This work presents a unified framework for the unsupervised prediction of physically plausible interpolations between two 3D articulated shapes and the automatic estimation of dense correspondence between them. Interpolation is modelled as a diffeomorphic transformation using a smooth, time-varying flow field governed by Neural Ordinary Differential Equations (ODEs). This ensures topological consistency and non-intersecting trajectories while accommodating hard constraints, such as volume preservation, and soft constraints, e.g. physical priors. Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterisations. By providing a simple skeleton for the source shape only, we impose physically motivated constraints on the deformation field and resolve symmetric ambiguities. This is achieved without relying on skinning weights or any prior knowledge of the skeleton's target pose configuration. Qualitative and quantitative results demonstrate competitive or superior performance over existing state-of-the-art approaches in both shape correspondence and interpolation tasks across standard datasets.

We present an unsupervised framework for physically plausible shape interpolation and dense correspondence estimation between 3D articulated shapes. Our approach intentionally focuses upon pose variation within the same identity, which we believe is a meaningful and challenging problem in its own right. Our method uses Neural Ordinary Differential Equations (NODEs) to generate smooth flow fields that define diffeomorphic transformations, ensuring topological consistency and preventing self-intersections while accommodating hard constraints, such as volume preservation. By incorporating a lightweight skeletal structure, we impose kinematic constraints that resolve symmetries without requiring manual skinning or predefined poses. We enhance physical realism by interpolating skeletal motion with dual quaternions and applying constrained optimisation to align the flow field with the skeleton, preserving local rigidity. Additionally, we employ an efficient formulation of Normal Cycles, a metric from geometric measure theory, to capture higher-order surface details like curvature, enabling precise alignment between complex articulated structures and recovery of accurate dense correspondence mapping. Evaluations on multiple benchmarks show notable improvements over state-of-the-art methods in both interpolation quality and correspondence accuracy, with consistent performance across different skeletal configurations, demonstrating broad utility for shape matching and animation tasks.

Station-keeping tasks for high-altitude balloons show promise in areas such as ecological surveys, atmospheric analysis, and communication relays. However, identifying the optimal time and position to launch a latex high-altitude balloon is still a challenging and multifaceted problem. For example, tasks such as forest fire tracking place geometric constraints on the launch location of the balloon. Furthermore, identifying the most optimal location also heavily depends on atmospheric conditions. We first illustrate how reinforcement learning-based controllers, frequently used for station-keeping tasks, can exploit the environment. This exploitation can degrade performance on unseen weather patterns and affect station-keeping performance when identifying an optimal launch configuration. Valuing all states equally in the region, the agent exploits the region’s geometry by flying near the edge, leading to risky behaviours. We propose a modification which compensates for this exploitation and finds this leads to, on average, higher steps within the target region on unseen data. Then, we illustrate how Bayesian Optimisation (BO) can identify the optimal launch location to perform station-keeping tasks, maximising the return from a given rollout. We show BO can find this launch location in fewer steps compared to other optimisation methods. Results indicate that, surprisingly, the most optimal location to launch from is not commonly within the target region. Please find further information about our project at https://sites.google.com/view/bo-lauch-balloon/.

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in correlation estimation will result in poor predictive performance and uncertainty quantification. We introduce a method that automatically accounts for temporal misalignment in a unified generative model that improves predictive performance. Our method uses Gaussian processes (GPs) to model the correlations both within and between the tasks. Building on the previous work by Kazlauskaite et al. (2019), we include a separate monotonic warp of the input data to model temporal misalignment. In contrast to previous work, we formulate a lower bound that accounts for uncertainty in both the estimates of the warping process and the underlying functions. Also, our new take on a monotonic stochastic process, with efficient path-wise sampling for the warp functions, allows us to perform full Bayesian inference in the model rather than MAP estimates. Missing data experiments, on synthetic and real time-series, demonstrate the advantages of accounting for misalignments (vs standard unaligned method) as well as modelling the uncertainty in the warping process (vs baseline MAP alignment approach).