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We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.

In recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second-order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

In recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second-order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

In recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second-order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.

Structural identifiablity of a third-order continuous time-invariant linear plant under an intrinsic pulse-modulated feedback is analyzed. The model represents a biomedical system, where the input signal to the continuous plant is immeasurable and the feedback modulation functions have to be identified along with the continuous dynamics. It is shown that two eigenvalues of the continuous plant system matrix (i.e. time constants), along with the times and weights of impulses occurring during a finite time interval, are identifiable from the measurement of one continuous system state over the interval in question. When an infinite time horizon is considered, all parameters are identifiable, up to gain scaling and linear block permutations.

We propose a framework for modeling structured nonlinear systems using nonparametric Gaussian processes. In particular, we introduce a two-layer stochastic model of latent interconnected Gaussian processes suitable for modeling Hammerstein-Wiener and Wiener-Hammerstein cascades. The posterior distribution of the latent processes is intractable because of the nonlinear interactions in the model; hence, we propose a Markov Chain Monte Carlo method consisting of a Gibbs sampler where each step is implemented using elliptical-slice sampling. We present the results on two example nonlinear systems showing that they can effectively be modeled and identified using the proposed nonparametric modeling approach.

Deep learning is a topic of considerable interest today. Since it deals with estimating - or learning - models, there are connections to the area of System Identification developed in the Automatic Control community. Such connections are explored and exploited in this contribution. It is stressed that common deep nets such as feedforward and cascadeforward nets are nonlinear ARX (NARX) models, and can thus be easily incorporated in System Identification code and practice. The case of LSTM nets is an example of NonLinear State-Space (NLSS) models., Koen Tiels: "Was with the dept in Uppsala. Now at Dept of Mechanical Engineering, Eindhoven University of Technology"

In recent years there has been an increased interest in stochastic adaptations of limited memory quasi-Newton methods, which compared to pure gradient-based routines can improve the convergence by incorporating second-order information. In this work we propose a direct least-squares approach conceptually similar to the limited memory quasi-Newton methods, but that computes the search direction in a slightly different way. This is achieved in a fast and numerically robust manner by maintaining a Cholesky factor of low dimension. The performance is demonstrated on real-world benchmark problems which shows improved results in comparison with already established methods.

Approaches to the estimation of the full state vector of a larger epidemiological model for the spread of Covid-19 in Sweden at the initial time instant from available data and with a simplified dynamical model are proposed and evaluated. The larger epidemiological model is based on a time-continuous Markov chain and captures the demographic composition of and the transport flows between the counties of Sweden. Its intended use is to predict the outbreak development in temporal and spatial coordinates as well as across the demographic groups. It can also support evaluations and comparisions of prospective intervention strategies in terms of, e.g., lockdown in certain areas or isolation of specific age groups. The simplified model is a discrete time-invariant linear system that has cumulative infectious incidence, infected population, asymptomatic population, exposed population, and infectious pressure as the state variables. Since the system matrix of the model depends on a number of transition rates, structural properties of the model are investigated for suitable parameter ranges. It is concluded that the model becomes unobservable for some parameter values. Two contrasting approaches to the initial state estimation are considered. One is a version of Rauch Tung Striebel smoother and another is based on solving a batch nonlinear optimization problem. The benefits and shortcomings of the considered estimation techniques are analyzed and compared.