David A. W. Barton

Roussel Desmond Nzoyem, David A. W. Barton, Tom Deakin

Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications. Our code is openly available at https://github.com/ddrous/ncflow.

Roussel Desmond Nzoyem, David A. W. Barton, Tom Deakin

The field of Optimal Control under Partial Differential Equations (PDE) constraints is rapidly changing under the influence of Deep Learning and the accompanying automatic differentiation libraries. Novel techniques like Physics-Informed Neural Networks (PINNs) and Differentiable Programming (DP) are to be contrasted with established numerical schemes like Direct-Adjoint Looping (DAL). We present a comprehensive comparison of DAL, PINN, and DP using a general-purpose mesh-free differentiable PDE solver based on Radial Basis Functions. Under Laplace and Navier-Stokes equations, we found DP to be extremely effective as it produces the most accurate gradients; thriving even when DAL fails and PINNs struggle. Additionally, we provide a detailed benchmark highlighting the limited conditions under which any of those methods can be efficiently used. Our work provides a guide to Optimal Control practitioners and connects them further to the Deep Learning community.

Max Yang, Chenghua Lu, Alex Church et al.

Human hands are capable of in-hand manipulation in the presence of different hand motions. For a robot hand, harnessing rich tactile information to achieve this level of dexterity still remains a significant challenge. In this paper, we present AnyRotate, a system for gravity-invariant multi-axis in-hand object rotation using dense featured sim-to-real touch. We tackle this problem by training a dense tactile policy in simulation and present a sim-to-real method for rich tactile sensing to achieve zero-shot policy transfer. Our formulation allows the training of a unified policy to rotate unseen objects about arbitrary rotation axes in any hand direction. In our experiments, we highlight the benefit of capturing detailed contact information when handling objects of varying properties. Interestingly, we found rich multi-fingered tactile sensing can detect unstable grasps and provide a reactive behavior that improves the robustness of the policy. The project website can be found at https://maxyang27896.github.io/anyrotate/.

Roussel Desmond Nzoyem, Grant Stevens, Amarpal Sahota et al.

As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on $K$-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

Roussel Desmond Nzoyem, Nawid Keshtmand, Enrique Crespo Fernandez et al.

We introduce WARP (Weight-space Adaptive Recurrent Prediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 5 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalisation capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Sandor Beregi, David A. W. Barton, Djamel Rezgui et al.

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and reality through measurement data. Our exploratory study focuses on training universal differential equation (UDE) models for physical nonlinear dynamical systems with limit cycles: an aerofoil undergoing flutter oscillations and an electrodynamic nonlinear oscillator. We consider examples where training data is generated by numerical simulations, whereas we also employ the proposed modelling concept to physical experiments allowing us to investigate problems with a wide range of complexity. To collect the training data, the method of control-based continuation is used as it captures not just the stable but also the unstable limit cycles of the observed system. This feature makes it possible to extract more information about the observed system than the open-loop approach (surveying the steady state response by parameter sweeps without using control) would allow. We use both neural networks and Gaussian processes as universal approximators alongside the mechanistic models to give a critical assessment of the accuracy and robustness of the UDE modelling approach. We also highlight the potential issues one may run into during the training procedure indicating the limits of the current modelling framework.

Elizabeth A. Stone, Nathan F. Lepora, David A. W. Barton

Little research into tactile feet has been done for walking robots despite the benefits such feedback could give when walking on uneven terrain. This paper describes the development of a simple, robust and inexpensive tactile foot for legged robots based on a high-resolution biomimetic TacTip tactile sensor. Several design improvements were made to facilitate tactile sensing while walking, including the use of phosphorescent markers to remove the need for internal LED lighting. The usefulness of the foot is verified on a quadrupedal robot performing a beam walking task and it is found the sensor prevents the robot falling off the beam. Further, this capability also enables the robot to walk along the edge of a curved table. This tactile foot design can be easily modified for use with any legged robot, including much larger walking robots, enabling stable walking in challenging terrain.

Elizabeth A. Stone, Nathan F. Lepora, David A. W. Barton

Tactile sensing has been used for a variety of robotic exploration and manipulation tasks but a common constraint is a requirement for a large amount of training data. This paper addresses the issue of data-efficiency by proposing a novel method for online learning based on a Gaussian Process Latent Variable Model (GP-LVM), whereby the robot learns from tactile data whilst performing a contour following task thus enabling generalisation to a wide variety of tactile stimuli. The results show that contour following is successful with comparatively little data and is robust to novel stimuli. This work highlights that even with a simple learning architecture there are significant advantages to be gained in efficient and robust task performance by using latent variable models and online learning for tactile sensing tasks. This paves the way for a new generation of robust, fast, and data-efficient tactile systems.

Kirsty Aquilina, David A. W. Barton, Nathan F. Lepora

Manipulation tasks often require robots to be continuously in contact with an object. Therefore tactile perception systems need to handle continuous contact data. Shear deformation causes the tactile sensor to output path-dependent readings in contrast to discrete contact readings. As such, in some continuous-contact tasks, sliding can be regarded as a disturbance over the sensor signal. Here we present a shear-invariant perception method based on principal component analysis (PCA) which outputs the required information about the environment despite sliding motion. A compliant tactile sensor (the TacTip) is used to investigate continuous tactile contact. First, we evaluate the method offline using test data collected whilst the sensor slides over an edge. Then, the method is used within a contour-following task applied to 6 objects with varying curvatures; all contours are successfully traced. The method demonstrates generalisation capabilities and could underlie a more sophisticated controller for challenging manipulation or exploration tasks in unstructured environments. A video showing the work described in the paper can be found at https://youtu.be/wrTM61-pieU

Kirsty Aquilina, David A. W. Barton, Nathan F. Lepora

Our human sense of touch enables us to manipulate our surroundings; therefore, complex robotic manipulation will require artificial tactile sensing. Typically tactile sensor arrays are used in robotics, implying that a straightforward way of interpreting multidimensional data is required. In this paper we present a simple visualisation approach based on applying principal component analysis (PCA) to systematically collected sets of tactile data. We apply the visualisation approach to 4 different types of tactile sensor, encompassing fingertips and vibrissal arrays. The results show that PCA can reveal structure and regularities in the tactile data, which also permits the use of simple classifiers such as $k$-NN to achieve good inference. Additionally, the Euclidean distance in principal component space gives a measure of sensitivity, which can aid visualisation and also be used to find regions in the tactile input space where the sensor is able to perceive with higher accuracy. We expect that these observations will generalise, and thus offer the potential for novel control methods based on touch.