Data-driven prediction in dynamical systems: recent developments
A Ghadami, BI Epureanu - Philosophical Transactions of …, 2022 - royalsocietypublishing.org
In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …
larger-scale systems in the majority of the grand societal challenges tackled in applied …
Constructing neural network based models for simulating dynamical systems
Dynamical systems see widespread use in natural sciences like physics, biology, and
chemistry, as well as engineering disciplines such as circuit analysis, computational fluid …
chemistry, as well as engineering disciplines such as circuit analysis, computational fluid …
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
It is widely known that neural networks (NNs) are universal approximators of continuous
functions. However, a less known but powerful result is that a NN with a single hidden layer …
functions. However, a less known but powerful result is that a NN with a single hidden layer …
On neural differential equations
P Kidger - arXiv preprint arXiv:2202.02435, 2022 - arxiv.org
The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …
Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
While it is widely known that neural networks are universal approximators of continuous
functions, a less known and perhaps more powerful result is that a neural network with a …
functions, a less known and perhaps more powerful result is that a neural network with a …
Efficient training of physics‐informed neural networks via importance sampling
MA Nabian, RJ Gladstone… - Computer‐Aided Civil and …, 2021 - Wiley Online Library
Physics‐informed neural networks (PINNs) are a class of deep neural networks that are
trained, using automatic differentiation, to compute the response of systems governed by …
trained, using automatic differentiation, to compute the response of systems governed by …
A deep collocation method for the bending analysis of Kirchhoff plate
In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed.
This method takes advantage of computational graphs and backpropagation algorithms …
This method takes advantage of computational graphs and backpropagation algorithms …
PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network
Partial differential equations (PDEs) are commonly derived based on empirical
observations. However, recent advances of technology enable us to collect and store …
observations. However, recent advances of technology enable us to collect and store …
PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs
Partial differential equations (PDEs) play a fundamental role in modeling and simulating
problems across a wide range of disciplines. Recent advances in deep learning have shown …
problems across a wide range of disciplines. Recent advances in deep learning have shown …
Disentangling physical dynamics from unknown factors for unsupervised video prediction
Leveraging physical knowledge described by partial differential equations (PDEs) is an
appealing way to improve unsupervised video forecasting models. Since physics is too …
appealing way to improve unsupervised video forecasting models. Since physics is too …