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Background: As available medical image datasets increase in size, it becomes infeasible for clinicians to review content manually for knowledge extraction. The objective of this study was to create an automated clustering resulting in human-interpretable pattern discovery. Methods: Images from the public HAM10000 dataset, including 7 common pigmented skin lesion diagnoses, were tiled into 29420 tiles and clustered via k-means using neural network-extracted image features. The final number of clusters per diagnosis was chosen by either the elbow method or a compactness metric balancing intra-lesion variance and cluster numbers. The amount of resulting non-informative clusters, defined as those containing less than six image tiles, was compared between the two methods. Results: Applying k-means, the optimal elbow cutoff resulted in a mean of 24.7 (95%-CI: 16.4-33) clusters for every included diagnosis, including 14.9% (95% CI: 0.8-29.0) non-informative clusters. The optimal cutoff, as estimated by the compactness metric, resulted in significantly fewer clusters (13.4; 95%-CI 11.8-15.1; p=0.03) and less non-informative ones (7.5%; 95% CI: 0-19.5; p=0.017). The majority of clusters (93.6%) from the compactness metric could be manually mapped to previously described dermatoscopic diagnostic patterns. Conclusions: Automatically constraining unsupervised clustering can produce an automated extraction of diagnostically relevant and human-interpretable clusters of visual patterns from a large image dataset.

A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine-learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A postprocessing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.

Grid maps, especially occupancy grid maps, are ubiquitous in many mobile robot applications. To simplify the process of learning the map, grid maps subdivide the world into a grid of cells, whose occupancies are independently estimated using only measurements in the perceptual field of the particular cell. However, the world consists of objects that span multiple cells, which means that measurements falling onto a cell provide evidence on the occupancy of other cells belonging to the same object. This correlation is not captured by current models. In this work, we present a way to generalize the update of grid maps relaxing the assumption of independence by modeling the relationship between the measurements and the occupancy of each cell as a set of latent variables, and jointly estimating those variables and the posterior of the map. Additionally, we propose a method to estimate the latent variables by clustering based on semantic labels and an extension to the Normal Distributions Transfer Occupancy Map (NDT-OM) to facilitate the proposed map update method. We perform comprehensive experiments of map creation and localization with real world data sets, and show that the proposed method creates better maps in highly dynamic environments compared to state-of-the-art methods. Finally, we demonstrate the ability of the proposed method to remove occluded objects from the map in a lifelong map update scenario.

This work uses the entropy-regularised relaxed stochastic control perspective as a principled framework for designing reinforcement learning (RL) algorithms. Herein agent interacts with the environment by generating noisy controls distributed according to the optimal relaxed policy. The noisy policies on the one hand, explore the space and hence facilitate learning but, on the other hand, introduce bias by assigning a positive probability to non-optimal actions. This exploration-exploitation trade-off is determined by the strength of entropy regularisation. We study algorithms resulting from two entropy regularisation formulations: the exploratory control approach, where entropy is added to the cost objective, and the proximal policy update approach, where entropy penalises policy divergence between consecutive episodes. We focus on the finite horizon continuous-time linear-quadratic (LQ) RL problem, where a linear dynamics with unknown drift coefficients is controlled subject to quadratic costs. In this setting, both algorithms yield a Gaussian relaxed policy. We quantify the precise difference between the value functions of a Gaussian policy and its noisy evaluation and show that the execution noise must be independent across time. By tuning the frequency of sampling from relaxed policies and the parameter governing the strength of entropy regularisation, we prove that the regret, for both learning algorithms, is of the order $\mathcal{O}(\sqrt{N}) $ (up to a logarithmic factor) over $N$ episodes, matching the best known result from the literature.

Quantum reinforcement learning (QRL) has emerged as a framework to solve sequential decision-making tasks, showcasing empirical quantum advantages. A notable development is through quantum recurrent neural networks (QRNNs) for memory-intensive tasks such as partially observable environments. However, QRL models incorporating QRNN encounter challenges such as inefficient training of QRL with QRNN, given that the computation of gradients in QRNN is both computationally expensive and time-consuming. This work presents a novel approach to address this challenge by constructing QRL agents utilizing QRNN-based reservoirs, specifically employing quantum long short-term memory (QLSTM). QLSTM parameters are randomly initialized and fixed without training. The model is trained using the asynchronous advantage actor-aritic (A3C) algorithm. Through numerical simulations, we validate the efficacy of our QLSTM-Reservoir RL framework. Its performance is assessed on standard benchmarks, demonstrating comparable results to a fully trained QLSTM RL model with identical architecture and training settings.

This study focuses on the use of model and data fusion for improving the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions of separated flows. In particular, our goal is to develop of models that not-only assimilate sparse experimental data to improve performance in computational models, but also generalize to unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the Ensemble Kalman Filtering approach (EnKF), to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via a parameterization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected velocity profiles, skin friction, and pressure coefficients for separated flows. Despite using of observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the 2D-bump and modified BFS. Significant improvement is observed in the quantities of interest, i.e., skin friction coefficient ($C_f$) and pressure coefficient ($C_p$) for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for external, unseparated flows, such as flow around a NACA-0012 airfoil without any danger of extrapolation, and that the individually calibrated terms in the SA model are targeted towards specific flow-physics wherein the calibrated production term improves the re-circulation zone while destruction improves the recovery zone.

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric nonlinear Hamiltonian systems is challenged by several factors: (i) the geometric structure encoding the physical properties of the dynamics; (ii) the slowly decaying Kolmogorov n-width of conservative dynamics; (iii) the gradient structure of the nonlinear flow velocity; (iv) high variations in the numerical rank of the state as a function of time and parameters. We propose to address these aspects via a structure-preserving adaptive approach that combines symplectic dynamical low-rank approximation with adaptive gradient-preserving hyper-reduction and parameters sampling. Additionally, we propose to vary in time the dimensions of both the reduced basis space and the hyper-reduction space by monitoring the quality of the reduced solution via an error indicator related to the projection error of the Hamiltonian vector field. The resulting adaptive hyper-reduced models preserve the geometric structure of the Hamiltonian flow, do not rely on prior information on the dynamics, and can be solved at a cost that is linear in the dimension of the full order model and linear in the number of test parameters. Numerical experiments demonstrate the improved performances of the fully adaptive models compared to the original and reduced models.

We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement learning with no prior heuristics. The actions performed on the mesh are standard local and global element operations. The goal is to minimize the deviation of the node degrees from their ideal values, which in the case of interior vertices leads to a minimization of irregular nodes.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.