相关论文: A Neural Network Ensemble Approach to System Ident…
Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…
Seismic data often contain gaps due to various obstacles in the investigated area and recording instrument failures. Deep learning techniques offer promising solutions for reconstructing missing data parts by leveraging existing…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
Machine learning approaches have been widely used for discovering the underlying physics of dynamical systems from measured data. Existing approaches, however, still lack robustness, especially when the measured data contain a large level…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational…
We introduce an ensemble learning scheme for community detection in complex networks. The scheme uses a Machine Learning algorithmic paradigm we call Extremal Ensemble Learning. It uses iterative extremal updating of an ensemble of network…
Accurate simulations of the oceans are crucial in understanding the Earth system. Despite their efficiency, simulations at lower resolutions must rely on various uncertain parameterizations to account for unresolved processes. However,…
We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…
Most iterative neural network training methods use estimates of the loss function over small random subsets (or minibatches) of the data to update the parameters, which aid in decoupling the training time from the (often very large) size of…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
Data-driven discovery of partial differential equations (PDEs) has attracted increasing attention in recent years. Although significant progress has been made, certain unresolved issues remain. For example, for PDEs with high-order…
Space weather indices are used commonly to drive forecasts of thermosphere density, which directly affects objects in low-Earth orbit (LEO) through atmospheric drag. One of the most commonly used space weather proxies, $F_{10.7 cm}$,…
Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system…
We present a new approach to ensemble learning. Our approach constructs a tree of subsets of the feature space and associates a predictor (predictive model) - determined by training one of a given family of base learners on an endogenously…
We introduce algorithms for learning nonlinear dynamical systems of the form $x_{t+1}=\sigma(\Theta^{\star}x_t)+\varepsilon_t$, where $\Theta^{\star}$ is a weight matrix, $\sigma$ is a nonlinear link function, and $\varepsilon_t$ is a…