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There is growing interest in using machine learning (ML) methods for structural metamodeling due to the substantial computational cost of traditional simulations. Purely data-driven strategies often face limitations in model robustness,…
Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…
The classification of states of matter and their corresponding phase transitions is a special kind of machine-learning task, where physical data allow for the analysis of new algorithms, which have not been considered in the general…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
Meta-learning consists in learning learning algorithms. We use a Long Short Term Memory (LSTM) based network to learn to compute on-line updates of the parameters of another neural network. These parameters are stored in the cell state of…
Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on…
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…
Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional…
We develop a deep neural network (DNN) that accounts for the phase behaviors of polymer-containing liquid mixtures. The key component in the DNN consists of a theory-embedded layer that captures the characteristic features of the phase…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Deep learning (DL) techniques have been widely used in prestack three-parameter inversion to address its ill-posed problems. Among these DL techniques, Multi-task learning (MTL) methods can simultaneously train multiple tasks, thereby…