| 1. |
- Courts, Jarrad, et al.
(författare)
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Variational system identification for nonlinear state-space models
- 2023
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 147
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers parameter estimation for nonlinear state-space models, which is an important but challenging problem. We address this challenge by employing a variational inference (VI) approach, which is a principled method that has deep connections to maximum likelihood estimation. This VI approach ultimately provides estimates of the model as solutions to an optimisation problem, which is deterministic, tractable and can be solved using standard optimisation tools. A specialisation of this approach for systems with additive Gaussian noise is also detailed. The proposed method is examined numerically on a range of simulated and real examples focusing on the robustness to parameter initialisation; additionally, favourable comparisons are performed against state-of-the-art alternatives.
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| 2. |
- Hendriks, Johannes N., et al.
(författare)
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Data to Controller for Nonlinear Systems : An Approximate Solution
- 2022
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Ingår i: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 6, s. 1196-1201
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Tidskriftsartikel (refereegranskat)abstract
- This letter considers the problem of determining an optimal control action based on observed data. We formulate the problem assuming that the system can be modeled by a nonlinear state-space model, but where the model parameters, state and future disturbances are not known and are treated as random variables. Central to our formulation is that the joint distribution of these unknown objects is conditioned on the observed data. Crucially, as new measurements become available, this joint distribution continues to evolve so that control decisions are made accounting for uncertainty as evidenced in the data. The resulting problem is intractable which we obviate by providing approximations that result in finite dimensional deterministic optimization problems. The proposed approach is demonstrated in simulation on a nonlinear system.
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| 3. |
- Hendriks, Johannes N., et al.
(författare)
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Deep Energy-Based NARX Models
- 2021
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Ingår i: IFAC PapersOnLine. - : Elsevier. - 2405-8963. ; , s. 505-510
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Konferensbidrag (refereegranskat)abstract
- This paper is directed towards the problem of learning nonlinear ARX models based on observed input output data. In particular, our interest is in learning a conditional distribution of the current output based on a finite window of past inputs and outputs. To achieve this, we consider the use of so-called energy-based models, which have been developed in allied fields for learning unknown distributions based on data. This energy-based model relies on a general function to describe the distribution, and here we consider a deep neural network for this purpose. The primary benefit of this approach is that it is capable of learning both simple and highly complex noise models, which we demonstrate on simulated and experimental data.
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| 4. |
- Henningsson, Axel, et al.
(författare)
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Inferring the probability distribution over strain tensors in polycrystals from diffraction based measurements
- 2023
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier. - 0045-7825 .- 1879-2138. ; 417:Part A
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Tidskriftsartikel (refereegranskat)abstract
- Polycrystals illuminated by high-energy X-rays or neutrons produce diffraction patterns in which the measured diffraction peaks encode the individual single crystal strain states. While state of the art X-ray and neutron diffraction approaches can be used to routinely recover per grain mean strain tensors, less work has been produced on the recovery of higher order statistics of the strain distributions across the individual grains. In the setting of small deformations, we consider the problem of estimating the crystal elastic strain tensor probability distribution from diffraction data. For the special case of multivariate Gaussian strain tensor probability distributions, we show that while the mean of the distribution is well defined from measurements, the covariance of strain has a null-space. We show that there exist exactly 6 orthogonal perturbations to this covariance matrix under which the measured strain signal is invariant. In particular, we provide analytical parametrisations of these perturbations together with the set of possible maximum-likelihood estimates for a multivariate Gaussian fit to data. The parametric description of the null-space provides insights into the strain PDF modes that cannot be accurately estimated from the diffraction data. Understanding these modes prevents erroneous conclusions from being drawn based on the data. Beyond Gaussian strain tensor probability densities, we derive an iterative radial basis regression scheme in which the strain tensor probability density is estimated by a sparse finite basis expansion. This is made possible by showing that the operator mapping the strain tensor probability density onto the measured histograms of directional strain is linear, without approximation. The utility of the proposed algorithm is demonstrated by numerical simulations in the setting of single crystal monochromatic X-ray scattering. The proposed regression methods were found to robustly reject outliers and accurately predict the strain tensor probability distributions in the presence of Gaussian measurement noise.
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| 5. |
- Jidling, Carl, et al.
(författare)
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Memory efficient constrained optimization of scanning-beam lithography
- 2022
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Ingår i: Optics Express. - : Optica Publishing Group. - 1094-4087. ; 30:12, s. 20564-20579
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Tidskriftsartikel (refereegranskat)abstract
- This article describes a memory efficient method for solving large-scale optimizationproblems that arise when planning scanning-beam lithography processes. These processes require the identification of an exposure pattern that minimizes the difference between a desired and predicted output image, subject to constraints. The number of free variables is equal to the number of pixels, which can be on the order of millions or billions in practical applications. The proposed method splits the problem domain into a number of smaller overlapping subdomains with constrained boundary conditions, which are then solved sequentially using a constrained gradient search method (L-BFGS-B). Computational time is reduced by exploiting natural sparsity in the problem and employing the fast Fourier transform for efficient gradient calculation. When it comes to the trade-off between memory usage and computational time we can make a different trade-off compared to previous methods, where the required memory is reduced by approximately the number of subdomains at the cost of more computations. In an example problem with 30 million variables, the proposed method reduces memory requirements by 67% but increases computation time by 27%. Variations of the proposed method are expected to find applications in the planning of processes such as scanning laser lithography, scanning electron beam lithography, and focused ion beam deposition, for example.
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| 6. |
- Ribeiro, Antonio H., et al.
(författare)
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Beyond Occam's Razor in System Identification : Double-Descent when Modeling Dynamics
- 2021
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Ingår i: IFAC PapersOnLine. - : Elsevier. ; , s. 97-102
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Konferensbidrag (refereegranskat)abstract
- System identification aims to build models of dynamical systems from data. Traditionally, choosing the model requires the designer to balance between two goals of conflicting nature; the model must be rich enough to capture the system dynamics, but not so flexible that it learns spurious random effects from the dataset. It is typically observed that the model validation performance follows a U-shaped curve as the model complexity increases. Recent developments in machine learning and statistics, however, have observed situations where a "double-descent" curve subsumes this U-shaped model-performance curve. With a second decrease in performance occurring beyond the point where the model has reached the capacity of interpolating i.e., (near) perfectly fitting the training data. To the best of our knowledge, such phenomena have not been studied within the context of dynamic systems. The present paper aims to answer the question: "Can such a phenomenon also be observed when estimating parameters of dynamic systems?" We show that the answer is yes, verifying such behavior experimentally both for artificially generated and real-world datasets.
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| 7. |
- Wigren, Anna, et al.
(författare)
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Nonlinear System Identification : Learning While Respecting Physical Models Using a Sequential Monte Carlo Method
- 2022
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Ingår i: IEEE CONTROL SYSTEMS MAGAZINE. - : Institute of Electrical and Electronics Engineers (IEEE). - 1066-033X .- 1941-000X. ; 42:1, s. 75-102
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Tidskriftsartikel (refereegranskat)abstract
- The modern world contains an immense number of different and interacting systems, from the evolution of weather systems to variations in the stock market, autonomous vehicles interacting with their environment, and the spread of diseases. For society to function, it is essential to understand the behavior of the world so that informed decisions can be made that are based on likely future outcomes. For instance, consider the spread of a new disease such as COVID-19 coronavirus. It is of great importance to be able to predict the number of people that will be infected at different points in time to ensure that appropriate health-care facilities are available. It is also of interest to be able to make decisions based on accurate information to best attenuate the spread of disease. Moreover, understanding specific attributes of a disease-such as the incubation time and number of unreported cases-and how certain we are about this knowledge are also crucial.
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| 8. |
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| 9. |
- Wills, Adrian G., et al.
(författare)
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Sequential Monte Carlo : A Unified Review
- 2023
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Ingår i: ANNUAL REVIEW OF CONTROL ROBOTICS AND AUTONOMOUS SYSTEMS. - : ANNUAL REVIEWS. - 2573-5144. ; 6, s. 159-182
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Forskningsöversikt (refereegranskat)abstract
- Sequential Monte Carlo methods-also known as particle filters-offer approximate solutions to filtering problems for nonlinear state-space systems. These filtering problems are notoriously difficult to solve in general due to a lack of closed-form expressions and challenging expectation integrals. The essential idea behind particle filters is to employ Monte Carlo integration techniques in order to ameliorate both of these challenges. This article presents an intuitive introduction to the main particle filter ideas and then unifies three commonly employed particle filtering algorithms. This unified approach relies on a nonstandard presentation of the particle filter, which has the advantage of highlighting precisely where the differences between these algorithms stem from. Some relevant extensions and successful application domains of the particle filter are also presented.
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| 10. |
- Wills, Adrian G., et al.
(författare)
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Stochastic quasi-Newton with line-search regularisation
- 2021
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 127
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally attractive algorithms. In essence, this is achieved by learning the second-order (Hessian) information based on observing first-order gradients. We extend these ideas to the stochastic setting by employing a highly flexible model for the Hessian and infer its value based on observing noisy gradients. In addition, we propose a stochastic counterpart to standard line-search procedures and demonstrate the utility of this combination on maximum likelihood identification for general nonlinear state space models.
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