Research

Research Overview

My research sits at the intersection of $\color{#00a0d1}{\text{statistical theory,}}$ $\color{#00a0d1}{\text{probabilistic computation,}}$ and $\color{#00a0d1}{\text{scientific inference}}$. I enjoy developing principled frameworks for reasoning under uncertainty in complex, high-dimensional systems.

Specifically, my research spans the topics of Uncertainty quantification, Bayesian inverse problems, Monte carlo inference, Active learning and Optimization under uncertainty with application areas from computer experiments and engineering sciences to digital twins and mission-critical physical systems.

Bayesian inverse problems

$\color{#00a0d1}{\text{Inverse problems ask:}}$ given observations $y = \mathcal{G}(u) + \varepsilon$, can we recover the unknown field or parameter $u$? The forward operator $\mathcal{G}$ is typically a differential equation or physical model, making direct inversion ill-posed in the Hadamard sense.

The Bayesian formulation regularises this naturally: by placing a prior $\pi_0(u)$ over the unknown and conditioning on data, the posterior

encodes full uncertainty over plausible reconstructions. My work focuses on developping scalable computational methods for characterising this posterior and frequentist approaches to this problem with uncertainty guarantees.

Topics: Computer Model Calibration · Tikhonov–Bayes connections · pCN algorithms · posterior consistency

Uncertainty quantification

Complex computational models, from climate simulators to structural solvers, propagate uncertainty in a way that is rarely tractable analytically. $\color{#00a0d1}{\text{UQ provides the mathematical}}$ $\color{#00a0d1}{\text{toolkit}}$ to characterise how $\color{#00a0d1}{\text{input uncertainty p(x)}} $ maps to $\color{#00a0d1}{\text{output variability p(y)}},$ through a black-box or grey-box model $y = f(x)$.

My research addresses both:

• $\color{#00a0d1}{\text{Forward propagation:}}$ using surrogate modelling (typically GPs but trying to learn more about polynomial chaos expansions and neural networks nowadays) to push distributions through expensive simulators.
• $\color{#00a0d1}{\text{Sensitivity analysis:}}$ — via Sobol’ indices and variance decompositions to identify which inputs drive output uncertainty, formally expressed as \(S_i = \frac{\mathbb{V}[\mathbb{E}[Y \mid X_i]]}{\mathbb{V}[Y]}\)

I am particularly interested in settings where $f$ is expensive to evaluate, coupling emulator construction with rigorous statistical estimation of uncertainty measures and their confidence intervals.

Topics: Gaussian Process (and their variants) emulation · Sobol’ indices · error propagation · conformal prediction

Bayesian Optimization & Optimization under uncertainty

When the objective $f: \mathcal{X} \to \mathbb{R}$ is expensive, noisy, or unknown, classical optimisation methods are inapplicable. $\color{#00a0d1}{\text{Bayesian optimisation (BO) maintains a probabilistic}}$ $\color{#00a0d1}{\text{surrogate and sequentially evalautes points that maximise an acquisition }}$ $\color{#00a0d1}{\text{ function balancing exploration and exploitation,}}$ such as expected improvement

Beyond standard BO, I am interested in optimisation under uncertainty, where the objective itself involves an expectation over stochastic inputs:

requiring joint surrogate models over both inputs variables and “hyperparameters”. Applications span experiment design, hyperparameter tuning, and robust engineering design.

Topics: Sequential design · acquisition functions · Thompson sampling · batch BO ·

Active learning (AL)

$\color{#00a0d1}{\text{Active learning addresses the data-efficiency problem:}}$ given a budget of $N$ labelled observations, which input location $x_1, \ldots, x_N \in \mathcal{X}$ should be selected to maximise learning? The Bayesian framing connects directly to optimal experimental design — choosing experiments to maximise expected information gain

I aim to develop AL strategies for scientific and engineering applications where evaluations are costly, including batch-sequential designs and possibly online settings. A recurring theme is the interplay between the surrogate model’s epistemic uncertainty and the practical cost associated with new input location , particularly in settings with structured input spaces or physics-based constraints.

Topics: optimal experimental design · information gain · acquisition functions · surrogates · ALM/ALC/ALD

Monte carlo inference

Update coming soon!

$\color{#00a0d1}{\text{These areas are deeply interconnected!}}$ Monte Carlo inference underpins Bayesian inverse problems; active learning drives data collection for UQ; Bayesian optimisation uses the same GP machinery as uncertainty propagation.