Tim Dodwell

Sai-Aakash Ramesh, Archit Sood, Andrew Corbett et al.

Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While distributional reduction-encompassing joint clustering and dimensionality reduction-offers a principled way to summarize data, its supervised variants remain relatively under-explored, despite the importance of retaining task-relevant signal for downstream prediction and decision-making. We propose Supervised Distributional Reduction (SDR), an algorithm for learning target-aware representations by combining optimal transport with explicit dependence maximization. SDR builds on the Fused Gromov-Wasserstein (FGW) objective to align the relational structure of the input distribution with a set of representative points, while augmenting it with a direct dependence term that encourages the learned embeddings to capture predictive signal more explicitly. This results in compact representations that reflect both geometric structure and supervision. Beyond representation learning, SDR naturally induces a data-dependent, non-stationary geometry that can be leveraged for settings such as Gaussian Process (GP) modelling. By redefining distances through target-aware distributional alignment, SDR enables the construction of adaptive kernels that respond to local variations in both data geometry and supervision, offering an optimal transport-based perspective on non-stationary kernel design.

Gianluca Detommaso, Tim Dodwell, Rob Scheichl · amazon-science

In this paper, we present a generalisation of the Multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This Continuous Level Monte Carlo (CLMC) estimator provides a natural framework in PDE applications to adapt the model hierarchy to each sample. In addition, it can be made unbiased with respect to the expected value of the true quantity of interest provided the quantity of interest converges sufficiently fast. The practical implementation of the CLMC estimator is based on interpolating actual evaluations of the quantity of interest at a finite number of resolutions. As our new level parameter, we use the logarithm of a goal-oriented finite element error estimator for the accuracy of the quantity of interest. We prove the unbiasedness, as well as a complexity theorem that shows the same rate of complexity for CLMC as for MLMC. Finally, we provide some numerical evidence to support our theoretical results, by successfully testing CLMC on a standard PDE test problem. The numerical experiments demonstrate clear gains for sample-wise adaptive refinement strategies over uniform refinements.

Andrew Corbett, Archit Sood, Anna Tzatzopoulou et al.

Recent work on recursive architectures has shown that tiny neural networks can be surprisingly powerful on structured reasoning tasks. The trick is to model reasoning trajectories with a latent dynamical system. We argue that the inference-time behaviour of these architectures is best understood as approximate inference over latent reasoning trajectories, with deterministic recursion as the one-particle, zero-noise limit. We make this view operational through guided stochastic exploration: stochastic perturbations of the reasoning dynamics propose neighbouring trajectories, and the model's existing early-stopping head reweights them online. The framework yields three label-free diagnostics: local stability, guide alignment, and cloud-token entropy. These predict, from inference traces alone, whether the procedure will help and which of its outputs to trust. On Sudoku-Extreme it lifts exact-solve accuracy from $85.9\%$ to $98.0\%$ without retraining; on Maze-Hard the diagnostics flag a misaligned guide, as validation performance later confirms. The same machinery thus characterises both when recursive reasoning has room to improve at the trajectory level and when the model's internal guide can recover it.

Nick Pepper, George De Ath, Marc Thomas et al.

Trajectory prediction (TP) plays an important role in supporting the decision-making of Air Traffic Controllers (ATCOs). Traditional TP methods are deterministic and physics-based, with parameters that are calibrated using aircraft surveillance data harvested across the world. These models are, therefore, agnostic to the intentions of the pilots and ATCOs, which can have a significant effect on the observed trajectory, particularly in the lateral plane. This work proposes a generative method for lateral TP, using probabilistic machine learning to model the effect of the epistemic uncertainty arising from the unknown effect of pilot behaviour and ATCO intentions. The models are trained to be specific to a particular sector, allowing local procedures such as coordinated entry and exit points to be modelled. A dataset comprising a week's worth of aircraft surveillance data, passing through a busy sector of the United Kingdom's upper airspace, was used to train and test the models. Specifically, a piecewise linear model was used as a functional, low-dimensional representation of the ground tracks, with its control points determined by a generative model conditioned on partial context. It was found that, of the investigated models, a Bayesian Neural Network using the Laplace approximation was able to generate the most plausible trajectories in order to emulate the flow of traffic through the sector.

Anne Reinarz, Tim Dodwell, Tim Fletcher et al.

Finite element (FE) analysis has the potential to offset much of the expensive experimental testing currently required to certify aerospace laminates. However, large numbers of degrees of freedom are necessary to model entire aircraft components whilst accurately resolving micro-scale defects. The new module dune-composites, implemented within DUNE by the authors, provides a tool to efficiently solve large-scale problems using novel iterative solvers. The key innovation is a preconditioner that guarantees a constant number of iterations regardless of the problem size. Its robustness has been shown rigorously in Spillane et al. (Numer. Math. 126, 2014) for isotropic problems. For anisotropic problems in composites it is verified numerically for the first time in this paper. The parallel implementation in DUNE scales almost optimally over thousands of cores. To demonstrate this, we present an original numerical study, varying the shape of a localised wrinkle and the effect this has on the strength of a curved laminate. This requires a high-fidelity mesh containing at least four layers of quadratic elements across each ply and interface layer, underlining the need for dune-composites, which can achieve run times of just over 2 minutes on 2048 cores for realistic composites problems with 173 million degrees of freedom.