety margins are not fully understood, especially for materials other than…
Index tuning is crucial for optimizing database performance by selecting optimal indexes based on workload. The key to this process lies in an accurate and efficient benefit estimator. Traditional methods relying on what-if tools often…
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…
Electrical infrastructures provide services at the basis of a number of application sectors, several of which are critical from the perspective of human life, environment or financials. Following the increasing trend in electricity…