Related papers: Machine Learning for Initial Value Problems of Par…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
We study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
We study the initial value problem for actions which contain non-trivial functions of integrals of local functions of the dynamical variable. In contrast to many other non-local actions, the classical solution set of these systems is at…
This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the…
The paper contributes to strengthening the relation between machine learning and the theory of differential equations. In this context, the inverse problem of fitting the parameters, and the initial condition of a differential equation to…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
The system identification problem is to estimate dynamical parameters from the output data, obtained by performing measurements on the output fields. We investigate system identification for quantum linear systems. Our main objectives are…
This paper considers meta-learning problems, where there is a distribution of tasks, and we would like to obtain an agent that performs well (i.e., learns quickly) when presented with a previously unseen task sampled from this distribution.…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…
This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…
The empirical success of machine learning models with many more parameters than measurements has generated an interest in the theory of overparameterisation, i.e., underdetermined models. This paradigm has recently been studied in domains…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
In this brief paper, we provide a mathematical framework that exploits the relationship between the maximum principle and dynamic programming for characterizing optimal learning trajectories in a class of learning problem, which is related…