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This work focuses on a specific classification problem, where the information about a sample is not readily available, but has to be acquired for a cost, and there is a per-sample budget. Inspired by real-world use-cases, we analyze average…

In this work we discuss the impact of nuisance parameters on the effectiveness of machine learning in high-energy physics problems, and provide a review of techniques that allow to include their effect and reduce their impact in the search…

Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…

This paper deals with a unifying approach to the problems of computing the admissible sets of parametrical multi perturbations in appropriate bounded sets such that some fundamental properties of parameter-varying linear dynamic systems are…

The analysis of dynamical systems is a fundamental tool in the natural sciences and engineering. It is used to understand the evolution of systems as large as entire galaxies and as small as individual molecules. With predefined conditions…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

Learning to control unknown nonlinear dynamical systems is a fundamental problem in reinforcement learning and control theory. A commonly applied approach is to first explore the environment (exploration), learn an accurate model of it…

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

This paper introduces a novel direct approach to system identification of dynamic networks with missing data based on maximum likelihood estimation. Dynamic networks generally present a singular probability density function, which poses a…

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…

This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

We develop a data-driven machine learning approach to identifying parameters with steady-state solutions, locating such solutions, and determining their linear stability for systems of ordinary differential equations and dynamical systems…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

We are interested in the approximation of partial differential equations with a data-driven approach based on the reduced basis method and machine learning. We suppose that the phenomenon of interest can be modeled by a parametrized partial…

Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…

In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…

Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongly depends on loss function design, including the choice of…

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a…