arXiv subjects

David A. W. Barton

Publications and source records attributed to David A. W. Barton.

At least 19 recordsLinked to original sources

arXiv2026

Locating isolas in nonlinear oscillator systems using uncertainty quantification

Parametric uncertainty in nonlinear dynamical systems can fundamentally alter bifurcation behaviour, leading to qualitative response changes. Predicting operating margins/envelopes under such uncertainties is critical but challenging: conventional uncertainty quantification (UQ) methods struggle to efficiently propagate uncertainties across bifurcation boundaries, where response gradients become singular and solution branches emerge/vanish. We present a general UQ framework for bifurcation analysis of nonlinear dynamical systems with proportional parametric uncertainty, which systematically integrates continuation methods with parametric sensitivities and extremal conditions. The approach uses a two-step scheme: first, the loci of extremal response points are traced as the uncertainty domain is expanded from a deterministic reference point; second, these extremal points are tracked as the bifurcation parameter varies, thus determining the maximum and minimum response margins throughout. The continuation problem scales linearly with the number of uncertain parameters, enabling efficient analysis. The method is demonstrated on a two-degree-of-freedom nonlinear oscillator exhibiting a range of bifurcation phenomena, including multiple solutions, modal interactions, and symmetry breaking. In all cases, the framework efficiently captures uncertainty-induced shifts in bifurcation boundaries and response margins. Notably, the method reveals that parametric uncertainty induces topological changes in the bifurcation structure, including the emergence of an isolated response branch that is absent in the deterministic system with the reference parameters.

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arXiv2026

Weight-Space Linear Recurrent Neural Networks

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 4 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.

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arXiv2025

Neural Context Flows for Meta-Learning of Dynamical Systems

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.

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arXiv2025

Reevaluating Meta-Learning Optimization Algorithms Through Contextual Self-Modulation

Contextual Self-Modulation (CSM) (Nzoyem et al., 2025) is a potent regularization mechanism for Neural Context Flows (NCFs) which demonstrates powerful meta-learning on physical systems. However, CSM has limitations in its applicability across different modalities and in high-data regimes. In this work, we introduce two extensions: $i$CSM which expands CSM to infinite-dimensional variations by embedding the contexts into a function space, and StochasticNCF which improves scalability by providing a low-cost approximation of meta-gradient updates through a sampled set of nearest environments. These extensions are demonstrated through comprehensive experimentation on a range of tasks, including dynamical systems, computer vision challenges, and curve fitting problems. Additionally, we incorporate higher-order Taylor expansions via Taylor-Mode automatic differentiation, revealing that higher-order approximations do not necessarily enhance generalization. Finally, we demonstrate how CSM can be integrated into other meta-learning frameworks with FlashCAVIA, a computationally efficient extension of the CAVIA meta-learning framework (Zintgraf et al., 2019). Together, these contributions highlight the significant benefits of CSM and indicate that its strengths in meta-learning and out-of-distribution tasks are particularly well-suited to physical systems. Our open-source library, designed for modular integration of self-modulation into contextual meta-learning workflows, is available at https://github.com/ddrous/self-mod.

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arXiv2025

Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts

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.

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arXiv2024

AnyRotate: Gravity-Invariant In-Hand Object Rotation with Sim-to-Real Touch

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/.

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arXiv2024

Iterative method for real-time Hybrid testing: application to a cantilever beam with two interface degrees of freedom

In this paper, an iterative method for real-time hybrid testing (RTHT) is proposed. The method seeks to iteratively balance the interface conditions between the physical and numerical substructures by controlling the periodic demand of the actuators. It is then suitable for RTHT of structures undergoing a periodic response, e.g. structures excited at resonance. We demonstrate the capabilities of the method on a cantilever beam in bending motion with two degrees of freedom at the interface, which we use as a prototype for future testing of aircraft wings. We show that a number of challenges arise in these settings, such as the difficulty in measuring interface forces while controlling a continuous structure and the instability of the hybrid test for small time delays. Classical RTHT strategies could produce inaccurate or unstable outcomes, whereas the proposed method is able to attain very good interface synchronisation in a wide range of tested scenarios.

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arXiv2024

Real-time hybrid testing using iterative control for periodic oscillations

Real-time hybrid testing is a method in which a substructure of the system is realised experimentally and the rest numerically. The two parts interact in real time to emulate the dynamics of the full system. Such experiments however are often difficult to realise as the actuators and sensors, needed to ensure compatibility and force-equilibrium conditions at the interface, can seriously affect the predicted dynamics of the system and result in stability and fidelity issues. The traditional approach of using feedback control to overcome the additional unwanted dynamics is challenging due to the presence of an outer feedback loop, passing interface displacements or forces to the numerical substructure. We, therefore, advocate for an alternative approach, removing the problematic interface dynamics with an iterative scheme to minimise interface errors, thus, capturing the response of the true assembly. The technique is examined by hybrid testing of a bench-top four-storey building with different interface configurations, where using conventional hybrid measurement techniques is very challenging. A case where the physical part exhibits nonlinear restoring force characteristics is also considered. These tests show that the iterative approach is capable of handling even scenarios which are theoretically infeasible with feedback control.

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arXiv2023

A Comparison of Mesh-Free Differentiable Programming and Data-Driven Strategies for Optimal Control under PDE Constraints

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.

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arXiv2023

Sim-to-Real Model-Based and Model-Free Deep Reinforcement Learning for Tactile Pushing

Object pushing presents a key non-prehensile manipulation problem that is illustrative of more complex robotic manipulation tasks. While deep reinforcement learning (RL) methods have demonstrated impressive learning capabilities using visual input, a lack of tactile sensing limits their capability for fine and reliable control during manipulation. Here we propose a deep RL approach to object pushing using tactile sensing without visual input, namely tactile pushing. We present a goal-conditioned formulation that allows both model-free and model-based RL to obtain accurate policies for pushing an object to a goal. To achieve real-world performance, we adopt a sim-to-real approach. Our results demonstrate that it is possible to train on a single object and a limited sample of goals to produce precise and reliable policies that can generalize to a variety of unseen objects and pushing scenarios without domain randomization. We experiment with the trained agents in harsh pushing conditions, and show that with significantly more training samples, a model-free policy can outperform a model-based planner, generating shorter and more reliable pushing trajectories despite large disturbances. The simplicity of our training environment and effective real-world performance highlights the value of rich tactile information for fine manipulation. Code and videos are available at https://sites.google.com/view/tactile-rl-pushing/.

cs.RO↗

arXiv2023

Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified. The calibrated model provides a consistent description of the available data, able to extrapolate forecasts over a few weeks, making the proposed methodology very appealing for real-time epidemic modeling.

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arXiv2022

Using scientific machine learning for experimental bifurcation analysis of dynamic systems

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.

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arXiv2021

Robustness of nonlinear parameter identification in presence of process noise using control-based continuation

In this study, we consider the experimentally-obtained, periodically-forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions while different levels of noise are injected into the system. Using this data, the robustness of the control-based continuation algorithm and its ability to capture the noise-free system response is assessed by identifying the parameters of an associated Duffing-like model. We demonstrate that control-based continuation extracts system information more robustly, in the presence of a high level of noise, than open-loop parameter sweeps and so is a valuable tool for investigating nonlinear structures.

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arXiv2020

Learning to Live Life on the Edge: Online Learning for Data-Efficient Tactile Contour Following

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.

cs.RO↗

arXiv2020

Walking on TacTip toes: A tactile sensing foot for walking robots

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.

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arXiv2019

Shear-invariant Sliding Contact Perception with a Soft Tactile Sensor

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

cs.RO↗

arXiv2018

Principal Components of Touch

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.

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arXiv2015

Control-based continuation: bifurcation and stability analysis for physical experiments

Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target is used as a proxy for the state. The challenge then becomes to determine a control target such that the control is non-invasive, that is, it stabilises a steady-state (or periodic orbit) of the original open-loop experiment without altering it otherwise. Once implemented, control-based continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses methods from the system identification community to extract stability information in the form of Floquet multipliers from the closed-loop experiment, thus enabling the direct detection of bifurcations. In particular, it is shown that a periodic auto-regressive model with exogenous inputs (ARX) can be constructed that approximates the time-varying linearisation of the experiment around a particular periodic orbit. This method is demonstrated using a physical nonlinear tuned mass damper.

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