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Molecular Dynamics (MD) simulation is widely used to analyze the properties of molecules and materials. Most practical applications, such as comparison with experimental measurements, designing drug molecules, or optimizing materials, rely…
We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…
We train a set of Restricted Boltzmann Machines (RBMs) on one- and two-dimensional Ising spin configurations at various values of temperature, generated using Monte Carlo simulations. We validate the training procedure by monitoring several…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…
Model-based reinforcement learning is an effective approach for controlling an unknown system. It is based on a longstanding pipeline familiar to the control community in which one performs experiments on the environment to collect a…
Parametric models, and particularly neural networks, require weight initialization as a starting point for gradient-based optimization. Recent work shows that a specific initial parameter set can be learned from a population of supervised…
We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
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…
The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are…
We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques…
We propose to use deep learning to estimate parameters in statistical models when standard likelihood estimation methods are computationally infeasible. We show how to estimate parameters from max-stable processes, where inference is…
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
Control problems frequently arise in scientific and industrial applications, where the objective is to steer a dynamical system from an initial state to a desired target state. Recent advances in deep learning and automatic differentiation…