arXiv subjects

Niklas Wahlström

Publications and source records attributed to Niklas Wahlström.

At least 19 recordsLinked to original sources

arXiv2026

Simultaneous State Estimation and Online Model Learning in a Soft Robotic System

Operating complex real-world systems, such as soft robots, can benefit from precise predictive control schemes that require accurate state and model knowledge. This knowledge is typically not available in practical settings and must be inferred from noisy measurements. In particular, it is challenging to simultaneously estimate unknown states and learn a model online from sequentially arriving measurements. In this paper, we show how a recently proposed gray-box system identification tool enables the estimation of a soft robot's current pose while at the same time learning a bending stiffness model. For estimation and learning, we only need a nominal constant-curvature robot model and measurements of the robot's base reactions (e.g., base forces). The estimation scheme -- relying on a marginalized particle filter -- allows us to conveniently interface nominal constant-curvature equations with a Gaussian Process (GP) bending stiffness model to be learned. This, in contrast to estimation via a random walk over stiffness values, enables prediction of bending stiffness and improves overall model quality. We demonstrate, using a real-world soft robot, that the method learns a bending-stiffness model online while accurately estimating the robot's pose. Notably, reduced error in multi-step forward predictions indicates that the learned bending-stiffness GP improves overall model quality.

eess.SY↗

arXiv2026

Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations

In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert principle, which governs the motion of dynamical systems, is preserved by construction in the absence of external forces. This allows learning physically consistent models that overcome erroneous drift in the system's energy, thereby providing stable long-term predictions. At the core of our approach lie linear operators for Gaussian process conditioning, constructed from discrete forced Euler-Lagrange equations and variational discretization schemes. Thereby and unlike prior work, the method enables learning dynamics from discrete position snapshots, i.e., without access to a system's velocities or momenta. This is particularly relevant for a large class of practical scenarios where only position measurements are available, for instance, in motion capture or visual servoing applications. We demonstrate the data-efficiency and generalization capabilities of the LGPs in various synthetic and real-world case studies, including a real-world soft robot with hysteresis. The experimental results underscore that the LGPs learn physically consistent dynamics with uncertainty quantification solely from sparse positional data and enable stable long-term predictions.

cs.LG↗

arXiv2026

Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes

Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements.

cs.LG↗

arXiv2026

A Differentiable Surrogate Model for the Generation of Radio Pulses from In-Ice Neutrino Interactions

The planned IceCube-Gen2 radio neutrino detector at the South Pole will enhance the detection of cosmic ultra-high-energy neutrinos. It is crucial to utilize the available time until construction to optimize the detector design. A fully differentiable pipeline, from signal generation to detector response, would allow for the application of gradient descent techniques to explore the parameter space of the detector. In our work, we focus on the aspect of signal generation, and propose a modularized deep learning architecture to generate radio signals from in-ice neutrino interactions conditioned on the shower energy and viewing angle. The model is capable of generating differentiable signals with amplitudes spanning multiple orders of magnitude, as well as consistently producing signals corresponding to the same underlying event for different viewing angles. The modularized approach ensures physical consistency of the samples and leads to advantageous computational properties when using the model as part of a bigger optimization pipeline.

astro-ph.IM↗

arXiv2025

Repulsive Ensembles for Bayesian Inference in Physics-informed Neural Networks

Physics-informed neural networks (PINNs) have proven an effective tool for solving differential equations, in particular when considering non-standard or ill-posed settings. When inferring solutions and parameters of the differential equation from data, uncertainty estimates are preferable to point estimates, as they give an idea about the accuracy of the solution. In this work, we consider the inverse problem and employ repulsive ensembles of PINNs (RE-PINN) for obtaining such estimates. The repulsion is implemented by adding a particular repulsive term to the loss function, which has the property that the ensemble predictions correspond to the true Bayesian posterior in the limit of infinite ensemble members. Where possible, we compare the ensemble predictions to Monte Carlo baselines. Whereas the standard ensemble tends to collapse to maximum-a-posteriori solutions, the repulsive ensemble produces significantly more accurate uncertainty estimates and exhibits higher sample diversity.

stat.ML↗

arXiv2024

Probabilistic Matching of Real and Generated Data Statistics in Generative Adversarial Networks

Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, there is no guarantee that they will follow the true data distribution. For scientific applications in particular, it is essential that the true distribution is well captured by the generated distribution. In this work, we propose a method to ensure that the distributions of certain generated data statistics coincide with the respective distributions of the real data. In order to achieve this, we add a new loss term to the generator loss function, which quantifies the difference between these distributions via suitable f-divergences. Kernel density estimation is employed to obtain representations of the true distributions, and to estimate the corresponding generated distributions from minibatch values at each iteration. When compared to other methods, our approach has the advantage that the complete shapes of the distributions are taken into account. We evaluate the method on a synthetic dataset and a real-world dataset and demonstrate improved performance of our approach.

stat.ML↗

arXiv2024

Physics-informed Neural Networks with Unknown Measurement Noise

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak Gaussian noise. We show that the standard PINN framework breaks down in case of non-Gaussian noise. We give a way of resolving this fundamental issue and we propose to jointly train an energy-based model (EBM) to learn the correct noise distribution. We illustrate the improved performance of our approach using multiple examples.

stat.ML↗

arXiv2023

Invertible Kernel PCA with Random Fourier Features

Kernel principal component analysis (kPCA) is a widely studied method to construct a low-dimensional data representation after a nonlinear transformation. The prevailing method to reconstruct the original input signal from kPCA -- an important task for denoising -- requires us to solve a supervised learning problem. In this paper, we present an alternative method where the reconstruction follows naturally from the compression step. We first approximate the kernel with random Fourier features. Then, we exploit the fact that the nonlinear transformation is invertible in a certain subdomain. Hence, the name \emph{invertible kernel PCA (ikPCA)}. We experiment with different data modalities and show that ikPCA performs similarly to kPCA with supervised reconstruction on denoising tasks, making it a strong alternative.

cs.LG↗

arXiv2023

Incorporating Sum Constraints into Multitask Gaussian Processes

Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of the outputs to be constant. This is achieved by conditioning the prior distribution on the constraint fulfillment. The approach allows for both linear and nonlinear constraints. We demonstrate that the constraints are fulfilled with high precision and that the construction can improve the overall prediction accuracy as compared to the standard Gaussian process.

stat.ML↗

arXiv2021

Learning deep autoregressive models for hierarchical data

We propose a model for hierarchical structured data as an extension to the stochastic temporal convolutional network. The proposed model combines an autoregressive model with a hierarchical variational autoencoder and downsampling to achieve superior computational complexity. We evaluate the proposed model on two different types of sequential data: speech and handwritten text. The results are promising with the proposed model achieving state-of-the-art performance.

cs.LG↗

arXiv2021

Deep State Space Models for Nonlinear System Identification

Deep state space models (SSMs) are an actively researched model class for temporal models developed in the deep learning community which have a close connection to classic SSMs. The use of deep SSMs as a black-box identification model can describe a wide range of dynamics due to the flexibility of deep neural networks. Additionally, the probabilistic nature of the model class allows the uncertainty of the system to be modelled. In this work a deep SSM class and its parameter learning algorithm are explained in an effort to extend the toolbox of nonlinear identification methods with a deep learning based method. Six recent deep SSMs are evaluated in a first unified implementation on nonlinear system identification benchmarks.

eess.SY↗

arXiv2019

Deep Convolutional Networks in System Identification

Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures when it comes to sequence modeling tasks. Inspired by these results we explore the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models. We end the paper with an experimental study where we provide results on two real-world problems, the well-known Silverbox dataset and a newer dataset originating from ground vibration experiments on an F-16 fighter aircraft.

eess.SY↗

arXiv2019

Probabilistic approach to limited-data computed tomography reconstruction

In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process prior to model the target function and estimate its (hyper)parameters from measured data. In contrast to other established methods, this comes with the advantage of not requiring any manual parameter tuning, which usually arises in classical regularization strategies. Our method uses a basis function expansion technique for the Gaussian process which significantly reduces the computational complexity and avoids the need for numerical integration. The approach also allows for reformulation of come classical regularization methods as Laplacian and Tikhonov regularization as Gaussian process regression, and hence provides an efficient algorithm and principled means for their parameter tuning. Results from simulated and real data indicate that this approach is less sensitive to streak artifacts as compared to the commonly used method of filtered backprojection.

cs.CV↗

arXiv2018

Probabilistic modelling and reconstruction of strain

This paper deals with modelling and reconstruction of strain fields, relying upon data generated from neutron Bragg-edge measurements. We propose a probabilistic approach in which the strain field is modelled as a Gaussian process, assigned a covariance structure customised by incorporation of the so-called equilibrium constraints. The computational complexity is significantly reduced by utilising an approximation scheme well suited for the problem. We illustrate the method on simulations and real data. The results indicate a high potential and can hopefully inspire the concept of probabilistic modelling to be used within other tomographic applications as well.

physics.data-an↗

arXiv2018

Data-Driven Impulse Response Regularization via Deep Learning

We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical finite-dimensional model structures. Inspired by this development and the success of deep learning we propose a new flexible data-driven model. Our experiments indicate that the new model is capable of exploiting even more of the hidden patterns that are present in the input-output data as compared to the non-parametric models.

eess.SY↗

arXiv2018

Modeling and interpolation of the ambient magnetic field by Gaussian processes

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

cs.RO↗

arXiv2017

Linearly constrained Gaussian processes

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.

stat.ML↗

arXiv2015

Data-Efficient Learning of Feedback Policies from Image Pixels using Deep Dynamical Models

Data-efficient reinforcement learning (RL) in continuous state-action spaces using very high-dimensional observations remains a key challenge in developing fully autonomous systems. We consider a particularly important instance of this challenge, the pixels-to-torques problem, where an RL agent learns a closed-loop control policy ("torques") from pixel information only. We introduce a data-efficient, model-based reinforcement learning algorithm that learns such a closed-loop policy directly from pixel information. The key ingredient is a deep dynamical model for learning a low-dimensional feature embedding of images jointly with a predictive model in this low-dimensional feature space. Joint learning is crucial for long-term predictions, which lie at the core of the adaptive nonlinear model predictive control strategy that we use for closed-loop control. Compared to state-of-the-art RL methods for continuous states and actions, our approach learns quickly, scales to high-dimensional state spaces, is lightweight and an important step toward fully autonomous end-to-end learning from pixels to torques.

cs.AI↗