Related papers: Numerical Method for Parameter Inference of Nonlin…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and…
Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…
An incremental/online state dynamic learning method is proposed for identification of the nonlinear Gaussian state space models. The method embeds the stochastic variational sparse Gaussian process as the probabilistic state dynamic model…
We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact…
Identifying and calibrating quantitative dynamical models for physical quantum systems is important for a variety of applications. Here we present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…
We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small…
Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
This paper deals with the identification of linear stochastic dynamical systems, where the unknowns include system coefficients and noise variances. Conventional approaches that rely on the maximum likelihood estimation (MLE) require…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series…
In this paper, we propose a semi-parametric model for autonomous nonlinear dynamical systems and devise an estimation procedure for model fitting. This model incorporates subject-specific effects and can be viewed as a nonlinear…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…