Related papers: A Taylor Based Sampling Scheme for Machine Learnin…

The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…

This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are…

Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…

In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced.…

We present a new machine learning technique for training small resource-constrained predictors. Our algorithm, the Sparse Multiprototype Linear Learner (SMaLL), is inspired by the classic machine learning problem of learning $k$-DNF Boolean…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Differential machine learning (DML) is a recently proposed technique that uses samplewise state derivatives to regularize least square fits to learn conditional expectations of functionals of stochastic processes as functions of state…

Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…

An efficient approximate version of implicit Taylor methods for initial-value problems of systems of ordinary differential equations (ODEs) is introduced. The approach, based on an approximate formulation of Taylor methods, produces a…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat…

We study the problem of learning neural network models for Ordinary Differential Equations (ODEs) with parametric uncertainties. Such neural network models capture the solution to the ODE over a given set of parameters, initial conditions,…

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…

Machine Learning (ML) methods and tools have gained great success in many data, signal, image and video processing tasks, such as classification, clustering, object detection, semantic segmentation, language processing, Human-Machine…

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…