Related papers: Data-driven polynomial chaos expansion for machine…

To facilitate robust and trustworthy deployment of large language models (LLMs), it is essential to quantify the reliability of their generations through uncertainty estimation. While recent efforts have made significant advancements by…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…

While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

To use machine learning in high stakes applications (e.g. medicine), we need tools for building confidence in the system and evaluating whether it is reliable. Methods to improve model reliability often require new learning algorithms (e.g.…

Computational cardiac modelling is a mature area of biomedical computing, and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…

Data-driven control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, besides measurement noise, stochastic disturbances might also directly affect…

A robust adaptive model predictive control (MPC) algorithm is presented for linear, time invariant systems with unknown dynamics and subject to bounded measurement noise. The system is characterized by an impulse response model, which is…

Scenario-based optimization and control has proven to be an efficient approach to account for system uncertainty. In particular, the performance of scenario-based model predictive control (MPC) schemes depends on the accuracy of uncertainty…

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…

Microgrids (MGs) are regarded as effective solutions to provide ramping support to the main grid during heavy-load periods. Nevertheless, the uncertain renewable energy sources (RES) and electric vehicles (EVs) integrated into an MG may…

Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of…

Although deep neural networks have made remarkable achievements in the field of automatic modulation recognition (AMR), these models often require a large amount of labeled data for training. However, in many practical scenarios, the…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…

Predictive coding (PC) is an influential theory of information processing in the brain, providing a biologically plausible alternative to backpropagation. It is motivated in terms of Bayesian inference, as hidden states and parameters are…