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SUMMARY:dNNsolve: an efficient NN-based PDE solver - Yvette Welling 
DTSTART:20210322T163000Z
DTEND:20210322T170000Z
UID:TALK158257@talks.cam.ac.uk
CONTACT:Bingqing Cheng
DESCRIPTION:Neural Networks (NNs) can be used to solve Ordinary and Partia
 l Differential Equations (ODEs and PDEs) by redefining the question as an 
 optimization problem. The objective function to be optimized is the sum of
  the squares of the PDE to be solved and of the initial/boundary condition
 s. A feed forward NN is trained to minimise this loss function evaluated o
 n a set of collocation points sampled from the domain where the problem is
  defined. A compact and smooth solution\, that only depends on the weights
  of the trained NN\, is then obtained. This approach is often referred to 
 as ‘Physics Informed Neural Network' (PINN). Despite the success of the 
 PINN approach in solving various classes of PDEs\, an implementation of th
 is idea that is capable of solving a large class of ODEs and PDEs with goo
 d accuracy and without the need to finely tune the hyperparameters of the 
 network\, is not available yet. In this paper\, we introduce a new impleme
 ntation of this concept - called dNNsolve - that makes use of dual Neural 
 Networks to solve ODEs/PDEs. We show that dNNsolve is capable of solving a
  broad range of ODEs/PDEs in 1\,2 and 3 spatial dimensions\, without the n
 eed of hyperparameter fine-tuning.
LOCATION:virtual ZOOM meeting ID: 263 591 6003\, Passcode: 000042\, https:
 //us02web.zoom.us/j/2635916003?pwd=ZlBEQnRENGwxNmJGMENGMWxjak5nUT09
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