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Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…

This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…

We present a critical survey on the consistency of uncertainty quantification used in deep learning and highlight partial uncertainty coverage and many inconsistencies. We then provide a comprehensive and statistically consistent framework…

As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…

We present a deep learning framework for quantifying and propagating uncertainty in systems governed by non-linear differential equations using physics-informed neural networks. Specifically, we employ latent variable models to construct…

Uncertainty quantification is a key pillar of trustworthy machine learning. It enables safe reactions under unsafe inputs, like predicting only when the machine learning model detects sufficient evidence, discarding anomalous data, or…

Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and demands…

When a robot autonomously performs a complex task, it frequently must balance competing objectives while maintaining safety. This becomes more difficult in uncertain environments with stochastic outcomes. Enhancing transparency in the…

This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…

While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…

Machine-learning models of atomic-scale interactions achieve the accuracy of the quantum mechanical calculations on which they are trained, but at a dramatically lower computational cost. Their predictions can be made trustworthy by…

The work focuses on gathering high-fidelity and low-fidelity numerical simulations data using Nektar++ (Solver based on Applied Mathematics) and XFOIL respectively. The utilization of the higher polynomial distribution in calculating the…

We consider ill-posed inverse problems where the forward operator $T$ is unknown, and instead we have access to training data consisting of functions $f_i$ and their noisy images $Tf_i$. This is a practically relevant and challenging…

Representation learning plays a critical role in the analysis of time series data and has high practical value across a wide range of applications. including trend analysis, time series data retrieval and forecasting. In practice, data…

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process…

Federated Learning (FL) is a collaborative machine learning paradigm for enhancing data privacy preservation. Its privacy-preserving nature complicates the explanation of the decision-making processes and the evaluation of the reliability…

Reliable uncertainty quantification is critical in high-stakes applications, such as medical diagnosis, where confidently incorrect predictions can erode trust in automated decision-making systems. Traditional uncertainty quantification…

Uncertainty estimation in machine learning is paramount for enhancing the reliability and interpretability of predictive models, especially in high-stakes real-world scenarios. Despite the availability of numerous methods, they often pose a…

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration,…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…