Related papers: pDANSE: Particle-based Data-driven Nonlinear State…
The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and…
Density tempering (also called density annealing) is a sequential Monte Carlo approach to Bayesian inference for general state models; it is an alternative to Markov chain Monte Carlo. When applied to state space models, it moves a…
We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor…
We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…
Polynomial chaos expansion (PCE) is a powerful surrogate model-based reliability analysis method. Generally, a PCE model with a higher expansion order is usually required to obtain an accurate surrogate model for some complex non-linear…
We consider the problem of learning stabilizable systems governed by nonlinear state equation $h_{t+1}=\phi(h_t,u_t;\theta)+w_t$. Here $\theta$ is the unknown system dynamics, $h_t $ is the state, $u_t$ is the input and $w_t$ is the…
This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems with bounded uncertainties. The novel method builds upon essential properties and computational advantages of constrained zonotopes (CZs)…
In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is…
In this paper, we present a data-driven controller design method for continuous-time nonlinear systems, using no model knowledge but only measured data affected by noise. While most existing approaches focus on systems with polynomial…
The Statistical Finite Element Method (statFEM) offers a Bayesian framework for integrating computational models with observational data, thus providing improved predictions for structural health monitoring and digital twinning. This paper…
The increasing deployment of distribution-level phasor measurement units (PMUs) calls for dynamic distribution state estimation (DDSE) approaches that tap into high-rate measurements to maintain a comprehensive view of the…
Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are…
We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on…